Early-warning signals in ecogeomorphology: the example of a hillslope system
Derek Karssenberg, Faculty of Geosciences, Utrecht University, the Netherlands, d.karssenberg@geo.uu.nl
Introduction
Complex dynamical systems may have critical thresholds at which the system shifts abruptly from one state to another. It is notably difficult to predict the timing of a transition, because the state
variables of the system show little change before the threshold is reached. A possible solution is the use of spatio-temporal patterns in state variables as leading indicators of a transition. It is becom- ing clear that critically slowing down of a system causes spatio-
temporal autocorrelation and variance to increase before the tran- sition (Scheffer et al, 2009). In this research we show that these
early-warning signals also exist in geomorphological systems.
The system
We consider the evolution over hundreds of years of a modelled hillslope system, with spatially distributed processes. The figure above shows key positive (+) and negative effects (-). Biomass is linearly increased (below). At a threshold of appr. 15000 weeks, a shift towards lower regolith thickness occurs.
Regolith thickness remains relatively constant up to a biomass
threshold below which runoff initiates soil wash and rill, gully for- mation (above). Due to reduced regolith thickness, infiltration ca- pacity reduces increasing runoff and soil wash, resulting in a posi- tive feedback.
Main finding
Increase in variance and temporal correlation length of regolith thickness and runoff are leading indicators for soil degradation and can thus be used for forecasting.
Early-warning signals in regolith thickness
Rate of recovery is smaller close to the shift (see above). As a result, under a constant perturbation (added random noise), the variance of system variables increases towards the shift.
As expected from theory (top figure), variance in regolith thickness (above, blue line) increases well ahead of the shift. Also, the ratio
between short and long range variation over time (above, red line) decreases, indicating critically slowing down of the system.
Early-warning signals in runoff
A similar increase in variance is found for runoff, both in temporal variance of the total runoff from the plot (below, left) and in tem- poral variance in runoff at grid cells (below, right). The latter is
partly caused by high dynamics in the rill system when wash ero- sion starts.
References
Scheffer et al., 2009. Early warning signals for critical transitions. Nature 461 (7260): 53-59.
biomass
creep regolith
thickness
wash
rills,
gullies
transition
elevation (m)
regolith thickness (m)
Infiltration capacity (m)
flow directionflow directionflow direction
time (years)
Flowdirections (m)
1000 750
500 0 250
regolith thickness, rate of increase (m/y) 0 + -
regolith thickness 2 m
perturbation
rates of recovery
regolith thickness, rate of increase (m/y) 0 + -
regolith thickness 2 m
perturbation rates of recovery
Far from shift Close to shift
stable
equilibirum
stable
equilibirum
