calculate_vf: Calculate the theoretical drainage according to the viscous...

In ChrisBogner/ViscousFlow: Analysis of tracer experiments with the viscous flow approach by Peter Germann

Description

According to the viscous flow approach (e.g. Germann, 2018), the theoretical drainage can be calculated as follows:

\loadmathjax \mjdeqn

q(Z,t) = 0 \quad \mathrmif \quad T_B \leq t \leq T_W

\mjdeqn

q(Z,t) = q_S \quad \mathrmif \quad T_W \leq t \leq T_D

\mjdeqn

q(Z,t) = q_S \cdot \left( \fracT_D - T_Et - T_E \right) ^\frac32 \quad \mathrmif \quad T_D \leq t \leq \infty

where \mjeqnq(Z,t) is the drainage flow in a depth \mjeqnZ and time \mjeqnt, \mjeqnq_s is the flux density applied at the top of the soil column (i.e. irrigation intensity), \mjeqnT_B, T_E, T_W, T_D are the beginning and the end of irrigation, and the arrival times of the wetting and drainage fronts, respectively.

Usage

calculate_vf(drainage_data, qS, TW, TD, TE, exponent = 3/2)

Arguments

drainage_data	tibble or data.frame. Drainage data from a column experiment. The first column must contain the time, the second the drainage data.
qS	numeric. The volume flux density applied to the top of the soil column (i.e. the irrigation rate or the stationary flow rate, which should be equal at steady state).
TW	numeric. Arrival time of the wetting front.
TD	numeric. Arrival time of the drainage front
TE	numeric. Time of the end of the irrigation.
exponent	numeric. The exponent in the viscous flow calculation. Default is 2/3.

Value

tibble. The original drainage data with a new column "viscous_flow" with the calculated viscous flow.

References

\insertRef

Germann2018ViscousFlow \insertRefBogner2019ViscousFlow

Examples

data(drainage)
flow <- calculate_vf(drainage_data = drainage, qS = 10.1, TE = 64410,
TD = 64404 +100, TW = 1000)

ChrisBogner/ViscousFlow documentation built on June 13, 2021, 7:47 a.m.