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Modeling and Complexity in Climate Science
Transcript of Modeling and Complexity in Climate Science
University of Southern California
The 5 Minute History of Models in Science
...but not so well for complex non-linear systems
What is a model, anyway?
A Critique of Pure Equations
Classical (equation-based) science assumes the world is:
Modeling and Complexity in Climate Science
In Other Words...
The "decomposable" assumption of "equation based" science fails to hold
In Closing, an Inspirational Quote
"Equation-based expression allows noun-based science; algorithmic expressions allows verb-based (procedural) science...
Can We Trust Them?
GCMs are "pragmatic idealizations"
What role does modeling play in science?
How are climate models (un)like other models?
(Why) should we trust models?
(also kind of sucks, but less)
Forget the world!
No way dude
Check out all this stuff I can do with algebra!
I, for one, welcome our machine overlords
Science by first principles
Science by geometry
Science by equations
Science by algorithms
At (or near) equilibrium
This works great for
Julien: "A simplified though internally consistent representation of reality."
Unpacking That Statement
"A simplified though internally consistent representation of reality."
Models ignore some features of the world
Models (at least in science) are tools to study the world
X is a model of Y iff X is a
of Y, and X can be examined to learn interesting things about the structure and dynamics of Y.
One way to think about linearity is as feature called "convexity."
A set is convex iff when X and Y are in the set, then the "weighted average" of X and Y is in the set too.
Spheres are convex
X "+" Y
Toroids are not
X "+" Y passes outside the set
You can't break a non-linear system apart, study the parts in isolation, and then understand the whole thing.
As you know, climate models aren't just systems of equations.
High-level climate models are
(also known as simulations)
How Are Climate Models Different?
The solar system's behavior is chaotic, but we often ignore that fact.
its behavior as if it were non-chaotic
GCMs like GISS involve approximations too, but not just approximations
Flux capacitors couplers
“...merely describe a target system inexactly.”
“...refer to new systems whose properties approximate those of the target system.”
* Norton, John "Approximation and Idealization: Why the Difference Matters" Philosophy of Science, 79 (2012), pp. 207-232
They're different from more standard models (e.g. systems of equations) in that they involve the creation of
novel physical systems
that share a partial isomorphism of
inputs and outputs
(rather than internal structure) with the global climate
So, complaints that elements like flux adjustments have no physical analogue are not well-formed. We're after partial isomorphism of output, not (directly) dynamics
One consequence of thinking of climate modeling as a business of pragmatic idealization is that the violent incompatibility between different models is no longer an issue.
Climate models are
tools for deciding
, not isomorphic representations of the climate
Complexity sciences study systems whose elements react to the patterns they make, i.e. the context they themselves help create."
- Brian Arthur
"That is, how might we individuate the global climate system so that we can notice the patterns that might help us predict the outcome of various climate policies?
The answer to this question depends in part upon what we consider valuable
; if we want to maximize long-term economic growth for human society, for instance, our set of macrostates will likely look very different than it would if we wanted to simply ensure that the average global temperature remained below a particular value...the microstructure of the system does not provide an obvious and uncontroversial answer to the question of which individuation we should choose.
There is no clearly best way to go about individuating the world."
Lawhead (forthcoming). "Structural Modeling Error and the System Individuation Problem." The British Journal for the Philosophy of Science.
If models are tools for deciding, then what does it mean for one model to be "better" than another?
It can't just be a matter of getting things "more correct," because (I'm arguing) that's not the point of climate models.
Building a model involves making value-laden choices about what you prioritize, and what you want to accomplish. How you answer those questions shapes what even
as a "system to be modeled" in a given context.
Computing With Physical Systems
Soap bubbles seek to minimize their surface area
This physical property can be leveraged to do all sorts of interesting computation, including solve some NP-complete optimization problems in seconds
The bubbles act as a model, just like GCMs do.
Is this approximation? Idealization? Both? Neither?
Network degree (fault tolerance)
Number of edges (cost)
Actual Iberian roads
Path length (efficiency)
By noticing partial isomorphisms in nature, we can turn some physical systems into models of others