Applications

Applications
Artificial Intelligence
And
Simulations

Applications
Pallet of
Data Structures
Algorithms
Choose which to use and
Combine them To form your model
Of reality
Reality to modelThe modelerThe computer
You are the artist and the computer is your
canvas

Knowledge Representation
Abstraction
You choose how to represent reality
The choice is not unique
It depends on what aspect of reality you want to represent and how

Applications:
Acquisition, management and use
of knowledge
Theme of lecture:
Abstractionof reality through knowledge engineering

Applications:
Acquisition, management and use of
knowledge
• Storage and management of Information
• Making Sense of Knowledge
• Acquisition of knowledge
– Feature Acquistion
– Concept Abstraction
• Problem Solving
• Use of knowledge in and as models
– Problem Solving
– Simulations

Storing and Managing Information
Table of data
Database management Systems (DBMS)
Storage and retrieval of properties of objects
Spreadsheets
Manipulations of and calculations with the data in the table
Each row is a particular object
Each column is a property associated with that objects
Two examples/paradigms of management systems

Database Management System (DBMS)
Organizes data
in sets of
tables

Relational Database Management System
(RDBMS)
Name Address Parcel #
John Smith 18 Lawyers Dr.756554
T. Brown 14 Summers Tr. 887419
Table A
Table B
Parcel # Assessed Value
887419 152,000
446397 100,000
Provides relationships
Between
data in the tables

Using SQL- Structured Query Language
• SQL is a standard database protocol, adopted by most
‘relational’ databases
• Provides syntax for data:
– Definition
– Retrieval
– Functions (COUNT, SUM, MIN, MAX, etc)
– Updates and Deletes
• SELECT list FROM table WHERE condition
• list - a list of items or * for all items
o WHERE - a logical expression limiting the number of records selected
o can be combined with Boolean logic: AND, OR, NOT
o ORDER may be used to format results

Spreadsheets
Every row is
a different “object”
with a set of properties
Every column is
a different property
of the row object

Spreadsheet
Organization of elements
Column A Column B Column C
Row 1
Row 2
Row 3
Row and column
indicies
Cells with addresses
A7 B4 C10 D5
Accessing each cell

Spreadsheet Formulas
Formula: Combination of
values or cell references
and mathematical
operators such as +, -, /, *
The formula displays in
the entry bar. This
formula is used to add the
values in the four cells.
The sum is displayed in
cell B7.
The results of a formula
display in the cell.
With cell, row and column functions
Ex. Average, sum, min,max,

Applications:
knowledge
– Problem Solving
– Simulations

Making Sense of Knowledge
Time flies like an arrow proverb
Fruit flies like a banana Groucho Marx
There is a semantic and context behind all words
Flies:
1. The act of flying
2. The insect
Like:
1. Similar to
2. Are fond of
There is also the elusive “Common Sense”
1. One type of fly, the fruit fly, is fond of bananas
2. Fruit, in general, flies through the air just like a banana
3. One type of fly, the fruit fly, is just like a banana
A bit complicated because we are speaking metaphorically,
Time is not really an object, like a bird, which flies
Translation is not just doing a one-to-one search in the dictionary
Complex Searches is not just searching for individual words
Google translate

Adding Semantics:
Ontologies
Concept
conceptual entity of the domain
Attribute
property of a concept
Relation
relationship between concepts
or properties
Axiom
coherent description between
Concepts / Properties /
Relations via logical expressions
16
Person
Student Professor
Lecture
isA – hierarchy (taxonomy)
name email
student
nr.
research
field
topic
lecture
nr.
attends
holds
Structuring of:
• Background Knowledge
• “Common Sense” knowledge

Structure of an Ontology
Ontologies typically have two distinct components:
Names for important concepts in the domain
– Elephant is a concept whose members are a kind of animal
– Herbivore is a concept whose members are exactly those animals who eat
only plants or parts of plants
– Adult_Elephant is a concept whose members are exactly those elephants
whose age is greater than 20 years
Background knowledge/constraints on the domain
– Adult_Elephants weigh at least 2,000 kg
– All Elephants are either African_Elephants or Indian_Elephants
– No individual can be both a Herbivore and a Carnivore
17

