Thresholds, Memory, and a Physical Mechanism for the Sadler Effect in Geomorphic Systems

The Sadler effect is defined as a systematic decrease in estimated rates with increasing measurement interval and is widely observed in stratigraphic and geomorphic systems. In natural systems, statistics themselves do not cause phenomena; rather, physical processes operate across landscapes, generating responses that can be characterized by statistics. However, it is statistical phenomena (a heavy-tailed distribution via random walks or stochastic memory formulations) that are frequently invoked to explain the Sadler effect, which provides no insight into the physical processes that generate a heavy-tailed distribution. Here, we explore how the Sadler effect might arise in a system where thresholds must be exceeded to produce an erosive event. We argue that apparent heavy-tailed hiatus distributions can emerge naturally when considering physically reasonable geomorphic dynamics. Using a simple stream power-based stochastic threshold-incision framework, we show that systems governed by static thresholds and stationary forcing produce exponential hiatus distributions. In such circumstances, a Sadler-like effect is observed, but only over a finite time span set by the characteristic hiatus return time, after which rates remain constant. In contrast, when thresholds evolve through time—either via event-driven perturbations with recovery (system memory) or through temporal changes in the forcing distribution (e.g., climate variability)—the system samples a sequence of exponential hiatus distributions with distinct characteristic timescales. The superposition of these exponential hiatus distributions produces an apparent heavy tail and sustains Sadler-like scaling across multiple orders of magnitude in time. This framework provides a physically interpretable alternative to purely statistical explanations of the Sadler effect and highlights the central role of variable threshold magnitude, recovery timescales, and climate variability in controlling signal preservation in geomorphic systems. Importantly, these concepts likely extend to interpreting the Sadler effect in the stratigraphic record. The results suggest that apparent long-memory behavior in erosion and deposition records may reflect evolving thresholds and forcing regimes, rather than intrinsic heavy-tailed dynamics.