dc.description.abstract | Introduction: Green roofs are one of the most common multifunctional types of Nature Based Systems
(NBS) serving primarily for mitigation of the urban runoff (Stovin et al. 2012, Versini et al. 2020). Since
relying on the soil water interaction, green roofs also have a significant impact on reduction of the local
temperature, which has not been so deterministically investigated in the past. To simulate the change of
substrate temperature and water content accurately and continuously, it is necessary to couple models
for water and heat transport through (un)saturated porous media which has been done in many studies
(Campbell 1985, Bittelli et al. 2008). The core of these models are the partial differential equations that
are strongly nonlinear, especially Richards (1931) equation describing the unsaturated water flow, and
hence their numerical solving is still challenging from the perspective of the computational time, numerical
stability, and accuracy. Linearization of Richards equation has first been proposed by Ross (2003) who
developed a stable explicit numerical scheme for solving it by using Taylor series and Kirchhoff potential
to express unsaturated water fluxes, while similar approach has not been applied yet to Heat equation.
The main deficiency of this approach as far as Richards equation is concerned is the necessity to use finer
time discretization to avoid greater water balance errors, as well as the complex and often inaccurate
transition from the unsaturated to saturated state and vice versa.
To develop a robust and accurate numerical tool for consecutive solving of Richards and Heat equations,
several improvements compared to the existing approaches have been made. Firstly, Taylor series has also
been applied on soil heat fluxes creating rather simple and mathematically elegant explicit numerical
scheme for solving Heat equation. Secondly, unlike in Ross’s method where only the first term of Taylor
series is used, here are used the first and the second term to create more accurate approximation of water
fluxes. Also, unlike in Ross (2003), here Richards equation is solved strictly with respect to Kirchhoff
potential to smooth the transition between unsaturated and saturated water flow. Finally, the
evapotranspiration rate at the top surface is not predefined but determined from the latent heat flux
computed through the iterative solving of Richards and Heat equations. Here are presented preliminary
simulation results of the proposed coupled model obtained by using approximately six days long timeseries
of the measured meteorological data taken from Bittelli et al. (2008). | sr |