Solving Nonlinear Partial Differential Equations with PDE toolbox

I have the following PDE which I have tried to solve via Laplace Transform but could not. Can anybody help me solve or give me an insight into how this could be done using PDE toolbox.

The PDE is a Richard's equation for describing water movement in saturated soils

 ∂θ/∂t=∂/∂z (D(θ)∂θ/∂z)-∂K/∂z

 where D = soil diffusivity
      θ = soil moisture content
      z = elevation above a vertical datum
      t = time
      K = soil hydraulic conductivity

If the following are the boundary conditions, solve the PDE
1. Initial BCs
θ(z,0) = θi = 0.01, for z>=0,t=0
2. Upper BCs
θ(0,t) = (θs-0.001), for z=0, t>=0
3. Lower BCs
θ(z=L,t) = θs-0.001
where L is the depth of the ground water table and θs = 0.287,K = 28cm/h, D(θ) = 0.25.