Percolation / Capillary rise

Vertical soil water flux \(q_{v}\) (mm \(\Delta t^{-1}\)):

\[\begin{split}q_{v}=\left\{\begin{array}{lr} \frac{(z_{sat} / h_a)^{-n}-(h / h_a)^{-n}}{1+(h / h_a)^{-n_{+}}(n-1)(z_{sat} / h_a)^{-n}} & z_{gw} \leq 10 \\ \frac{(z_{sat} / h_a)^{-n}}{1+(n-1)(z_{sat} / h_a)^{-n}} & z_{gw} > 10 \end{array}\right.\end{split}\]

where \(z_{gw}\) is the depth of groundwater table (m). For \(q_v\) \(<\) 0 soil water moves in downward direction and for with \(q_v\) \(>\) 0 soil water moves in upward direction.

Percolation

Percolation \(q_{perc}\) (mm \(\Delta t^{-1}\)):

\[\begin{split}q_{perc}=\begin{cases} k_s & z_{sat} > 0\\ q_v \cdot (-1) & q_v < 0 \& z_{sat} = 0 \\ 0 & q_v \geq 0 \& z_{sat} = 0 \end{cases}\end{split}\]

where \(z_{sat}\) is saturation water level at the soil-bedrock interface (mm). Percolation might be limited by permeability of bedrock (\(k_f\), mm \(\Delta t^{-1}\)), if \(q_{perc}\) exceeds \(k_f\).

Saturation water level \(z_{sat}\) (mm) rises while saturation from top is connected to the bedrock interface:

\[\begin{split}z_{sat}=\left\{\begin{array}{lr} \frac{S_{lp-ss}}{\theta_{ac}} & \frac{S_{lp-ss}}{\theta_{ac}} \geq z_{nomp}\\ z_{sat} & \frac{S_{lp-ss}}{\theta_{ac}} < z_{nomp} \end{array}\right.\end{split}\]

with thickness without macropores \(z_{nomp}\) (mm):

\[\begin{split}z_{nomp}=\left\{\begin{array}{lr} 0 & z_{soil} - l_{mpv} - z_{sat} < 0\\ z_{soil} - l_{mpv} - z_{sat} & z_{soil} - l_{mpv} - z_{sat} > 0 \end{array}\right.\end{split}\]

where \(S_{lp-ss}\) is soil water content in large pores of subsoil (mm). \(z_{sat}\) is reduced by percolation \(q_{perc}\).

Capillary rise

Capillary rise \(q_{cpr}\) (mm \(\Delta t^{-1}\)):

\[\begin{split}q_{cpr}=\left\{\begin{array}{lr} 0 & q_v < 0 \\ q_v & q_v \geq 0 \& z_{sat} = 0 \end{array}\right.\end{split}\]