Ontology Definition
18
Formal, explicit specification of a shared conceptualization
commonly accepted
understanding
conceptual model
of a domain
(ontological theory)
unambiguous
terminology definitions
machine-readability
with computational
semantics
[Gruber93]

The Semantic Web
Ontology implementation
19
"The Semantic Web is an extension of the current web in which information is given
well-defined meaning, better enabling computers and people to work in
cooperation." -- Tim Berners-Lee
“the wedding cake”

Applications:
knowledge
– Feature Acquisition
– Problem Solving
– Simulations

Abstracting
Knowledge
Several levels and reasons to abstract knowledge
Feature abstraction
Simplifying “reality” so the know can be used in
Computer data structures and algorithms
Concept Abstraction
Organizing and making sense of the immense amount of
data/knowledge we have
Modeling abstraction
Making usable and predictive models of reality

Feature Abstraction
Simplifying “reality” so the knowledge can be used in
A photograph of a face
Set
Of
pixels
Is it a face?
Who’s face?

Feature Abstraction
A photograph
of a face
Is it a face?
Who’s face?
The eye sees the pixels
In the visual cortex,
Features are detected

Feature Abstraction
n!º
1 n =1
n*(n-1)! n >1
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í
ï
îï
ü
ý
ï
þï
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Photograph made up of pixels
The pixels need to be converted to
Data structures the algorithms can understand

FeatureAbstract:
Boundary Detection
• Is this a boundary?

Feature Detection
“flat” region:
no change in all
directions
“edge”:
no change along
the edge direction
“corner”:
significant change
in all directions
Harris Detector: Intuition
From a square sampling of pixels

Principle Component Analysis (PCA)
27
• Finding a map of principle components (PCs) of data into an
orthogonal space
• Method: Find the set of eigenvalues in a vector space:
– The eigen vectors are the principle components
– The eigenvalues are the ranking of the vectors
• PCs – Variables with the largest variances
– Orthogonality (each coordinate is orthogonal)
– Linearity – Optimal least mean-square error
• Limitations?
– Strict linearity
– specific distribution
– Large variance assumption
x1
x2
Rotates coordinate system

Feature Detection
 ( , ) ,
u
E u v u v M
v
 
  
 
Intensity change in shifting window: eigenvalue analysis
1, 2 – eigenvalues of M
direction of the
slowest change
direction of the
fastest change
(max)-1/2
(min)-1/2
Ellipse E(u,v) = const
Harris Detector: Mathematics of the analysis of pixels
Transformation of coordinates
Principle component analysis

Can reduce the set of coordinates
One coordinate
The other coordinate is noise
(all points are “shifted” to the Principle component)

Harris Detector: Mathematics
1
2
“Corner”
1 and 2 are large,
1 ~ 2;
E increases in all
directions
1 and 2 are small;
E is almost constant
in all directions
“Edge”
1 >> 2
“Edge”
2 >> 1
“Flat”
region
Classification
of the
new coordinates

PCA: Feature from pixels
1
2
“Corner”
1 ~ 2;
E increases in all
directions
“Edge”
1 >> 2
“Edge”
2 >> 1
“Flat”
region
One principle component
Along the line
The other component is
small
Note that line can be in any direction
Principle component follows line
Rotation invariant

1
2
“Corner”
1 ~ 2;
E increases in all
directions
“Edge”
1 >> 2
“Edge”
2 >> 1
“Flat”
region
There is no line
No principle component

1
2
“Corner”
1 ~ 2;
E increases in all
directions
“Edge”
1 >> 2
“Edge”
2 >> 1
“Flat”
region
There are two lines
(almost) in orthogonal
(perpendicular)
Directions
Two principle components

Feature Detection
Ellipse rotates but its shape (i.e. eigenvalues) remains
the same
Corner response R is invariant to image rotation
Important property: Rotationally invariant

SIFT Descriptor
• 16x16 Gradient window is taken. Partitioned into 4x4 subwindows.
• Histogram of 4x4 samples in 8 directions
• Gaussian weighting around center( is 0.5 times that of the scale of a
keypoint)
• 4x4x8 = 128 dimensional feature vector

