Hydrologie II, part II

θ = lim(V_w/ΔV)

Θ_sat is the water content at full saturation and is almost equal to Porosity n

Θ_r is the water content that cannot be extracted through mech forces

Ψ(Θ) or opposite

Θ_sat |------_\

        |        \

        |          \

Θr    |             \_{-----------------}

        |_{-------------------------------->} -Ψ

soil water suction, soil water tension

kPa, MPa, m, mm

it is the potential energy of water per unit volume, relative to pure water in reference conditions.

it quantifies the tendency of water to move due to osmosis, gravity, mach pressure or matric effects such as surface tension.

only the matric potential (capillarity)

≈0

≈-infitity

S=θ/θ_sat

S_e=(θ-θ_r)/(θ_sat-θ_r) =[0...1]

gravitational: 0...-33kPa

Capillary: -33kPa...-3MPa

Hygroscopic, unavailable: <-3MPa

free aspiration, possible because Ψ is higher than air pressure

wilting point of plants, plants are not able to extract water below that potential

Field capacity. point where gravity processes starts to become less important.

gravity <-> capillarity

.

Ψ= Ψ_b*(S_e)^-1/lambda0

or

Ψ=1/alpha*[(S_e)^-1/m-1]^1/n

parameters are soil type dependent

time domain reflectometry

vol=(K_sat*A(h₃-h₄)*t)/L

where h=z+Ψ, Ψ≈0

saturated

homogenous

isothermal

isotropic

steady state

q= -K_sat*dh/dz [m/s or mm/h]

isotropic: K_H=K_v

homogenous: dK/dz=0

when in parallel: simple mean: K=(K1*z1+K2*z2)/(z1+z2)

when in serie: harmonic mean: K=(z1+z2)/(z1/K1+z2/K2)

depends on domain seize due to:

macropores, preferential paths, spatial var of properties

follows soil water content. decreases strongly for high water contents, because large pores empty first

K=K_sat(S_e)^{(2/lambda0+3)}

or

K=K_sat(S_e)^0.5[1-(1-S_e^1/m)^m]²

parameters are soil dependent

soil: 0.1-500mm/h

gravel: 1m/s

rock: 10^-8...10^-9m/s

D(θ)=K(θ)*dψ/dθ

conservation of mass (continuity eq) + conservation of momentum (darcy) = richards eq

-> governs for unsaturated flows! difficult to solve

dθ/dt = ∇(K(θ)+∇h)

for isotropic, homogenous media in the vertical direction:

dθ/dt = d/dz"K(θ)*(dψ/dz+1)

for 2 different K's, 2 richards eq are needed

exchange between K's cannot be neglected

-> difficult to parameterize and to resolve numerically

water into the river after subtracting the losses

precipitation minus inflitration and other losses

flow occuring above the surface in slopes and plains

horton runoff

v.a. in semi-arid regions, where soils are crusted/compacted (roads, rocks, farm). very rare in vegetated areas

if P>f_c -> R_H = P-f_c

if P<f_c -> R_H = 0

Dunne runoff

v.a. in humide climate

soil is saturated from re-emerging subsurface flow

mostly in wetlands or riparian areas