Homework #1;	ES 10 -- Geologic Principles	Name___________________

	The goal of this homework exercise is to use steady state box models to investigate the
hydrologic and tectonic systems. Always assume steady state, which means that the total flows
into the reservoir of interest are equal to the total flows out of the reservoir of interest. Remember
that the basic governing equation is F=M/T where F=flows in or out measured in units of mass or
volume/units of time, M=mass, volume, or number of the material or thing of interest, and
T=time. 

Table 1. Distribution of Water on Earth

Surface water
  Lakes and rivers (fresh)		125,000 km3 
  Lakes and inland seas (salty)		104,000 km3 
Groundwater
  Shallow, fresh			4,167,000 km3 
  Deep, salty				4,167,000 km3 
Ice caps and glaciers			29,000,000 km3 
Atmosphere				12,500 km3 
Oceans					1,321,000,000 km3 

Data Source: J.H. Feth, U.S. Geological Survey Circular 601-1, 1973, ÒWater Facts and Figures
for planners and Managers.Ó

Table 2. Flows of water between major reservoirs.

Precipitation
  on land			101,000 km3 /yr
  at sea				299,000 km3 /yr
Evaporation at sea		336,000 km3 /yr
Evapotranspiration 		 63,000 km3 /yr
Discharge from Land to Sea
  from surface waters		32,000 km3 /yr 
  from groundwater		 6,000 km3 /yr

 Data Source: W.K. Hamblin and E.H. Christiansen, 1995, ÒEarthÕs Dynamic Systems.Ó

1) Draw the hydrologic system, showing all major reservoirs and flows of water.

See attached

2) What is the average residence time of water beneath the surface, i.e., groundwater? Using the
answer as a rough indication, is groundwater a renewable resource? What are at least two
assumptions implicit in these calculations as applied to the groundwater case?

Fin=Fout=6,000 km3 /yr; M=4,167,000 km3 

T=M/F=694.5 years
The average residence time for groundwater is about 700 years -- longer than human timescales,
therefore not a good renewable resource.
Assumptions are 1) steady state, 
	2) anything reasonable, like Òall groundwater systems operate the same wayÓ
or	Òall of the shallow, fresh water is potable.Ó 
	We didnÕt specifically discuss these 2nd issues in class.

3) If 60% of the worldÕs trees were cut down, decreasing the rate of evapotranspiration from land
by 30%, how would the rate of precipitation on land be affected? Assume steady state and that the
total amount of water in each of the reservoirs remains constant. How do think your answer would
affect the rest of the trees and plants on Earth.

0.7 X 63,000 km3 /yr = 44,100 km3 /yr

Fout now equals 44,100 + 6,000 (groundwater recharge) + 32,000 (surface H2O discharge) =
82,100 km3 /yr

Fin must still equal Fout.

Therefore Fin (precipitation on land) = 82,100 km3 /yr -- the on land precipitation is decreased by
18,900 km3 /yr, or 19%. 

less precipitation would not be a good sign for the rest of the plants on Earth. Or perhaps the
distribution of plant type would change drastically to those favoring dryer conditions.

4) Consider the following information concerning the EarthÕs ocean basins:

Area of oceanic crust:			3.1X108 km2
Average thickness of oceanic crust	8 km
Average age of oceanic crust		80 million years

How much crust must be created each year at divergent margins to produce the EarthÕs oceanic
crust at steady state? Draw a picture to help you figure this out.

Amount of crust created each year = Fin. Amount of crust down subduction zones = Fout.
Fin = Fout.

Fin=M/T 

M = volume in this case = Area X Thickness = 3.1X108 km2 X 8 km = 2.48X109 km3 
T = the average age = 80 million years
Fin=M/T=2.48X109 km3/8X107 years = 31 km3 /yr