Another localized feature from the pixels

Feature Detection
• Use the
scale/orientation to
determined by
detector to in a
normalized frame.
• compute a descriptor
in this frame.
Scale example:
• moments integrated over an adapted window
• derivatives adapted to scale: sIx
Scale & orientation example:
Resample all points/regions to 11X11 pixels
• PCA coefficients
•Principle components of all points.
SIFT Descriptors also invariant to Scale/Orientation

Feature Abstraction
n!º
1 n =1
n*(n-1)! n >1
ì
í
ï
îï
ü
ý
ï
þï
43210 5
76 8 90 1 2 3 4 5
New “features”
represented
in data structures that can be used
in algorithms

Hierarchy of analysis
Hierarchy of features
Simple primitive features
Complex combinations
of simple features
Face detection

Example: Face Detection
• Scan window over image
• Classify window as either:
– Face
– Non-face
ClassifierWindow
Face
Non-face
From the established features

Face Detection Algorithm
Face Localization
Lighting Compensation
Skin Color Detection
Color Space Transformation
Variance-based Segmentation
Connected Component &
Grouping
Face Boundary Detection
Verifying/ Weighting
Eyes-Mouth Triangles
Eye/ Mouth Detection
Facial Feature Detection
Input Image
Output Image

Concept Abstraction
Organizing and making sense of the immense amount of
data/knowledge we have
Generalization
The ability of an algorithm to perform accurately on new, unseen
examples after having trained on a learning data set

Generalization
Consider the following regression problem:
Predict real value on the y-axis from the real value on the x-axis.
You are given 6 examples: {Xi,Yi}.
X*
What is the y-value for a new query ?

Generalization
X*

Generalization
which curve is best?
X*

Generalization
Occam’s razor:
prefer the
simplest hypothesis
consistent with data.
Have to find
a balance
of constraints

Two Schools of Thought
48
1. Statistical “Learning”
The data is reduced to vectors of numbers
Statistical techniques are used for the tasks to be performed.
2. Structural “Learning”
The data is converted to a discrete structure
(such as a grammar or a graph) and the
techniques are related to computer science
subjects (such as parsing and graph matching).

A spectrum of machine learning tasks
• High-dimensional data (e.g. more
than 100 dimensions)
• The noise is not sufficient to
obscure the structure in the data
if we process it right.
• There is a huge amount of
structure in the data, but the
structure is too complicated to be
represented by a simple model.
• The main problem is figuring out
a way to represent the
complicated structure that allows
it to be learned.
• Low-dimensional data (e.g. less
than 100 dimensions)
• Lots of noise in the data
• There is not much structure in the
data, and what structure there is,
can be represented by a fairly
simple model.
• The main problem is
distinguishing true structure from
noise.
Statistics--------------------- Artificial Intelligence

Supervised
learning
Un-Supervised
learning
Concept Acquisition
Statistics

learning with the presence of an expert
Data is labelled with a class or value
Goal:: predict class or value label
c1
c2
c3
Supervised Learning
Learn a properties of a classification
Decision making
Predict (classify) sample → discrete set of class labels
e.g. C = {object 1, object 2 … } for recognition task
e.g. C = {object, !object} for detection task
Spa
m
No-
Spam

learning without the presence of an expert
Data is unlabelled with a class or value
Goal::
determine data patterns/groupings
and the properties of that classification
Unsupervised Learning
Association or clustering::
grouping a set of instances by attribute similarity
e.g. image segmentation
Key concept: Similarity

Statistical Methods
Regression::
Predict sample → associated real (continuous) value
e.g. data fitting
x
1
x
2
Learning within the constraints of the method
Data is basically n-dimensional set of numerical attributes
Deterministic/Mathematical algorithms based on
probability distributions
Principle Component Analysis::
Transform to a new (simpler) set of coordinates
e.g. find the major component of the data

Pattern Recognition
Another name for machine learning
• A pattern is an object, process or event that can be given a
name.
• A pattern class (or category) is a set of patterns sharing
common attributes and usually originating from the same
source.
• During recognition (or classification) given objects are
assigned to prescribed classes.
• A classifier is a machine which performs classification.
“The assignment of a physical object or event to one of several prespecified
categeries” -- Duda & Hart

