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.