Exam2008

Exam2008 - University of California, Santa Barbara ESM 236:...

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University of California, Santa Barbara Jeff Dozier, Mike Colee, ESM 236: The Mountain Snowpack Ned Bair, Karl Rittger Final Exam, March 28, 2008 - 1 - The Final Examination counts 100% of your course grade. Answer all three questions, which are equally weighted. The exam is open-book and open-notes, but you should be able to answer the questions without them. You do not have to repeat the question in your answer; just use the number designations. Put your name on each page. 1. Temperature and vapor pressure gradients in the upper part of the snowpack The diffusion equation for heat transfer in a conducting medium is 2 2 , where T K T tC z  temperature time thermal conductivity density specific heat depth T t K C z This has an analytic solution when the medium is uniform and the temperature at the surface is a periodic function, i.e. 0 (0, ) cos( ) T t T T t   , where 2 P  and P is the period (e.g., 86,400 seconds in a day). Under these restrictions, the equation for temperature at any time and depth is / 0 ( , ) cos zd z T z t T T e t d      2 where the damping parameter and is the thermal diffusivity P d K C   Using a mean temperature o 10 C T  and daily temperature variability o 0 8C T  (half amplitude), along with
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Exam2008 - University of California, Santa Barbara ESM 236:...

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