Particle Tracking Module in 1D
The Particle Tracking algorithm from Šimůnek [1991] was implemented first into the Particle Tracking module of HYDRUS-1D [Zhou et al., 2021], and then in Version 5 of HYDRUS. This module tracks the position of hypothetical particles, which are either initially defined in the soil profile, or are released at its boundaries. The results of this module can be used to calculate soil water travel times and water age for different locations in the soil profile. This is a one-dimensional add-on module.
The algorithm itself proceeds as follows: From the known position of the particles at the beginning of the time interval, the pre-solved development of the moisture profile and the actual values of infiltration, evaporation and transpiration, the new position of the first monitored particle is calculated first. The new positions of all other particles are then calculated based on the mass balance calculations. On the surface and in the bottom of the soil profile, new particles may be created or may leave the soil profile, depending on the current development of the moisture profile.
By calculating the trajectories of flowing particles, the movement of inert substances not subject to dispersion can be modeled. The average concentration in the individual regions between the two following particles can be easily determined from the initial concentration (defined for the individual regions) and from a decrease of the water content in these layers due to the extraction term S.
The initial position of particles is defined based on mass balance calculations (by water storage). The release of new particles at the boundary can be defined chronologically (at specified times) or meteorologically (rainfall events or depths). The particle tracking module requires two input parameters: wStand and wPrec. The wStand parameter represents the water storage, which separates neighboring particles in the soil profile at the beginning of the simulation. Therefore, the particles are not geometrically evenly distributed when the soil profile's initial water content is not uniform. The wPrec parameter is the amount of water that passes through the soil surface before a new particle is released. This means that particles are released at the soil surface only under wet conditions. When wPrec is set to be negative, a new particle is released with each precipitation event (i.e., when vTop becomes negative). Under dry conditions, the surface flux is directed out of the soil profile, and thus, new particles will not be released.
Details about the Particle Tracking module and its algorithm are given in the Hydrus technical manual (Šimůnek et al., 2022).
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An example of the graphical display of the Particle Tracking module results.
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References:
- Šimůnek, J., Numerical simulation of the transport processes in soil (in Czech, English abstract), Vodohosp. Čas., 39(1), 20 34, 1991.
- Zhou, T., J. Šimůnek, and I. Braud, Adapting HYDRUS-1D to simulate the transport of soil water isotopes with evaporation fractionation, Environmental Modeling & Software, 143, 105118, 18 p., doi: 10.1016/j.envsoft.2021.105118, 2021.
- Šimůnek, J., M. Šejna, G. Brunetti, and M. Th. van Genuchten, The HYDRUS Software Package for Simulating the One-, Two, and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Technical Manual I, Hydrus 1D, Version 5.0, PC Progress, Prague, Czech Republic, 334p., 2022. (PDF 3.9MB)