Climate Change: An Inter-disciplinary Approach to Problem Solving��How do I build a climate model?

Richard B. Rood

rbrood@umich.edu

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Winter 2021

Modeling Resources

• Modeling is hard to teach and hard to communicate.
• However, we use models all the time. Sometimes we don’t even realize that. It is how we understand things, how we think about things.
• Please refer to other resources provided on modeling for more introductory material.

What do we do?

• We develop climate models based on the conservation of energy and mass and momentum, the fundamental ideas of classical physics. (Budget equations)
• We are going to identify the sources (production) and the sinks (losses)
• Things that absorb and things that reflect

What do we do?

• We develop climate models based on the conservation of energy and mass and momentum, the fundamental ideas of classical physics. (Budget equations)
• We are going to identify the sources (production) and the sinks (loss)

Source, Production: Water comes in

Sink, Loss: Water goes out

What do we do?

• We develop climate models based on the conservation of energy and mass and momentum, the fundamental ideas of classical physics. (Budget equations)
• We are going to identify the sources (production) and the sinks (losses).
• Sources and sinks will be related to those things that can alter, for example, heating and cooling – the “forcing.”
• Greenhouse gases
• Aerosols
• Transfer
• Transport by Motion
• Feedbacks

The Earth System

ATMOSPHERE

ICE

(cryosphere)

OCEAN

LAND

SUN

Symbolic Energy Balance Equation

E^a_t+Δt = E^a_t + Δt((P^a – L^aE^a) + (Tr^a🡨🡪oil + M^a ))

Atmosphere:

Symbols

E = “Energy”

P = Production

L = Loss rate

Tr = Transfer

M = Motion (Transport)

Superscripts

a is for atmosphere

o is for ocean

i is for ice

l is for land

Variables

t = time

Δt = time increment

What do we do? – An Example

• We determine the characteristics of production and loss from theory and observations.
• Example: the eruption of a major volcano and the temperature response as measured by the global observing system.

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What do we do? – An Example

• We determine the characteristics of production and loss from theory and observations.
• Example: the eruption of a major volcano and the temperature response as measured by the global observing system.

​

What do we do? – An Example

• We determine the characteristics of production and loss from theory and observations.
• Example: the eruption of a major volcano and the temperature response as measured by the global observing system.
• For this problem we would emphasize
• Aerosols
• Transport by Motion
• Feedbacks
• Transfer

The Earth System

ATMOSPHERE

ICE

(cryosphere)

OCEAN

LAND

SUN

Symbolic Energy Balance Equation�(Earth System)

E^a_t+Δt = E^a_t + Δt((P^a – L^aE^a) + (Tr^a🡨🡪oil + M^a ))

Atmosphere:

E^o_t+Δt = E^o_t + Δt((P^o – L^oE^o) + (Tr^o🡨🡪ail + M^o ))

Ocean:

Eⁱ_t+Δt = Eⁱ_t + Δt((Pⁱ – LⁱEⁱ) + (Tr^i🡨🡪oal + Mⁱ ))

Ice:

E^l_t+Δt = E^l_t + Δt((P^l – L^lE^l) + (Tr^l🡨🡪oia + M^l ))

Land:

A point

• With this model we are now existing inside of the climate system rather than sitting out in space looking at the global balance.
• Inside – we are especially interested in what goes on at the surface of the Earth
• Inside – we must worry about the climate every day, we don’t have the benefit of the average
• Inside – we must deal with the complexity

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• This is your point of view or frame of reference.

A point, continued

• Conservation is still true, but you must think about being embedded in the system, not a distant observer of the system.
• Open versus isolated versus closed systems

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• In your design of the model and model experiment, you are often trying to ”isolate” a system so you can study it.

Consider just the Production and Loss Rate�(We call this forcing.)

P^a – L^aE^a

We can divide this, conceptually, into two:

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• That in absence of the influence of the “industry” of humans (natural)

• That which includes the influence of the “industry” of humans (anthropogenic)

• Variability of the sun
• What volcanoes put in the atmosphere
• Greenhouse gases prior to industrial revolution
• Aerosols from, for instance, sea salt and desert dust

• Changes in greenhouse gases due to burning of fuel
• Aerosols from “industrial” emissions
• Changes in gases due to changes in what is growing
• Change in absorption and reflection due to land use change
• More?

More points

• Models are how we organize our knowledge.
• The model is a world that you control, you make the decisions. Therefore, you can design experiments.
• A model is designed for purpose, for an application.
• Without an application, it is difficult to make decisions of model design.
• We, naturally, seek to apply models to problems for which they were not designed.
• We need to remember this.

Finally: How we can design an experiment?

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• We look at some historical observations of, for example, temperature.
• We attempt to predict the temperature response. (What does the “Energy” do.)
• We evaluate (“validate”) how well we did, characterize the quality of the prediction relative to the observations, and determine, sometimes with liberal interpretation, whether we can establish cause and effect.

What do we do?

• We attempt to predict the temperature (“Energy”) response.
• We evaluate (validate) how well we did, characterize the quality of the prediction relative to the observations, and determine, sometimes with liberal interpretation, whether we can establish cause and effect.

For example, can we explain the last 1000 years?

Surface temperature and CO₂ data from the past 1000 years. Temperature is a northern hemisphere average. Temperature from several types of measurements are consistent in temporal behavior.