Theory and equations

Atmospheric inputs: partitioning, daily variation, interception, snow

Partitioning of the potential evapotranspiration

When only the potential evapotranspiration ET_p is known, it is divided into potential transpiration T_p and potential evaporation E_p with the leaf area index LAI Ritchie (1972):

SCF = 1 − exp(−k · LAI)

T_p = ET_p · SCF, E_p = ET_p (1 − SCF)

SCF is the soil cover fraction and k the extinction coefficient of the radiation in the canopy (HYDRUS default 0.463). The same partitioning is used with meteorological data.

Daily variation of evaporation and transpiration

Daily values of evaporation and transpiration can be distributed over the day with the functions of Fayer (2000), as in HYDRUS: during the night (t < 0.264 d and t > 0.736 d) the rate is 24 % of the daily mean, during the day it follows a sine wave:

T_p(t) = 2.75 T_p sin(2π t − π/2) for 0.264 d ≤ t ≤ 0.736 d; T_p(t) = 0.24 T_p otherwise

with t the time of the day in days; the integral over the day equals the daily rate. The same applies to the evaporation.

Canopy interception

Part of the precipitation is intercepted by the leaves and evaporates. The interception follows von Hoyningen-Hüne (1983) and Braden (1985):

I = a · LAI [ 1 − 1 / (1 + SCF · P / (a · LAI)) ]

with the precipitation P, the interception constant a [L] (the interception capacity is a·LAI) and the soil cover fraction SCF. The intercepted water evaporates first and reduces the potential transpiration; the rest reaches the soil.

Snow

With snow accumulation, precipitation falls as snow at air temperatures below −2 °C, as rain above +2 °C, and as a mixture in between (the snow fraction decreases linearly from 1 to 0 between −2 and +2 °C). Once a snow layer exists, all precipitation is added to it. The snow melts at air temperatures above 0 °C with a degree-day factor m_f [L/T/°C]:

M = m_f · T_a for T_a > 0 °C

(a temperature-index approach, see Hock (2003)); the HYDRUS default is 0.43 cm/d/°C. Evaporation is taken from the snow layer first. Solutes in the precipitation are stored in the snow and released with the melt water.

Sinusoidal precipitation

With sinusoidal precipitation, the precipitation of each record follows a sine wave over the record's interval instead of a constant rate, with the same total.

Literature cited in this topic

Braden, H. (1985). Ein Energiehaushalts- und Verdunstungsmodell für Wasser- und Stoffhaushaltsuntersuchungen landwirtschaftlich genutzter Einzugsgebiete. Mitteilungen der Deutschen Bodenkundlichen Gesellschaft 42: 294–299.
Fayer, M. J. (2000). UNSAT-H Version 3.0: Unsaturated Soil Water and Heat Flow Model. Theory, User Manual, and Examples. Report PNNL-13249, Pacific Northwest National Laboratory, Richland, WA.
Hock, R. (2003). Temperature index melt modelling in mountain areas. Journal of Hydrology 282(1–4): 104–115. doi:10.1016/S0022-1694(03)00257-9
Ritchie, J. T. (1972). Model for predicting evaporation from a row crop with incomplete cover. Water Resources Research 8(5): 1204–1213. doi:10.1029/WR008i005p01204
von Hoyningen-Hüne, J. (1983). Die Interception des Niederschlags in landwirtschaftlichen Beständen. Schriftenreihe des DVWK 57: 1–53.

All sources: References.