1. Soil physics Magnus Persson

2. Surface tension   2·R·cos  R 2·r P1P1 P2P2 z Due to surface tension water can be held at negative pressure in capillary tubes. (P 1 <P 2 = P atm ) The smaller the diameter of the tube, the higher capillary rise. An useful analogy is that the soil can be considered to act like a bundle of cappilary tubes with different diameters (representing the range of pore sizes)

3. pF curve The soil moisture potential, or soil water suction, is sometimes given in pF = log(-pressure in cm H 2 O). The water retention curve, soil moisture characteristic, or pF curve, is the relationship between the water content, θ, and the soil water potential, ψ. This curve is characteristic for different types of soil (1 bar = 100 kPa = 1000 cm H 2 O)

4. Soil water potential  The total potential consists of the moisture potential (synonyms; pore water tension, soil water suction)  and the elevation potential, z.  Normally the groundwater surface is used as a reference level (z = 0)

5. Water movement Water movement is driven by total potential gradients

6. Theory of one-dimensional unsaturated water flow z q dz Using continuity (inflow – outflow = change in storage over time) we get where  is the volumetric water content and t is time. (1)

7. Theory of one-dimensional unsaturated water flow The Darcy law gives us that where H is the total potential. The total potential consists of the moisture potential (synonyms; pore water tension, soil water suction)  and the elevation potential, z. Thus Combining (1) and (3) we get This is called the Richard equation. Remember that  and K both are functions of . (2) (4) (3)

8. Theory of one-dimensional unsaturated water flow There is a soil specific relationship between soil water content and moisture potential and hydraulic conductivity. The soil moisture potential, or soil water suction, is sometimes given in pF = log(-pressure in cm H 2 O)

9. Theory of one-dimensional unsaturated water flow Several models exists for these relationships, today, the most commonly used were presented by van Genuchten (1980). (5) where n, m, and  are soil specific parameters,  r and  s are residual and saturated water content, respectively. The term K s is the saturated hydraulic conductivity. The parameter  r is usually assumed to be equal to the water content at a suitable low pressure head, e.g., -150 m H 2 O, i.e., the wilting point (pF 4.2). (6)

10. Infiltration  A special case of one-dimensional unsaturated water flow is infiltration  Infiltration is of interest in hydrology (rainfall-runoff relationship) and Agriculture (irrigation).  Infiltration parameters for different soil types are determined in infiltration experiments

11. Infiltration Two cases of wetting fronts, in the first, the infiltration rate i is lower than the saturated hydraulic conductivity Ks

12. Infiltration models  Green-Ampt where I is the cumulative infiltration, L f is the wetting front depth, ΔΨ is the change in potential between the soil surface and the wetting front (tabled values exists, see next slide) It can be assumed that I = L f (θ t - θ i )

13. Infiltration models Soil parameters (Green-Ampt)

14. Infiltration models Horton where f o = infiltration capacity in dry soil (mm/h) f c = = infiltration capacity in wet soil (mm/h) k = time factor (h -1 )

15. Solute transport Solute transport processes in unsaturated soil advection

16. Solute transport The dispersion coefficient includes effect of both molecular diffusion and mechanical dispersion. Dispersivity = Dispersion coefficient/velocity

17. Solute transport The solute transport in the saturated and unsaturated zones can be modeled using the advection-dispersion equation (ADE) where D is the dispersion coefficient, R is the retardation coefficient (sorption), and v z is the (vertical) water velocity. In the groundwater, the water velocity is calculated by the Darcy law, in the unsaturated zone the water velocity is calculated using Richards’s equation. Can also include source/sink terms, (chemical reactions, biodegredation)

18. Solute transport Analythical solution of the CDE for a pulse input and constant v and D where M is the applied mass and A is the cross sectional area.

19. Different concepts In the ADE concept described above, transport is governed by advection and dispersion. A different approach is the stochastic-advective concept. In this concept, solutes are transported in isolated stream tubes by advection only. The velocity distribution of the stream tubes can be described by a stochastic probability density function (pdf).

20. Different concepts Convective-dispersive Stochastic-convective Solute transport concepts

21. Stochastic convective approach where  l is the mean of the lognormal pdf and  l2 is the corresponding variance for the reference depth l. Assuming that the solute is spread instantaneously at z=0 and that the average solute transport velocity is constant, the C rt *(z,t) can be described by

22. Stochastic convective approach The  l parameter of the CLT model is related to the variability of the velocity distribution. This can be considered to be a soil specific parameter, however, it will also be slightly dependent on the magnitude of the soil water flux. The where  l can be used to calculate the average pore water velocity v using

23. ALT vs. ADE Both models calibrated to measurements at 0.235 m depth.

24. ALT vs. ADE Predicted BTCs at 0.6 m depth

25. Questions Discuss one of these questions in small groups and present the answer to the others

26. Spatial variability Soil properties may change dramatically over short distances. Water will not flow uniformly in the soil profile, but may flow in so called macropores, i.e., along roots, desiccation cracks or worm holes. This is called preferential flow. Macropore flow is often triggered at a specific water content and may lead to that large amounts of solutes are transported directly to the groundwater.

27. Macropores Macropores (desiccation cracks) in a clay soil in Egypt

28. Dye infiltration patterns

29. Water drop penetration test Water repellency can be determined with the water drop penetration test (WDPT) The procedure is as follows: 5 – 30 g sample of dry soil is put on a horizontal surface. The samples are leveled and a small 2-3 mm drop of water is added to the surface of the soil. On non-wetting soils the water will form a ball and stay on the surface for a time. Record the time for the drop to infiltrate. The test should be repeated at least three times and the average time should be recorded.

30. Water drop penetration test Time for water to infiltrate (s) Description 0-5Not water repellent 5-60Slightly water repellent 60-600Moderately water repellent 600-3600Severely water repellent >3600Extremely water repellent

31. How to account for variability  Dual porosity models (e.g., MACRO)  Stream tube models  Stochastic models  Fractal models

32. Fractal models  One model capable of generating fractal clusters i the DLA model. Diffusion limited aggregation conceptually describes the growth of crystals.  This model has been successfully applied to solute transport

33. DLA models

40. DLA cluster

41. DLA modeling

42. Literature and links  http://www.ars.usda.gov/Services/docs.htm?docid=1 5992 (models for download) http://www.ars.usda.gov/Services/docs.htm?docid=1 5992  http://wwwbrr.cr.usgs.gov/projects/GW_Unsat/Unsat _Zone_Book/index.html (online textbook) http://wwwbrr.cr.usgs.gov/projects/GW_Unsat/Unsat _Zone_Book/index.html  Persson and Berndtsson, 1999. Water application frequency effects on steady-state solute transport parameters J. Hydrol. 225:140-154  http://www.pc-progress.cz/Default.htm (hydrus 1D code) http://www.pc-progress.cz/Default.htm  http://bgf.mv.slu.se/ShowPage.cfm?OrgenhetSida_ID =5658 (MACRO model) http://bgf.mv.slu.se/ShowPage.cfm?OrgenhetSida_ID =5658