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Hydroelectricity generated by dams has some environmental advantages over other sources of electricity such as nuclear reactors and coal-fired power plants. Hydropower generates essentially no greenhouse gases and produces essentially no solid or toxic wastes, once the facility is constructed. Hydropower is renewable; no finite resources such as uranium ore, coal or petroleum are consumed, once the facility is built. Hydropower also can re-use the same water over and over to generate electricity, if a single river or stream has a series of facilities along its course. Hydropower is not without its problems, however. Dams alter habitat in many ways; fertile agricultural valleys are often lost, salmon and other migratory fish are severely impacted, etc.

The United States Geological Survey has compiled data on the hydroelectric power production of each state and territory in 1990, as well as the amount of water used to generate this electricity. Though not stated, hydropower presumably includes both dams and in-stream turbines, though dams must account for practically all of the production. The units are quite interesting. Water use is given in millions of gallons per day; Washington State uses the better part of a million million gallons every day. Why did the USGS choose the very tiny unit, gallon per day? Electricity production is given in millions of kilowatt-hours; a million kilos is a billion, thus the data are actually given in Gigawatt-hours. Washington generates just under 105 Gwh of hydroelectricity each year; how many hours in a year, and therefore how much hydroelectric capacity is there in Washington State?

The data range over 4 or 5 orders of magnitude, making it difficult to see the data on a conventional linear diagram. The scatterplot shows the logarithm of water use versus the logarithm of hydroelectric production. As might be expected, there is a strong positive correlation between these two variables, though with some scatter. The student should recognize that this scatter is actually quite large, as each increment on the graph represents one order of magnitude in size. Students can fit a linear regression to the "logged" data, and then use algebra to determine the best fit power law regression, if necessary. Is the data actually linear?

The graph might give some indication of the efficiency of hydropower generation. Points below the line indicate larger quantities of water used to generate smaller amounts of electricity than the "average" represented by the regression; Iowa, Kansas, and Rhode Island, for example. Why are these states inefficient? Points above the line might indicate higher efficiency; California, Colorado and Nevada, for example. Why are these states efficient?

Reference:   U.S. Department of the Interior, Estimated Use of Water in the United States in 1990, USGS National Circular 1081. http://water.usgs.gov/watuse/wucircular2.html.

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 1990 hydropower data from the USGS water used to generate hydropower in Millions of gallons per day electricity generation in Millions of kilowatthours state water (Mg/d) elec (M kwh) log water log elec Alabama 218,199 10,340 5.34 4.01 Alaska 1,790 98 3.25 1.99 Arizona 31,801 8,180 4.50 3.91 Arkansas 60,367 4,885 4.78 3.69 California 75,013 23,906 4.88 4.38 Colorado 4,161 1,318 3.62 3.12 Connecticut 6,875 452 3.84 2.66 Delaware 0 0 D.C. 0 0 Florida 7,257 173 3.86 2.24 Georgia 51,678 4,706 4.71 3.67 Hawaii 264 8 2.42 0.90 Idaho 67,778 7,447 4.83 3.87 Illinois 27,108 771 4.43 2.89 Indiana 11,598 441 4.06 2.64 Iowa 1,148 13 3.06 1.11 Kansas 1,302 12 3.11 1.08 Kentucky 83,008 2,880 4.92 3.46 Louisiana 21,667 697 4.34 2.84 Maine 82,676 3,962 4.92 3.60 Maryland 25,912 2,307 4.41 3.36 Massachusetts 24,534 1,090 4.39 3.04 Michigan 109,602 3,043 5.04 3.48 Minnesota 18,808 843 4.27 2.93 Mississippi 0 0 Missouri 13,904 2,192 4.14 3.34 Montana 66,797 10,688 4.82 4.03 Nebraska 12,947 833 4.11 2.92 Nevada 3,492 1,617 3.54 3.21 New Hampshire 45,980 1,976 4.66 3.30 New Jersey 167 17 2.22 1.23 New Mexico 964 215 2.98 2.33 New York 459,199 29,355 5.66 4.47 North Carolina 66,876 7,074 4.83 3.85 North Dakota 10,941 1,720 4.04 3.24 Ohio 7,800 173 3.89 2.24 Oklahoma 47,943 2,865 4.68 3.46 Oregon 480,545 40,784 5.68 4.61 Pennsylvania 68,039 3,192 4.83 3.50 Puerto Rico 362 108 2.56 2.03 Rhode Island 339 6 2.53 0.78 South Carolina 63,407 3,885 4.80 3.59 South Dakota 41,116 4,267 4.61 3.63 Tennessee 159,743 11,758 5.20 4.07 Texas 15,825 1,566 4.20 3.19 Utah 1,880 481 3.27 2.68 Vermont 17,669 1,097 4.25 3.04 Virginia 22,854 4,052 4.36 3.61 Virgin Islands 0 0 Washington 670,103 87,295 5.83 4.94 West Virginia 32,707 1,329 4.51 3.12 Wisconsin 43,972 1,148 4.64 3.06 Wyoming 4,355 611 3.64 2.79

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