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Problem 3 Lakes in the temperate zone can become thermally stratified during the summer. Warm, buoyant water near the surface overlies colder, denser water on the lake bottom. Such stratification effectively divides the lake vertically into two layers: the epilimnion and the hypolimnion separated by a plane called the thermocline. Thermal stratification has great significance for environmental engineers studying the pollution of such systems. In particular, the thermocline greatly diminishes mixing between the two layers. As a result, decomposition of organic matter can lead to severe depletion of oxygen in the isolated bottom waters. The location of the thermocline can be defined as the point at which the absolute value of the gradient of the temperature (7) vs. depth (2) is a maximum. Mathematically, this will also be the inflection d'T point of the temperature-depth curve that is, the point at which -= 0. dz² The table below contains temperature vs. depth data for Ice Lake in Minnesota, taken about 6pm on 25 September 2000. Use cubic splines to determine the thermocline depth for Ice Lake on this date. depth (m) T (°C) 1 22 4 21.1 5.9 12.7 8.2 7.4 10.1 6.2 12.8 5.9

Problem 3 Lakes in the temperate zone can become thermally stratified during the summer. Warm, buoyant water near the surface overlies colder, denser water on the lake bottom. Such stratification effectively divides the lake vertically into two layers: the epilimnion and the hypolimnion separated by a plane called the thermocline. Thermal stratification has great significance for environmental engineers studying the pollution of such systems. In particular, the thermocline greatly diminishes mixing between the two layers. As a result, decomposition of organic matter can lead to severe depletion of oxygen in the isolated bottom waters. The location of the thermocline can be defined as the point at which the absolute value of the gradient of the temperature (7) vs. depth (2) is a maximum. Mathematically, this will also be the inflection d'T point of the temperature-depth curve that is, the point at which -= 0. dz² The table below contains temperature vs. depth data for Ice Lake in Minnesota, taken about 6pm on 25 September 2000. Use cubic splines to determine the thermocline depth for Ice Lake on this date. depth (m) T (°C) 1 22 4 21.1 5.9 12.7 8.2 7.4 10.1 6.2 12.8 5.9

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
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Problem 3 Lakes in the temperate zone can become thermally stratified during the summer. Warm, buoyant water near the surface overlies colder, denser water on the lake bottom. Such stratification effectively divides the lake vertically into two layers: the epilimnion and the hypolimnion separated by a plane called the thermocline. Thermal stratification has great significance for environmental engineers studying the pollution of such systems. In particular, the thermocline greatly diminishes mixing between the two layers. As a result, decomposition of organic matter can lead to severe depletion of oxygen in the isolated bottom waters. The location of the thermocline can be defined as the point at which the absolute value of the gradient of the temperature (7) vs. depth (2) is a maximum. Mathematically, this will also be the inflection d²T point of the temperature-depth curve that is, the point at which = 0. dz² The table below contains temperature vs. depth data for Ice Lake in Minnesota, taken about 6pm on 25 September 2000. Use cubic splines to determine the thermocline depth for Ice Lake on this date. depth (m) T (°C) 1 22 4 21.1 5.9 12.7 8.2 7.4 + 10.1 6.2 12.8 5.9
Transcribed Image Text:Problem 3 Lakes in the temperate zone can become thermally stratified during the summer. Warm, buoyant water near the surface overlies colder, denser water on the lake bottom. Such stratification effectively divides the lake vertically into two layers: the epilimnion and the hypolimnion separated by a plane called the thermocline. Thermal stratification has great significance for environmental engineers studying the pollution of such systems. In particular, the thermocline greatly diminishes mixing between the two layers. As a result, decomposition of organic matter can lead to severe depletion of oxygen in the isolated bottom waters. The location of the thermocline can be defined as the point at which the absolute value of the gradient of the temperature (7) vs. depth (2) is a maximum. Mathematically, this will also be the inflection d²T point of the temperature-depth curve that is, the point at which = 0. dz² The table below contains temperature vs. depth data for Ice Lake in Minnesota, taken about 6pm on 25 September 2000. Use cubic splines to determine the thermocline depth for Ice Lake on this date. depth (m) T (°C) 1 22 4 21.1 5.9 12.7 8.2 7.4 + 10.1 6.2 12.8 5.9
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