Infiltration Equations

1. Infiltration Equations Fundamental Mass Balance Equation: Darcy’s Law (z direction): Where

2. Infiltration Equations h(q), y(q), K(q)

3. Infiltration Equations h(q), y(q), K(q)

4. Infiltration Equations h(q), y(q), K(q)

5. Infiltration Equations Vertical Darcy’s Law is then Soil water diffusivity is defined combining

6. Infiltration Equations In three dimensions, using K(y): defining the specific moisture capacity as C(y) = dq/dy

7. Infiltration Equations For 1-D vertical, saturated flow:

8. Infiltration Equations Boundary conditions for infiltration at ground surface:

9. Infiltration Equations Lower boundary conditions for infiltration

10. Infiltration Equations Mixed form of Richards Equation

11. Infiltration Equations Parameters (van Genuchten, 1980): where m = 1-1/n for n > 1 Se = (q - qr)/(qs - qr) qr is the residual volumetric moisture content l, a and n are van Genuchten model parameters

12. Infiltration Equations Parameters: Rosetta by Marcel G. Schaap (1999) • Soil textural classes; • Sand, silt and clay percentages; • Sand, silt and clay percentages and bulk density; • Sand, silt and clay percentages, bulk density and the value of q at y = 330 cm (33 kPa); and • Sand, silt and clay percentages, bulk density and the value of q at y = 330 and 15,000 cm (33 and 1500 kPa).

13. Infiltration Equations

14. Infiltration Equations Green-Ampt from conceptualization: Darcy’s Law: combining:

15. Infiltration Equations since f = dF/dt how is this solved?

16. Infiltration Equations Green-Ampt ponding time for t < tp, how are f and F computed?

17. Infiltration Equations Green-Ampt with a hyetograph • discrete, steady pulses of rainfall of Dt duration is used to describe i(t) • F(t + Dt) = F(t) + i(t)Dt while f < i • when the surface is ponded throughout the time increment:

18. Infiltration Equations Green-Ampt with hyetograph continued... • If f(t + Dt) < i(t), then ponding occurs during the time interval and using f(t) = i(t) and F(t) = Fp : • then tp = t + Dt'where

19. after Chow et al., 1988

20. Infiltration Equations Green-Ampt parameters, after Chow et al., 1988

21. Infiltration Equations Kostiakov

22. Infiltration Equations Horton

23. Infiltration Equations Holtan

24. Infiltration Equations Phillip

25. Infiltration Equations Smith-Parlange