HomeworkÐModule 2 Name: 
(text) Key


1) The length of day has steadily increased throughout the earthÕs history. Geological evidence1 suggests 
that it was only 21.9 hours 620 million years ago (Mya). In other words, the earth rotated nearly 
10% faster 620 Mya. If we assume the earth's atmosphere had the same temperature 
distribution then as it does now (which it did not), what changes in the geostrophic wind speeds 
(faster or slower) would you expect 620 Mya ago relative to today's conditions over the middle 
latitudes? Use concepts of chapter 6 of Ahrens to defend your answer. 
(text) We would expect slower geostrophic winds. 
Because temperature differences determine the pressure field, the same temperature distribution would produce the same horizontal pressure gradient force (PGF) and require the same Coriolis force to balance the PGF as today too. Recall that the geostrophic wind results from a balance between the pressure gradient force and the Coriolis force, and that the Coriolis force is defined as the product of the earth's rotation rate and the wind speed. This implies wind speeds slower than today would produce the same Coriolis force 620 Mya. Hence, geostrophic winds would be slower.

Thought progression:
-Same temperature distribution would yield the same pressure field and PGF.
-Same PGF 620 Mya as today would require the same Coriolis force as today for geostrophic balance.
-Since Coriolis force is product of earthÕs rotation rate times wind speed, a 10% faster rotation rate would require a 10% slower wind for geostrophic balance.
-Hence, one would expect slower wind speeds.  

The most recent assessment from International Panel on Climate Change (IPCC 2103) states that during 
the next 20 years (2016-2036; see Fig. 11-10 of AR5-WG1), the average surface temperatures over high 
latitudes of the wintertime Northern Hemisphere are expected to warm by 3¡C, which is more than any 
other region of the world. On the other hand, the tropics are expected to warm the least, 1¡C or less. If the 
IPCC temperature projections materialize, it follows that features of the global circulation during northern 
hemisphere winter could change too. Answer the last two questions based on the IPCC projections. 

2) What changes in the intensity (i.e. average speed) of the polar jet stream (increase or decrease) would 
you expect if the polar troposphere warms 2¡C more than the tropics? Explain your answer using 
concepts of module 2. Material in chapters 6 and 7 of Ahrens should prove especially useful. 
(text) We would expect a slowing of the jet stream. 
Greater warming of the polar regions relative to the tropics would decrease north-south temperature differences, which in turn would decrease the north-south PGF. A weaker PGF requires a smaller Coriolis force to balance it, and a smaller Coriolis force could only be produced by slower winds.

Thought progression
-More warming in polar regions than the tropics would decrease the north-south temperature difference.
-Weaker N-S temperature gradient would yield a weaker N-S pressure gradient.
-A weaker PGF requires a smaller Coriolis force to establish geostrophic balance.
-Smaller Coriolis force means slower winds.

3) What changes in the intensity and frequency of extratropical cyclones during winter would you expect 
if average tropics-to-pole temperature difference decreases by 2¡C? Again, explain your answer using 
concepts of module 2. Material in chapter 8 of Ahrens should prove quite valuable. 
(text) We would expect a decrease in the intensity and frequency of cyclones. 
Horizontal temperature differences are the energy reservoir from which extratropical cyclones form. Hence, a weaker north-south temperature gradient would mean that there is less energy to develop extratropical cyclones. It follows that cyclones in 2036 would likely be weaker and fewer in number because the temperature gradient is smaller.

Thought progression
-Horizontal temperature differences are the energy reservoir from which extratropical form.
-A weaker N-S temperature means less available energy to develop extratropical cyclones.
-It follows that cyclones would be weaker and fewer in number with a reduced temperature gradient.


1https://www.scientificamerican.com/article/earth-rotation-summer-solstice/