Cross-Validation
In the mathematics of statistics
A mathematical definition of the error
Function of the probability distribution
Average
Standard deviation
In machine learning,
no such distribution exists
Full
Data set
Training set
Test set
Build the ML
Data structure
Determine Error

Classification algorithms
– Fisher linear discriminant
– KNN
– Decision tree
– Neural networks
– SVM
– Naïve bayes
– Adaboost
– Many many more ….
– Each one has its properties wrt bias, speed,
accuracy, transparency…

Feature extraction
Task: to extract features which are good for classification.
Good features: • Objects from the same class have similar feature values.
• Objects from different classes have different values.
“Good” features “Bad” features

Similarity
Two objects
belong to the
same classification
If
The are “close”
x1
x2
?
?
?
?
?
Distance between them is small
Need a function
F(object1, object1) = “distance” between them

Similarity measure
Distance metric
• How do we measure what it means to be “close”?
• Depending on the problem we should choose an appropriate
distance metric.
For example: Least squares distance
f (a,b) = (ai -bi )2
i=1
n
å

Types of Model
Discriminative Generative
Generative vs. Discriminative

Overfitting and underfitting
Problem: how rich class of classifications q(x;θ) to use.
underfitting overfittinggood fit
Problem of generalization: a small emprical risk Remp does not imply small true expected
risk R.

Generative
Cluster Analysis
Create “clusters”
Depending on distance metric
Hierarchial
Based on “how close”
Objects are

KNN – K nearest neighbors
x1
x2
?
?
?
?
– Find the k nearest neighbors of the test example , and infer
its class using their known class.
– E.g. K=3
?

Discrimitive:
Support Vector Machine
• Q: How to draw the optimal linear
separating hyperplane?
 A: Maximizing margin
• Margin maximization
– The distance between H+1 and H-1:
– Thus, ||w|| should be minimized
64
Margin

Prediction Based on Bayes’ Theorem
• Given training data X, posteriori probability of a hypothesis H,
P(H|X), follows the Bayes’ theorem
• Informally, this can be viewed as
posteriori = likelihood x prior/evidence
• Predicts X belongs to Ci iff the probability P(Ci|X) is the highest
among all the P(Ck|X) for all the k classes
• Practical difficulty: It requires initial knowledge of many
probabilities, involving significant computational cost
65
)(/)()|(
)(
)()|()|( XX
X
XX PHPHP
P
HPHPHP 

Naïve Bayes Classifier
age income studentcredit_ratingbuys_comput
<=30 high no fair no
<=30 high no excellent no
31…40 high no fair yes
>40 medium no fair yes
>40 low yes fair yes
>40 low yes excellent no
31…40 low yes excellent yes
<=30 medium no fair no
<=30 low yes fair yes
>40 medium yes fair yes
<=30 medium yes excellent yes
31…40 medium no excellent yes
31…40 high yes fair yes
>40 medium no excellent no
66
Class:
C1:buys_computer = ‘yes’
C2:buys_computer = ‘no’
P(buys_computer = “yes”)
= 9/14 = 0.643
P(buys_computer = “no”)
= 5/14= 0.357
X = (age <= 30 , income = medium, student =
yes, credit_rating = fair)

67
Class:
Want to classify
X =
(age <= 30 ,
income = medium,
student = yes,
credit_rating = fair)
Will X buy a computer?

68
Key: Conditional probability
P(X|Y) The probability that X is true, given Y
P(not rain| sunny) > P(rain | sunny)
P(not rain| not sunny) < P(rain | not sunny)
Classifier: Have to include the probability of the condition
P(not rain | sunny)*P(sunny)
How often did it really not rain, given that it was actually sunny

69
Class:
Want to classify
X =
(age <= 30 ,
income = medium,
student = yes,
Will X buy a computer?
Which “conditional probability” is greater?
P(X|C1)*P(C1) > P(X|C2) *P(C2) X will buy a computer
P(X|C1) *P(C1) < P(X|C2) *P(C2) X will not buy a computer

70
Class:
X =
(age <= 30 ,
income = medium,
student = yes,
P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6

• Compute P(X|Ci) for each class
P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6
P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444
P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4
P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667
P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2
P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667
P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4
71

