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Time Scales – Human vs Physical Processes

Time Scales – Human vs Physical Processes. A big source of trouble… Most policy makers and voters just don’t get it. Time scales of physical processes roughly scale with size – bigger size = longer time scale. “Size” can be…. Length, mass, thermal capacitance.

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Time Scales – Human vs Physical Processes

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  1. Time Scales – Human vs Physical Processes A big source of trouble… Most policy makers and voters just don’t get it

  2. Time scales of physical processes roughly scale with size – bigger size = longer time scale • “Size” can be…. Length, mass, thermal capacitance. • For significant changes in position to happen, we look at Newton’s 2nd Law --- F = ma Force=mass x acceleration

  3. For movement under influence of force… • Solving for dt ~ time scale, gives • Time scale ~ (m/F) * dv • So, larger mass means longer time scale, for a given forcing. • Time scale for what? For “significant” change in position

  4. Now, mass goes up very rapidly with physical dimension… • For a block of any material of a given density, • Therefore, time scale goes up rapidly with physical size. • --Microbes dance like crazy • --People move like “normal” • --Big things like oceans and atmospheres take years or decades to change visibly. • --Stars take millions or billions of years to change significantly.

  5. For temperature change, it’s THERMAL MASS that’s important as well • This is the “heat equation”. The rate of change of the internal energy u of an object is proportional to the conductivity k divided by the thermal capacitance times density, times the gradient of the gradient of the internal energy over space

  6. Without Getting Lost in Differential Calculus… • …let’s just note that solving for dt shows it is proportional to both mass density and thermal capacitance (remember, water has a very high thermal capacitance) • …times a physical size over which the gradient of internal energy changes

  7. The Essence of the Physics is this… • – that the time scale for significant change in the thermal energy of the system is proportional to the thermal mass which is to be forced… (add heat to something twice as big, it’ll change temperature only half as fast, in everyday language) • …and inversely proportional to the amount of forcing (force it twice as hard, it’ll change in half the time, in everyday language) • Ts ~ Mt/Ft

  8. Implications? • The atmosphere is a tiny fraction of the ocean’s mass, and thermal mass. Its time scale for change is therefore much faster • ….but not fast enough as we’ll see • The time scale for the ocean to completely turn over and come to equilibrium with a constant atmosphere (if we had one) is roughly 1000 years • The time scale for “significant change” in the atmospheric forcing due to human-caused CO2 is a few decades. CO2 levels in the atmosphere have increased by ~50% in 100 years. That’s a change approaching “of order 1”. • Unfortunately, a time scale of 50-100 years falls “between the cracks” as far as us humans…

  9. It’s an… UNFORTUNATE time scale • ~50-100 years for significant climate change – unfortunate • If it were many centuries, we could forget about it perhaps and let smarter, wealthier people of the future deal with it • If it were just a few years, like e.g. impending WW II, we’d motivate, we’d do what was necessary – spending 10%, 20% even 30% of world GDP to solve the problem before it became serious. • If it were less than 4 years, even our politicians might be motivated to focus on the truth, instead of short term pay-offs from Big Oil or pressure from right wing ideologs • It’s long compared to human attention spans, and it’s long enough that ignorant people can feel “if this was serious, it’d be changing obviously right now”. Slow = non-existent, in this kind of mind • It’s too long, and it’s too short. • It’s…. Unfortunate – for our kids, and future generations. We just don’t deal well with this kind of time scale. The risk is that we’ll do little things in order to salve our conscience; but avoid the big changes necessary to actually head off disaster

  10. Key Points – Time Scales • Time scales for physical climate processes are longer for systems of higher thermal mass Mt • Time scales for physical processes are faster for stronger forcings Ft … • Time Scale ~ Mt/Ft • Simple calc’s show 50-100 yrs for significant climate change – very unfortunate! Too long to keep our personal attention, too short for the safety of our children and future generations

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