Global Warming: Simple Physics in a Compex System Richard B. Rood Cell: Space Research Building (North Campus) November 3, Dept of Physics, University of Michigan

Some Basic References Rood Climate Change Class –Reference list from courseReference list from course Rood Blog Data Base Koshland Science Museum: Global Warming IPCC (2007) Working Group 1: Summary for Policy MakersIPCC (2007) Working Group 1: Summary for Policy Makers IPCC (2007) Synthesis Report, Summary for Policy MakersIPCC (2007) Synthesis Report, Summary for Policy Makers Osborn et al., The Spatial Extent of 20th-Century Warmth in the Context of the Past 1200 Years, Science, 311, , 2006Osborn et al., The Spatial Extent of 20th-Century Warmth in the Context of the Past 1200 Years, Science, 311, , 2006

Outline

Starting point: Scientific foundation (1) The scientific foundation of our understanding of the Earth’s climate is based on fundamental principles of the conservation of energy, momentum, and mass. The scientific foundation of our understanding of the Earth’s climate is based on an enormous and diverse number of observations.

Starting point: A fundamental conclusion Based on the scientific foundation of our understanding of the Earth’s climate, we observe that with virtual certainty –The average global temperature of the Earth’s surface has increased due to the human- caused addition of gases into the atmosphere that hold heat close to the surface.

Starting point: A fundamental conclusion Based on the scientific foundation of our understanding of the Earth’s climate, we predict with virtual certainty –The average global temperature of the Earth’s surface will continue to rise because of the continued increase of human-caused addition of gases into the atmosphere that hold heat close to the surface. –Stable masses of ice on land will melt. –Sea level will rise. –The weather will change.

Let’s look at just the last 1000 years Surface temperature and CO 2 data from the past 1000 years. Temperature is a northern hemisphere average. Temperature from several types of measurements are consistent in temporal behavior. Note that on this scale, with more time resolution, that the fluctuations in temperature and the fluctuations in CO 2 do not match as obviously as in the long, 350,000 year, record. What is the cause of the temperature variability? Can we identify mechanisms, cause and effect? How? {

What do we see from the past 1000 years On time scales of, say, decades the CO 2 and T are not highly correlated. Periods on noted warmth and coolness are separated by changes in average temperature of only 0.5 F. Changes of average temperature on this scale seem to matter to people. –Regional changes, extremes? Recent changes in both T and CO 2 are unprecedented in the past several hundred thousands of years. –And the last 10,000 years, which is when humans have thrived in the way that we have thrived.

Let’s Build up the Scientific Foundation Which means lets build up –The observational foundation –The theory foundation –The validation foundation

Conservation Principle

Conservation (continuity) principle There are certain parameters, for example, energy, momentum, mass (air, water, ozone, number of atoms, … ) that are conserved. –“classical” physics, we’re not talking about general or special relativity! –Simple stuff, like billiard balls hitting each other, ice melting Conserved? That means that in an isolated system that the parameter remains constant; it’s not created; it’s not destroyed. Isolated system? A collection of things, described by the parameter, that might interact with each other, but does not interact with other things. Nothing comes into or goes out of the system … or, perhaps, nothing crosses the boundary that surrounds the system.

Conservation (continuity) principle There are many other things in the world that we can think of as conserved. For example, money. –We have the money that we have. If we don’t spend money or make money then the money we have today is the same as the money we had yesterday. M today = M yesterday That’s not very interesting.

Conservation (continuity) principle M today = M yesterday Living in splendid isolation

Conservation (continuity) principle M today = M yesterday + I - E Let’s get some money and buy stuff. Income Expense

Conservation (continuity) principle M today = M yesterday + N(I – E) And let’s get a car Expense per month = E Get a job Income per month = I N = number of months I = NxI and E= NxE Income Expense

Some algebra and some thinking M today = M yesterday + N(I – E) Rewrite the equation to represent the difference in money (M today - M yesterday ) = N(I – E) This difference will get more positive or more negative as time goes on. Saving money or going into debt. Divide both sides by N, to get some notion of how difference changes with time. (M today - M yesterday )/N = I – E

Some algebra and some thinking If difference does NOT change with time, then (M today - M yesterday )/N = I – E I = E Income equals Expense With a balanced budget, how much we spend, E, is related to how much we have: E = eM (M today - M yesterday )/N = I – eM

Some algebra and some thinking If difference does NOT change with time, then M = I/e Amount of money stabilizes Can change what you have by either changing income or spending rate (M today - M yesterday )/N = I – eM All of these ideas lead to the concept of a budget: What you have = what you had plus what you earned minus what you spent

Conservation Principle seems intuitive for money The conservation principle is posited to apply to energy, mass (air, water, ozone,... ), momentum. Much of Earth science, science in general, is calculating budgets based on the conservation principle –What is the balance or imbalance If balanced, then we conclude we have factual information on a quantity. If unbalanced, then there are deficiencies in our knowledge. Tangible uncertainties.

Conservation (continuity) principle M today = M yesterday + I - E Let’s get some money and buy stuff. Income Expense Energy from the Sun Energy emitted by Earth (proportional to T) Earth at a certain temperature, T

Some jargon, language Income is “production” is “source” Expense is “loss” is “sink” Exchange, transfer, transport all suggest that our “stuff” is moving around.