P(X|Ci) :
P(X|buys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 0.044
P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
P(X|Ci)*P(Ci) :
P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007
Therefore, X belongs to class (“buys_computer = yes”)
Bigger

Decision Tree Classifier
Ross Quinlan
AntennaLength
10
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
Abdomen Length
Abdomen Length > 7.1?
no yes
KatydidAntenna Length > 6.0?
no yes
KatydidGrasshopper

Grasshopper
Antennae shorter than body?
Cricket
Foretiba has ears?
Katydids Camel Cricket
Yes
Yes
Yes
No
No
3 Tarsi?
No
Decision trees predate computers

• Decision tree
– A flow-chart-like tree structure
– Internal node denotes a test on an attribute
– Branch represents an outcome of the test
– Leaf nodes represent class labels or class distribution
• Decision tree generation consists of two phases
– Tree construction
• At start, all the training examples are at the root
• Partition examples recursively based on selected attributes
– Tree pruning
• Identify and remove branches that reflect noise or outliers
• Use of decision tree: Classifying an unknown sample
– Test the attribute values of the sample against the decision tree
Decision Tree Classification

• Basic algorithm (a greedy algorithm)
– Tree is constructed in a top-down recursive divide-and-conquer manner
– At start, all the training examples are at the root
– Attributes are categorical (if continuous-valued, they can be discretized
in advance)
– Examples are partitioned recursively based on selected attributes.
– Test attributes are selected on the basis of a heuristic or statistical
measure (e.g., information gain)
• Conditions for stopping partitioning
– All samples for a given node belong to the same class
– There are no remaining attributes for further partitioning – majority
voting is employed for classifying the leaf
– There are no samples left
How do we construct the decision tree?

Information Gain as A Splitting Criteria
• Select the attribute with the highest information gain (information gain is the
expected reduction in entropy).
• Assume there are two classes, P and N
– Let the set of examples S contain p elements of class P and n elements of
class N
– The amount of information, needed to decide if an arbitrary example in S
belongs to P or N is defined as















np
n
np
n
np
p
np
p
SE 22 loglog)(
0 log(0) is defined as 0

nformation Gain in Decision Tree Induction
• Assume that using attribute A, a current set will be
partitioned into some number of child sets
• The encoding information that would be gained by
branching on A
)()()( setschildallEsetCurrentEAGain 
Note: entropy is at its minimum if the collection of objects is completely uniform

Person Hair
Length
Weight Age Class
Homer 0” 250 36 M
Marge 10” 150 34 F
Bart 2” 90 10 M
Lisa 6” 78 8 F
Maggie 4” 20 1 F
Abe 1” 170 70 M
Selma 8” 160 41 F
Otto 10” 180 38 M
Krusty 6” 200 45 M
Comic 8” 290 38 ?

Hair Length <= 5?
yes no
Entropy(4F,5M) = -(4/9)log2(4/9) - (5/9)log2(5/9)
= 0.9911















np
n
np
n
np
p
np
p
SEntropy 22 loglog)(
Gain(Hair Length <= 5) = 0.9911 – (4/9 * 0.8113 + 5/9 * 0.9710 ) = 0.0911
Let us try splitting on
Hair length

Weight <= 160?
yes no
= 0.9911















np
n
np
n
np
p
np
p
Gain(Weight <= 160) = 0.9911 – (5/9 * 0.7219 + 4/9 * 0 ) = 0.5900
Weight

age <= 40?
yes no
= 0.9911















np
n
np
n
np
p
np
p
Gain(Age <= 40) = 0.9911 – (6/9 * 1 + 3/9 * 0.9183 ) = 0.0183
Age

Weight <= 160?
yes no
Hair Length <= 2?
yes no
Of the 3 features we had, Weight was best.
But while people who weigh over 160 are
perfectly classified (as males), the under 160
people are not perfectly classified… So we
simply recurse!
This time we find that we can split on
Hair length, and we are done!

Weight <= 160?
yes no
Hair Length <= 2?
yes no
We need don’t need to keep the data around,
just the test conditions.
Male
Male Female
How would these
people be
classified?

