Soil Physics 2010 Announcements Review sessions this week: Today, 11-1 in G217 Wednesday, 11-1, 1581 No quiz today!
Soil Physics 2010 You are monitoring soil temperature, wetness, and CO 2 concentrations, and want to calculate the CO 2 efflux. A spreadsheet of your data (SP_HW6_gasdiff.xls) is available on the course website. Plot the calculated (a) CO 2 diffusivity as a function of depth and time. (see pdf online for more details) Homework 6, question 3a
Soil Physics 2010 Plot the calculated (b) CO 2 efflux (diffusion across the soil surface) as a function of time for the period given. State your assumptions. Homework 6, question 3b Temperature CO 2 10 0 30 – 63 96 – 12 1512 – 1815 2118 – 24 2724 – 3027 3630 – 36 4236 – 4245 60 10075 What is D( ,T) for How do you average diffusivity (or conductivity)? Conductors in series use a harmonic mean (in parallel, they use the arithmetic mean) ?
Soil Physics 2010 Plot the calculated (b) CO 2 efflux (diffusion across the soil surface) as a function of time for the period given. State your assumptions. Homework 6, question 3b y-axis units are ppm / cm 2 s series: harmonic mean =harmean(1,2,3…) in excel parallel: arithmetic mean =average(1,2,3…) in excel
Soil Physics 2010 Back to the soil thermal regime = 2 / period ( say, 24 hours ): normalizes the “clock time” t to the 2 sine wave period. d = “damping depth”: depth z at which thermal amplitude is A 0 /e: normalizes “physical depth” z to exponential function depth. Specifically, T a = Average Temperature A 0 = amplitude of temperature at the surface
Soil Physics 2010 The sine part This is about the soil surface warming during the day, and cooling at night.
Soil Physics 2010 More sine stuff For a period of 24 hours, and a peak at the surface at 3:00 pm (the 13 th hour), Clock time at the surface, normalized to 2 Phase shift with depth Phase constant: adjust so peak is at the right time of day noon midnight 6:00 am 3:00 pm
Soil Physics 2010 The e -z part exponential decay, half-lives, etc.
Soil Physics 2010 Summary Thermal properties (specifically D T ) appear only in the definition of damping depth: Phase shifts (delays) as sine wave propagates downward Amplitude decreases as the wave propagates downward Temperature is constant at infinite depth
Soil Physics 2010 Applications The questions we ask this equation are usually about either timing and phase shift, or amplitude but not both. When it’s a timing question, focus on the sin() part When it’s about amplitude, concentrate on the e -z/d part
Soil Physics 2010 Example application On the coldest day of the year, at what depth is the warmest soil found? Translation: what depth z is ½ cycle (i.e., ) later than the surface? ½ cycle delay requires that, where and, so
Soil Physics 2010 Example application Around June 20, the soil surface temperature may have an amplitude of 15 °C in one day. At what depth is the amplitude only 2.5 °C in one day? This is an amplitude problem, so we are only concerned with the e -z/d part.