Due 13 October 2003

The fundamental principles of geochemical cycling were stumbled upon by John Joly in the latter 1800's when he attempted to determine the age of the Earth by estimating the time required for "salt" to accumulate in the oceans. To do this, Joly simply calculated the total mass of salt in the oceans (by multiplying the concentration of salt in seawater by the volume of the oceans) and dividing this mass by the annual flux of salt to the oceans from rivers. While this method is computationally correct, it does not yield the age of the Earth, but rather the RESIDENCE TIME (i.e. the average length of time "salt" resides in the oceanic reservoir).

1. Let's reenact Joly's computation to see how much fun it might be! To do this, you need some basic data about the ocean and rivers.

  1. Calculate the total volume of water in the ocean. Assume the average depth is 3700 m and the area of the ocean is 360 x 106 km2. What is your answer in km3? What is your answer in liters?

  2. Calculate the total mass of sodium in the ocean. Assume the average concentration of sodium in seawater is 10,500 mg/L. What is this mass in grams?

  3. Use the table below to calculate the annual flux of water from rivers to the ocean.

AMAZON 6300 42.4 42.4
CONGO (ZAIRE) 1250 8.4 50.8
ORINOCO 1100 7.4 58.2
YANGTZE 900 6.1 64.2
BRAHMAPUTRA 603 4.1 68.3
MISSISSIPPI 580 3.9 72.2
YENISEI 560 3.8 76.0
LENA 514 3.5 79.4
MEKONG 470 3.2 82.6
LA PLATA 470 3.2 85.7
GANGES 450 3.0 88.8
IRRAWADDY 428 2.9 91.6
ST. LAWRENCE 447 3.0 94.7
MACKENZIE 306 2.1 96.7
COLUMBIA 251 1.7 98.4
INDUS 238 1.6 100.0

What is the value of the total annual flux of water from rivers to the ocean?

Assume water entering the ocean from rivers has an average sodium concentration of 5.15 mg/L

What is the total mass of sodium delivered to the ocean each year by rivers (i.e. the sodium flux)?

  1. What is the residence time of sodium in the ocean?
  2. Calculate the discharge in cubic feet per second for the rivers above.

3. "The Magnesium Problem" was resolved in 1977, following the discovery of hydrothermal vents along a portion of the mid-ocean ridge system near the Galapagos Islands. Here it was discovered that the Mg flux into rocks near the ridge crest was approximately equal to the annual flux of Mg delivered to the ocean via rivers. Using the calculated Mg flux into ocean ridges, the residence time of Mg in the ocean was determined to be approximately 10 million years. Put another way, a volume of water equivalent to the entire volume of the ocean was cycled through the world mid-ocean ridge system every 10 million years! Using the information below, calculate the volume of water (in cubic feet per second) which must be processed through each meter length of the mid-ocean ridge every minute to accomplish this task.

  1. volume of ocean = 1.332 x 109 km3 = how many cubic feet is this?
  2. length of mid-ocean ridge system = 42,000 miles = 67,580 km

Your calculated answer may seem extraordinary to you. This is because we are using a somewhat misleading parameter (each meter length of ridge). A better figure would be to estimate the flow through each square meter of ridge. For the sake of argument, let's assume that hydrothermal activity is restricted to a region extending 20 km on either side of the ridge crest. Now calculate the required seawater flow through ridge rocks to process the ocean volume in 10 million years.

Compare this flow to the discharge of the rivers in the table above.