Applications:
knowledge
– Problem Solving
– Simulation

Using Knowledge
Problem Solving
Simulations
Searching for a solution
Combining models
to form a large comprehensive model

Problem Solving
Basis of the search
Order in which nodes are evaluated and expanded
Determined by Two Lists
OPEN: List of unexpanded nodes
CLOSED: List of expanded nodes
Searching for a solution through all possible solutions
Fundamental algorithm in artificial intelligence
Graph Search

Abstraction:
State of a system
chess
Tic-tak-toe
Water jug problem
Traveling salemen’s problem
In problem solving:
Search for the
steps
leading to the solution
The individual steps
are the
states of the system

Solution Space
The set of all states of the problem
Including the goal state(s)
All possible board combinations
All possible reference points
All possible combinations

Search Space
Each system state
(nodes)
is connected by rules
(connections)
on how to get
from one state to another

Search Space
How the states are connected
Legal moves
Paths between points Possible operations

Strategies to Search
Space of System States
• Breath first search
• Depth first search
• Best first search
Determines order
in which the states are searched
to find solution

Breadth-first searching
• A breadth-first search (BFS)
explores nodes nearest the
root before exploring nodes
further away
• For example, after searching
A, then B, then C, the search
proceeds with D, E, F, G
• Node are explored in the
order A B C D E F G H I J K L
M N O P Q
• J will be found before NL M N O P
G
Q
H JI K
FED
B C
A

Depth-first searching
• A depth-first search (DFS)
explores a path all the way to
a leaf before backtracking and
exploring another path
• For example, after searching
A, then B, then D, the search
backtracks and tries another
path from B
• Node are explored in the
order A B D E H L M N I
O P C F G J K Q
• N will be found before JL M N O P
G
Q
H JI K
FED
B C
A

Breadth First Search
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| |
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Items between red bars are siblings.
goal is reached or open is empty.
Expand A to new nodes B, C, D
Expand B to new node E,F
Send to back of queue
Queue: FILO

Depth first Search
Expand A to new nodes B, C, D
Expand B to new node E,F
Send to front of stack
Stack: FIFO

Best First Search
Breadth first search: queue (FILO)
Depth first search: stack (FIFO)
Uninformed searches:
No knowledge of how good the current solution is
(are we on the right track?)
Best First Search: Priority Queue
Associated with each node is a heuristic
F(node) = the quality of the node to lead to a final solution

A* search
• Idea: avoid expanding paths that are already expensive
•
• Evaluation function f(n) = g(n) + h(n)
•
• g(n) = cost so far to reach n
• h(n) = estimated cost from n to goal
• f(n) = estimated total cost of path through n to goal
This is the hard/unknown part
If h(n) is an underestimate, then the algorithm is guarenteed to find a solution

Admissible heuristics
• A heuristic h(n) is admissible if for every node n,
h(n) ≤ h*(n), where h*(n) is the true cost to reach
the goal state from n.
• An admissible heuristic never overestimates the cost
to reach the goal, i.e., it is optimistic
• Example: hSLD(n) (never overestimates the actual
road distance)
• Theorem: If h(n) is admissible, A* using TREE-
SEARCH is optimal

Graph Search
Several Structures Used
Graph Search
The graph as search space
Breadth first search Queue
Depth first search Stack
Best first search Priority Queue
Stacks and queues, depending on search strategy

Problem Solving
Simulations
Example: Climate Simulation

Climate Model
Climate Modeling
A multitude of sub-models
submodel
submodel
submodel
submodelsubmodel
submodel
submodel
submodelsubmodel
submodelsubmodel
submodel
submodel
submodel
Many stemming from the techniques discussed previously

Physical processes regulating climate
Physical models representing all the interactions that can occur

Radiation
Even one physical quantity can have many
source models, sink models and interaction models

“Earth System Model”
And ocean model, sea-ice model, land surface model, etc…
3D atmosphere
3D ocean
2D sea ice
Atmospheric
CO2
2D land surface
Land
biogeochemi
stry
Ocean
biogeochem
istry
Ocean sediments
3D ice sheets

Mathematical Models
representing
physical principles

Meteorological Primitive Equations
• Applicable to wide scale of motions; > 1hour,
>100km

