Soil Physics 2010

1. Outline • Announcements • Heitman’s soil E method • Solute movement Soil Physics 2010

2. Announcements • Review sessions this week: • Noon today, Agronomy 1581 • Another one later? • Homework due Wednesday • Quiz? Soil Physics 2010

3. Heitman’s soil E method Key concept #1: q = 0.01 is small relative to measurement error, but LE for q = 0.01 is big Key concept #2: LE in the soil is about E, not ET LE(evaporation from the soil) S(heating the soil) Soil Physics 2010

4. Sensible heat balance can be used to estimate the latent heat (LE) used for evaporation. <0 Condensation =0 No net change >0 Evaporation LE = (H1 – H2) –DS Upper sensible heat flux H1 LE Sensible heat storage DS Lower sensible heat flux H2 Soil Physics 2010

5. Heitman’s soil E method Components of heat flow into / out of this thin layer: Negligible in Stages II & III Liquid water flow up/down Soil temperature warming/cooling Phase change water evaporating / condensing Given by Fourier’s law Calculate by difference Soil Physics 2010

6. Heat Pulse (HP) sensors 1 T1 0 mm H1 dT/dz1 C1,k1 3 mm 2 T2 DS 6 mm H2 dT/dz2 C2,k2 9 mm 3 T3 12 mm Soil heat flux:H = -k(dT/dz) Change in soil heatstorage:DS = C (Dz) (dT/dt) a heat-pulse sensor LE = (H1 – H2) –DS Soil Physics 2010

7. Measuring heat flow into tiny layers Active Passive T1 C1 k 1 Dz1 T2 Dz2 C2 k2 T3 Fourier: Radiation Conduction Convection Latent heat LE = (H1 – H2) –DS → Soil Physics 2010

8. HP probes installed in top 6 cm of bare field 6 cm In 2007 Summer In 2008 Summer Soil Physics 2010

9. Improved Heat Pulse probe (“Model T”) First used summer 2009 mm Side view 0 6 12 18 24 30 36 42 48 10 mm Soil Physics 2010

10. Temperature (T , °C) T (˚C) 174 175 176 177 178 179 180 Day of year 2007 Soil Physics 2010

11. Temperature, Heat capacity, & Thermal conductivity T (˚C) k (W m -1 ˚C -1) C (MJ m-3 ˚C -1) 3 . 1.2 . C (3-9 mm) 2 0.8 k (3-9 mm) 1 0.4 0 0 174 175 176 177 178 179 180 Day of year 2007 Soil Physics 2010

12. Evaporation within soil layers Evaporation (mm/hr) 3-9 mm 1st depth 9-15 mm 2nd 15-21 mm 3rd 21-27 mm 4th Day of year 2007 This is the “drying front” we’ve mentioned earlier – now actually observed. Heitman, J.L., X. Xiao, R. Horton, and T. J. Sauer (2008), Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation, Water Resource Research44, W00D05 Soil Physics 2010

13. Comparison of methods Heitman, J.L., X. Xiao, R. Horton, and T. J. Sauer (2008), Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation, Water Resource Research44, W00D05 Soil Physics 2010

14. Solute Transport Flow Diffusion Convection Dispersion Soil Physics 2010

15. Steady-State Diffusion C1 C0 Under steady-state conditions we get a straight line, just as we did with Darcy’s law. just likeQ = -KiA L Soil Physics 2010

16. Transient diffusion For transient diffusion, we need to know the initial and boundary conditions. t0 Constant area under curve (constant mass) t1 Suppose we have Ci = 0 x > 0, t = 0 C0 = 1 x = 0, t = 0 Ci = 0 x = ∞, t > 0 C/C0 t2 t3 x Soil Physics 2010

17. Constant concentration C0 = 1 Ci = 0 Breakthrough C/C0 t So, what if we had Ci = 0 x > 0, t = 0 C0 = 1 x = 0, t≥ 0 Ci = 0 x = ∞, t > 0 Solute mass increases with time This is called a Breakthrough Curve Then at some distance x, we’d see Soil Physics 2010

18. Another breakthrough curve C/C0 t0 t t1 t2 t3 x Soil Physics 2010

19. t1 t0 t3 t2 Diffusion with Convection v Sir Geoffrey Taylor examined a “slug” of dye traveling in a tube of flowing water (early 1950s). The slug moved at the mean water velocity, and it spread out but remained symmetrical. This seemed remarkable to Taylor. Soil Physics 2010

20. Why was this remarkable? Taylor knew that water flowing through a tube has a parabolic velocity profile. Water in the center flows at twice the mean water velocity. The velocity profile is not symmetrical, but the dye slug was symmetrical. Soil Physics 2010