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Avalanche forecasting Avalanche forecasters measure the temperature gradient dT/dh, which is the rate at which the temperature in a snowpack T changes with respect to its depth h. A large temperature gradient may lead to a weak layer in the snowpack. When these weak layers collapse, avalanches occur. Avalanche forecasters use the following rule of thumb: If dT/dh exceeds l0°C/m anywhere in the snowpack, conditions are favorable for weak-layer formation, and the risk of avalanche increases. Assume the temperature function is continuous and differentiable.
- a. An avalanche forecaster digs a snow pit and takes two temperature measurements. At the surface (h = 0), the temperature is −16°C. At a depth of 1.1 m, the temperature is −2°C, Using the Mean Value Theorem, what can he conclude about the temperature gradient? Is the formation of a weak layer likely?
- b. One mile away, a skier finds that the temperature at a depth of 1.4 m is −1°C, and at the surface, it is −12°C. What can be concluded about the temperature gradient? Is the formation of a weak layer in her location likely?
- c. Because snow is an excellent insulator, the temperature of snow-covered ground is often near 0°C. furthermore, the surface temperature of snow in a particular area does not vary much from one location to the next. Explain why a weak layer is more likely to form in places where the snowpack is not too deep.
- d. The term isothermal is used to describe the situation where all layers of the snowpack are at the same temperature (typically near the freezing point). Is a weak layer likely to form in isothermal snow? Explain.
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Calculus: Early Transcendentals, 2nd Edition
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