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Time%20Scales%20

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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 ... – PowerPoint PPT presentation

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Title: Time%20Scales%20

1
Time Scales Human vs Physical Processes
• A big source of trouble Most policy makers and
voters just dont 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 Newtons 2nd Law
• --- F ma Forcemass 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, its THERMAL MASS thats
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
over space

6
Without Getting Lost in Differential Calculus
• lets 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, itll change
temperature only half as fast, in everyday
language)
• and inversely proportional to the amount of
forcing (force it twice as hard, itll change in
half the time, in everyday language)
• Ts Mt/Ft

8
Implications?
• The atmosphere is a tiny fraction of the oceans
mass, and thermal mass. Its time scale for change
is therefore much faster
• .but not fast enough as well 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. Thats a change
approaching of order 1.
• Unfortunately, a time scale of 50-100 years falls
between the cracks as far as us humans

9
Its 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, wed motivate, wed 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
• Its long compared to human attention spans, and
its long enough that ignorant people can feel
if this was serious, itd be changing obviously
right now. Slow non-existent, in this kind of
mind
• Its too long, and its too short.
• Its. Unfortunate for our kids, and future
generations. We just dont deal well with this
kind of time scale. The risk is that well do
little things in order to salve our conscience
but avoid the big changes necessary to actually

10
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11
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 calcs 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