Infiltration Equations
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Infiltration Equations Fundamental Mass Balance Equation: 0 z q y q x q t z y x Darcy’s Law (z direction): z h K q z z Where z h
description
Infiltration Equations. Fundamental Mass Balance Equation:. Darcy’s Law (z direction):. Where. Infiltration Equations. h ( q ), y ( q ), K ( q ). Infiltration Equations. h ( q ), y ( q ), K ( q ). Infiltration Equations. h ( q ), y ( q ), K ( q ). Infiltration Equations. - PowerPoint PPT Presentation
Transcript of Infiltration Equations
Infiltration EquationsFundamental Mass Balance Equation:
0
z
q
y
q
x
q
tzyx
Darcy’s Law (z direction):
z
hKq zz
Wherezh
Infiltration Equations
h(), K(
Infiltration Equations
h(), K(
Infiltration Equations
h(), K(
Infiltration Equations
)()(
)( zzz Kz
Kq
Vertical Darcy’s Law is then
Soil water diffusivity is defined
d
dKD
)()()(
combining
)()( zzz Kz
Dq
Infiltration EquationsIn three dimensions, using K)
z
hK
zy
hK
yx
hK
xt)()()(
defining the specific moisture capacity as C() = d/d
1)()()()(z
Kzy
Kyx
Kxt
C
Infiltration EquationsFor 1-D vertical, saturated flow:
01
zK
z s
Infiltration Equations
Boundary conditions for infiltration at ground surface:
ps ttttz
Kz
hKr
0),0(),0(1)()(
ps tttht ),0(),0( 0
Infiltration Equations
Lower boundary conditions for infiltration
00),( ttL
0)( tKqz
Infiltration Equations
Mixed form of Richards Equation
1)(z
Kzt
Infiltration EquationsParameters (van Genuchten, 1980):
0
01)(
s
mn
rsr
2/111)(mm
eles SSKK
where m = 1-1/n for n > 1Se = ( - r)/(s - r)r is the residual volumetric moisture content l, and n are van Genuchten model parameters
Infiltration EquationsParameters: 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); andSand, silt and clay percentages, bulk density and the value of at = 330 and 15,000 cm (33 and 1500 kPa).
Infiltration Equations
Infiltration Equations
LLF i )(
Green-Ampt
L
LK
L
LhKf
)(0
F
FKf
from conceptualization:
Darcy’s Law:
combining:
Infiltration Equations
KttF
tF
)(1ln)(
since f = dF/dt
how is this solved?
Infiltration EquationsGreen-Ampt ponding time
)( Kii
Kt p
for t < tp, how are f and F computed?
Infiltration EquationsGreen-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:
tKtF
ttFtFttF
)(
)(ln)()(
Infiltration EquationsGreen-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) = Fp :
Kti
KFp
)(
• then tp = t + t' where
)(
)('
ti
tFFt p
after Chow et al., 1988
Infiltration EquationsGreen-Ampt parameters, after Chow et al., 1988
Infiltration Equations
Kostiakov
tKf k
Infiltration Equations
Horton
tcoc effff )(
Infiltration Equations
Holtan
ca fSAGIf 4.1
Infiltration Equations
Phillip
sKStf 5.05.0
Infiltration Equations
Smith-Parlange
1)/exp(
1BF
Kf s
