4. Transient Catchment Response to Changes in Rainfall Patterns
Many of the ideas laid out above for 1-dimensional profiles intuitively
transfer to understanding how signals related to changing rainfall
patterns propagate through a drainage network, albeit with some
additional considerations. It is important to remember that trunk
(transverse) rivers control base level for tributaries. Complex
responses, like those described above where both the magnitude and mode
of transient adjustment vary along the trunk profile in space and time,
necessarily result in varying boundary conditions for tributaries. In
addition, tributary responses to these variable base level signals are
modulated by the rainfall history experienced by a given tributary,
which is always different from the trunk. Finally, adjustments migrate
upstream at a finite rate, so there is a time lag between a change in
rainfall pattern and arrival of the associated base level signals from
the trunk adjustment to a given tributary. The duration of this lag, as
well as local rainfall conditions within a tributary catchment, are a
function of its position.
Following Riihimaki et al. (2007), we use a quasi-two-dimensional model
to explore catchment response. We abstract river basin topology to
comprise a single one-dimensional trunk profile and 51 regularly spaced
(1 km spacing) one-dimensional tributary profiles. Tributary outlets are
fixed to the elevation of the trunk profile at their confluence.
Discharge does not pass from tributaries to the trunk river as drainage
area along the trunk and each tributary follows Hack’s Law (equation 2)
independently. This means that there is not two-dimensional hydrological
coupling between trunk and tributary rivers through discharge, but
transient signals are communicated through variations in tributary base
level. This approach allows closely spaced tributaries with identical
characteristics to isolate the influence of spatial variations in
rainfall within the larger catchment that would not be possible to the
same degree with 2-dimensional modelling approaches.
Although our model setup is abstract, it allows us to compare expected
patterns of erosion and channel response along the trunk and within
small trunk-stream tributaries in a way that is portable to natural
river networks. Because drainage area increases along the modeled trunk
river following Hack’s Law, independent of the distribution of modeled
tributaries, at each point along the trunk river discharge accumulation
approximates that of a typical drainage basin aligned along the
orographic rainfall gradient. In this light, the trellis configuration
of tributaries we model is representative of a subset of small,
approximately trellised trunk-stream tributaries that typically exist
within more complex river network structures and are often targeted for
sampling of detrital sediment (e.g., Ouimet et al., 2009). These small
tributaries also do not contribute significantly to downstream increases
in drainage area (or discharge) of larger rivers into which they drain,
meaning discharge accumulation along large rivers is largely decoupled
from the hydrology of small tributaries. Therefore, the simplifications
we make to the hydrology are also generally consistent with conditions
created by targeting small tributaries situated along large rivers in a
trellis-like fashion.
In the following, we explore the transient response of modelled river
basins to four representative climate change scenarios: (1) a spatially
uniform decrease in rainfall, (2) a spatially uniform increase in
rainfall, (3) a shift from spatially uniform rainfall to a bottom-heavy
rainfall gradient, and (4) a shift from spatially uniform rainfall to a
top-heavy rainfall gradient. The initial condition for all models is
steady state with spatially uniform rainfall. Imposed changes in
rainfall evolve at a linear rate over the first 10 kyr of model time at
all points along each channel. Tributaries are modelled with spatially
uniform rainfall set by their position along the trunk profile, and
individual tributaries experience spatially uniform changes in rainfall
as rainfall gradients evolve. This simplification is consistent with the
notion that, due to their smaller areal extent and orientation,
tributaries set within mountain-belt scale orographic rainfall patterns
generally experience relatively uniform rainfall. As we show in section
5.1, more realistic scenarios, such as the intensification or relaxation
of an existing orographic rainfall gradient, produce analogous behavior
to these simple scenarios. The simplicity of the idealized scenarios
described here makes them especially effective for developing intuition
about response characteristics in general.