The first place that we apply the conservation principle is energy Assume that Energy is proportional to temperature, T, if the average temperature of the Earth is stable, it does not vary with time.

And the conservation of CO 2 Assume that total CO 2 is balanced. It sloshes between reservoirs and gets transported around.

Let’s think of this as a cycle CHANGE SOURCES SINKS EXCHANGE

Equilibrium and balance We often say that a system is in equilibrium if when we look at everything production = loss. There might be “exchanges” or “transfers” or “transport,” but that is like changing money between a savings and a checking account. –We are used to the climate, the economy, our cash flow being in some sort of “balance.” As such, when we look for how things might change, we look at what might change the balance.

Need to think about our “system” What about carbon dioxide?

What are the mechanisms for production and loss of CO 2 ? Important things in this figure.

System? When we look at the Earth and talk about climate change what is our system?

System? When we look at the Earth and talk about climate change what is our system? Energy from the Sun Energy emitted by Earth (proportional to T)

System? But our focus is at the surface of the Earth. We change “stuff” in the system as a whole, and then we want to know how the balance of energy at the Earth’s surface will change. Energy from the Sun Energy emitted by Earth (proportional to T) In both of these cases our definition of system implicitly looks at the intersection of climate and people.

One of my rules In the good practice of science, of problem solving, to first draw a picture.

Conservation (continuity) principle Energy from the Sun Energy emitted by Earth (proportional to T) Earth at a certain temperature, T Stable Temperature of Earth could change from how much energy (production) comes from the sun, or by changing how we emit energy.

But the Earth’s surface temperature is observed to be, on average, about 15 C (~59 F). The Greenhouse Effect (Is this controversial?) SUN Earth Based on conservation of energy: If the Earth did NOT have an atmosphere, then, the temperature at the surface of the Earth would be about -18 C ( ~ 0 F). This surface temperature, which is higher than expected from simple conservation of energy, is due to the atmosphere. The atmosphere distributes the energy vertically; making the surface warmer, and the upper atmosphere cooler, which maintains energy conservation. This greenhouse effect in not controversial.

But the Earth’s surface temperature is observed to be, on average, about 15 C (~59 F). The Greenhouse Effect (Is this controversial?) SUN Earth Based on conservation of energy: If the Earth did NOT have an atmosphere, then, the temperature at the surface of the Earth would be about -18 C ( ~ 0 F). This surface temperature, which is higher than expected from simple conservation of energy, is due to the atmosphere. The atmosphere distributes the energy vertically; making the surface warmer, and the upper atmosphere cooler, which maintains energy conservation. We are making the atmosphere “thicker.” This greenhouse effect in not controversial.

Some aspects of the greenhouse effect Greenhouse warming is part of the Earth’s natural climate system. –It’s like a blanket – it holds heat near the surface for a while before it returns to space. Water is the dominant greenhouse gas. Carbon dioxide is a natural greenhouse gas. –We are adding at the margin – adding some blankets Or perhaps closing the window that is cracked open. N 2 0, CH 4, CFCs,... also important. But in much smaller quantities. –Molecule per molecule stronger than CO 2 We have been calculating greenhouse warming for a couple of centuries now.

The first place that we apply the conservation principle is energy If we change a greenhouse gas e.g. CO 2, we change the loss rate. For some amount of time we see that the Earth is NOT in balance, that is ΔT/Δt is not zero, temperature changes.

Conservation (continuity) principle Energy from the Sun Energy emitted by Earth (proportional to T) Earth at a certain temperature, T Stable Temperature of Earth could change from how much energy (production) comes from the sun, or by changing how we emit energy.

The first place that we apply the conservation principle is energy We reach a new equilibrium Changing a greenhouse gas changes this

But the Earth’s surface temperature is observed to be, on average, about 15 C (~59 F). The sun-earth system (What is the balance at the surface of Earth?) SUN Earth Based on conservation of energy: If the Earth did NOT have an atmosphere, then, the temperature at the surface of the Earth would be about -18 C ( ~ 0 F). What else could be happening in this system? This greenhouse effect in not controversial.

Conservation of Energy The heating could change. That is the sun, the distance from the sun,....

The first place that we apply the conservation principle is energy We reach a new equilibrium Changes in orbit or solar energy changes this Can we measure the imbalance when the Earth is not in equilibrium?

Still there are many unanswered questions We know that CO 2 in the atmosphere holds thermal energy close to the surface. Hence, more CO 2 will increase surface temperature. –Upper atmosphere will cool. –How will the Earth respond? Is there any reason for Earth to respond to maintain the same average surface temperature? Why those big oscillations in the past? –They are linked to solar variability. –Release and capture of CO 2 by ocean plausibly amplifies the solar oscillation. Solubility pump Biological pump What about the relation between CO 2 and T in the last 1000 years? –Look to T (temperature) variability forced by factors other than CO 2 Volcanic Activity Solar variability CO 2 increase Radiative forcing other than CO 2 ? –Other greenhouse gases –Aerosols (particulates in the atmosphere)