1. Outline • Announcements • Soil Thermal Regime Soil Physics 2010

2. Announcements • Homework 6 due now • Review sessions next week Quiz! Soil Physics 2010

3. Quiz, question 1 The diagram below shows how a specific soil thermal property varies as a function of some other soil property. What are those 2 properties? Label the axes, including units. DT (L2/T) q (L3/L3, or unitless) Soil Physics 2010

4. Quiz, question 2 Rank the following in order (most, middle, least) according to the heat energy required to raise the temperature by 1 K of a liter of: a) water b) saturated soil c) dry soil Most Middle Least Soil Physics 2010

5. Quiz, question 2 Two 1 L cubes of ice, temperature -10 °C, are surrounded by air that has a temperature of 40 °C. The ice cubes are not in direct sunlight, and are exposed to the same windspeed, but cube A is in the Amazon rain forest, and cube S is in the Sahara desert. Which cube melts faster, and why? The major difference in the cubes’ environments is the humidity of the air. Air in the Amazon has much more water vapor in it. When the water vapor touches the ice cube, it condenses, releasing its latent heat. So cube A receives much more heat from the air, and melts faster. Soil Physics 2010

6. Soil thermal regime Instantaneous change (like infiltration) Cyclical change New! Improved! Dynamic! Steady-state Transient Soil Physics 2010

7. Simple soil heat model Given: • Assume: • 1-D soil • DT constant • Constant temperature Ta at z = ∞ • Sinusoidal temperature at z = 0, with amplitude A0 Then: Soil Physics 2010

8. Some new terms • 1-D soil (depth z, positive down) • DT constant in z and t • Constant temperature Ta at z = ∞ • Sinusoidal temperature at z = 0, with amplitude A0 w = 2p / period (say, 24 hours): normalizes the “clock time” t to the 2p sine wave period. d = depth z at which thermal amplitude is A0/e:normalizes “physical depth” z to exponential function depth. Specifically, Soil Physics 2010

9. The sine part This is about the soil surface warming during the day, and cooling at night. Soil Physics 2010

10. More sine stuff Clock time at the surface Phase shift with depth Phase constant: adjust so peak is at the right time of day 1:00 pm 6:00 am midnight noon midnight For a period of 24 hours, and a peak at the surface at 1:00 pm (the 13th hour), Soil Physics 2010

11. The e-z part exponential decay, half-lives, etc. Soil Physics 2010

12. Summary • Thermal properties (specifically DT) appear only in the definition of damping depth: • Phase shifts (delays) as sine wave propagates downward • Amplitude decreases as the wave propagates downward • Temperature constant at infinite depth Soil Physics 2010

13. 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, you only need the sin() part • When it’s about amplitude, you only need the e-z/d part Soil Physics 2010

14. 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., p) later than the surface? ½ cycle delay requires that , where and , so Soil Physics 2010