Question

0 42. Avalanche forecasting Avalanche forecasters measure the tem- perature gradient, which is the rate at which the temperature in a snowpack 7 changes with respect to its depth h. A large tem- perature gradient may lead to a weak layer in the snowpack. When these weak layers collapse, avalanches occur. Avalanche forecast- dT Equ 49. dh the dT er use the following rule of thumb: I d exceeds 10C/m any- 50. 10 of where in the snowpack, conditions are favorable for weak-layer formation, and the risk of avalanche increases. Assume the tem- perature function is continuous and differentiable. Explor a. An avalanche forecaster digs a snow pit and takes two temper- ature measurements. At the surface (h = 0), the temperature is-16°C. At a depth of 1.1 m, the temperature is-TC. Using the Mean Value Theorem, what can he conclude about the tem- T52. L perature 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 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 iso- thermal snow? Explain. 51. Ve a. b. 53. S 54. S

#42 mean value theorem

Answer 1

b. The average temperature gradient from h 0 to h.4.6/m. While it is still possible that the temperature gradient exceeds 10° m somewhere in the snowpack, one may suspect that the formation of a weak layer is not likely in this case. 1.4-0 c. If the surface temperature and temperature at the bottom of the snowpack are both roughly constant, then the temperature gradient will be larger in areas where the snowpack is less deep d. If all layers of the snowbank are the same temperature, then the temperature gradient is 0 and a weak layer is not likely to form.