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

2. Infiltration Equations h(  ),  K( 

3. Infiltration Equations h(  ),  K( 

4. Infiltration Equations h(  ),  K( 

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

6. Infiltration Equations In three dimensions, using K  )  defining the specific moisture capacity as C(  ) = d  /d 

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 S e = (  -  r )/(  s -  r )  r is the residual volumetric moisture content l,  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  at  = 330 cm (33 kPa); and  Sand, silt and clay percentages, bulk density and the value of  at  = 330 and 15,000 cm (33 and 1500 kPa).

13. Infiltration Equations

14. 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 < t p, how are f and F computed?

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

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