Stuff for Katie

Probably should go to the library and check out these three books for the term.

1. An Introduction to Dynamic Meteorology - Holton
2. Atmosphere-Ocean Dynamics - Gill
3. Atmospheric Science - Wallace and Hobbs

The goal here is to get you to practice problems in dynamics, thermodyanics and fluid mechanics as this is the basic stuff that you need to get up to speed on. We will ignore all radiative transfer stuff because a) its hard, b) its esoteric and c) you probably won't need it anyway.

So to start off, the following are some sample problems for you to work on for the week and then we can discuss them next week. Some of these problems are designed to practice your math skills and some are designed to improve your physical reasoning skills. I am sure some of the terms will be unfamiliar to you, but should be researchable in the texts listed above. Don't worry if you end up not being able to do any of these problems because that will serve as a starting point.

Problem Set 1:

1. Prove that exactly half the area of the eart lies between +/- 30 degrees latitude. (This is a spherical trig problem)

2. How many days would it take a hot air ballon travelling eastward along a 40 degree N latitude line at a speed of 15 meters per second to circumnavigate the globe?

3. How far below the surface of the ocean is the pressure 2 atmopheres?

4. For each of the following physical situations, identify and justify whether the hydrostatic or Boussinesq approxiamations best apply to that particular kind of fluid flow.
   • Wind-driven turbulent mixing just beneath the ocean surface
   • Sound propogation through the atmospheric boundary layer
   • Flow around a large building during a wind strom
   • A tsunami propogating across the Ocean
   • Mid latitude atmospheric jet streams

5. Consider two water parcels each at a pressure of 1 bar. Parcel A has a salinty of 34 ppt and a temperature of 32 C. Parcel B has salinty of 25 and temperature of 0 C. Both have equal densitys of 1020 kg/m³. Assume that both parcels have equal speeds of sound at 1500 m/s.

   a) Show that if equal parcels of water are mixed, the mixture would be more dense than the original densities (this is strongly relatity to salinty driven currents in the real ocean)

   b) If both water parcels are adiabatically compressed to a pressure of 100 bars (remember they start at 1 bar), what are their respective densities ( hint: adiabatic compression is related to the speed of sound, which is the same for both parcels)

   c) At 100 bars, show that Parcel A will still be warmer than Parcel B

1. Cabin pressure in a typical commercial airliner is equivalent to a height of 1.7 km above sea level. If the sea level pressure and density of air are 1000 mbars and 1.25 kg/m^-3 respectively, what is the air pressure and density at this altitude?

2. If the earth's atmosphere consisted of an incompressible fluid whose density was everywhere equal to that observed at sea level (see previous question) - how thick would the atmosphere be to account for the mean surface pressure of 1000 mbars?

3. The mass flux of air into the topical belt located between +/- 15 degrees is 1.3 x10¹¹kg/s. If this air contains 20 g of water vapor per kg of air, what would be the daily annual rainfall rate assuming in this region, assuming that all of the water vapor does fall out as rain. Hint: treat the surface from -15 to +15 as a cylinder.

4. Suppose that the global atmosphere and a 50 m deep ocean mixed layer equally warm at a rate of 3K per century. What is the equivalent increase in incoming solar flux (in units of Watts per square meter).

   Notes:

   1) the net downward flux at the top of the atmosphere per unit area must equal the rate at which energy is stored in the atmosphere ( assume its air only) and the ocean mixed layer.

   2) you will need ot use the fractional area of the earth's surface that is covered by oceans.

   3) Your answer should be 0.15 Watts per sq meter (and then ask yourself if this is detectable?)

1. To make sure we get the units straight. Pressure in cgs units is in units of millibars. Pressure expressed in SI units is in hectoPascals (100 Pascals); cgs units are centimeters, grams, seconds and SI units are kg, meters and seconds. Show that 1 mb in fact is equal to 1 hPa.

2. On some winter day, cold air passes over the Gulf Stream and experiences a tempearture increase of 10 C over a distance of 300 km. Over that 300 km of Gulf stream, the mixed layer depth is 1 km and the average wind speed is 10 meters/second. Assume no condensation occurs. Calculate the sensible heat flux (units of Watts per square meter) from the sea surface. Assume that the lowest 1 km of our atmosphere is 100 hPa thick.

3. The radiative relaxation time of an atmosphere is defined as the time it takes for the atmosphere to cool to 1/e its present temperature, if all sources of input energy ceased. Hey look, the sun just disappeared. Calculate the timescale for the Earth's Atmosphere (you should get a value of about 830 days).

4. Consider two rigid containers with 1 m³ of air. The air temperature in container 1 is 0 C and in container 2 is 40 C, The air in each container is at a pressure of 1 bar.
   a) calculate the mass of air in each container

   b) Calculate the entropy difference between container 2 and container 1

   c) Voila - we mix the containers. Does the entropy of the total system change? If so, by how much? If not, well, why not?

5. At the top of Mt. Hood, the summertime air temperature and pressure average 270K and 600 millibars. What are the potential temperature and density of this air assuming a reference pressure of 1000 millibars? At sea level, the tempearture and pressure are 295K and 1000 millibars during the summer. From this data, show that the layer of air between sea level and the top of Mt. Hood is statically stable.