  From infiltration of water into the soil during rainstorms to seasonal plant
growth and death, the ecohydrological processes that are thought to be relevant
to the formation of banded vegetation patterns in drylands occur across
multiple timescales. We propose a new fast-slow switching model in order to
capture these processes on appropriate timescales within a conceptual modeling
framework based on reaction-advection-diffusion equations. The fast system
captures hydrological processes that occur on minute to hour timescales during
and shortly after major rainstorms, assuming a fixed vegetation distribution.
These include key feedbacks between vegetation biomass and downhill surface
water transport, as well as between biomass and infiltration rate. The slow
system acts between rain events, on a timescale of days to months, and evolves
vegetation and soil moisture. Modeling processes at the appropriate timescales
allows parameter values to be set by the actual processes they capture. This
reduces the number of parameters that are chosen expressly to fit pattern
characteristics, or to artificially slow down fast processes by the orders of
magnitude required to align their timescales with the biomass dynamics. We
explore the fast-slow switching model through numerical simulation on a
one-dimensional hillslope, and find agreement with certain observations about
the pattern formation phenomenon, including band spacing and upslope
colonization rates. We also find that the predicted soil moisture dynamics are
consistent with time series data that has been collected at a banded vegetation
site. This fast-slow model framework introduces a tool for investigating the
possible impact of changes to frequency and intensity of rain events in dryland
ecosystems.