Global Climate Model Physics
Terms F, Q, and Sq represent physical processes
• Equations of motion, F
– turbulent transport, generation, and dissipation of
momentum
• Thermodynamic energy equation, Q
– convective-scale transport of heat
– convective-scale sources/sinks of heat (phase change)
– radiative sources/sinks of heat
• Water vapor mass continuity equation
– convective-scale transport of water substance
– convective-scale water sources/sinks (phase change)

Model Physical Parameterizations
Physical processes breakdown:
• Moist Processes
– Moist convection, shallow convection, large scale
condensation
• Radiation and Clouds
– Cloud parameterization, radiation
• Surface Fluxes
– Fluxes from land, ocean and sea ice (from data or models)
• Turbulent mixing
– Planetary boundary layer parameterization, vertical
diffusion, gravity wave drag

Process Models and Parameterization
•Boundary Layer
•Clouds
Stratiform
Convective
•Microphysics

Evolution of
Global Climate
Models (GCMs)
… increasing complexity.
Due to demand
(want/need to model
more complex
systems)
Increased computing
power enables more
complex models

http://www.usgcrp.gov/usgcrp/images/ocp2003/ocpfy2003-fig3-4.htm
The past, present and future of climate models
During the last 25
years, different
components are added
to the climate model to
better represent our
climate system

Grid Discretizations
Equations are distributed on a sphere
• Different grid approaches:
– Rectilinear (lat-lon)
– Reduced grids
– ‘equal area grids’: icosahedral, cubed sphere
– Spectral transforms
• Different numerical methods for solution:
– Spectral Transforms
– Finite element
– Lagrangian (semi-lagrangian)
• Vertical Discretization
– Terrain following (sigma)
– Pressure
– Isentropic
– Hybrid Sigma-pressure (most common)
The heart of
Computational Fluid Dynamics
(CFD)

Different time and spacial scales
Macroscopic properties
intermingling with
macroscopic properties
Fast processes
(ex. Molecular reactions)
Interacting with
Very slow process
(ex. Transport/movement of molecules
To other regions)
This often makes mathematically solving the problems
very difficult

1.
How did I get here?
~106 m - 1m
~107 m ~105 m
~103 m
The planetary scale
Cloud cluster scale
Cloud scaleCloud microphysical
scale

Scales of Atmospheric Motions/Processes
Anthes et al.
Resolved Scales
Global Models
Future Global Models
Cloud/Mesoscale/Turbulence Models
Cloud Drops
Microphysics
CHEMISTRY

10 m 100 m 1 km 10 km 100 km 1000 km 10000 km
turbulence Cumulus
clouds
Cumulonimbus
clouds
Mesoscale
Convective systems
Extratropical
Cyclones
Planetary
waves
Large Eddy Simulation (LES)
Model Cloud System Resolving Model (CSRM)
Numerical Weather Prediction (NWP) Model
Global Climate Model
No single model can encompass all relevant processes
DNS
mm
Cloud
microphysics

Storage and management of
Information
Name Address Parcel #
John Smith 18 Lawyers Dr.756554
T. Brown 14 Summers Tr. 887419
Table A
Table BParcel # Assessed Value
887419 152,000
446397 100,000

Making Sense of Knowledge
Concept
conceptual entity of the domain
Attribute
property of a concept
Relation
relationship between concepts
or properties
Axiom
coherent description between
Concepts / Properties /
Relations via logical expressions
Person
Student Professor
Lecture
isA – hierarchy (taxonomy)
name email
student
nr.
research
field
topic
lecture
nr.
attends
holds

Acquisition of knowledge:
Feature Acquistion
“flat” region:
no change in all
directions
“edge”:
no change along
the edge direction
“corner”:
significant change
in all directions
From a square sampling of pixels

Acquisition of knowledge:
Concept Abstraction
P(X|C1)*P(C1) > P(X|C2) *P(C2)
X will buy a computer
Abdomen Length > 7.1?
no yes
KatydidAntenna Length > 6.0?
no yes
KatydidGrasshopper

Use of knowledge in and as models
Problem Solving
L M N O P
G
Q
H JI K
FED
B C
A
Breadth first search Queue
Depth first search Stack
Best first search Priority Queue

Use of knowledge in and as models
Simulations

Applications
You choose how to represent reality

Applications

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