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