Precipitation as Meteoric Sediment and Scaling Laws of Bedrock Incision: Assessing the Sadler Effect

Although it has been several decades since Sadler (1981) first showed that sediment accumulation rates exhibit a negative power law dependence on measurement interval (i.e., the Sadler effect), only recently has a manifestation of covariance in rate with duration become more widely appreciated in degradational settings. Because our collective understanding of rates of deposition and erosion are widely utilized to constrain the importance of active tectonism and climate forcing in shaping the surface of our planet, cognizance of the dependence of rate on duration of observation is of critical importance. Relations between elevation change (deposition, erosion) and rate scaling laws have often been examined by stochastic random walk simulations, but this approach is generally confounded by insufficient data on amounts of land-surface change, on durations of land-surface change, and on hiatal durations separating time intervals of change. Deposition or erosion rates measured over short intervals, such as during floods, are usually too large to be sustained over geologic timescales, and this difference implies that hiatuses of consequential duration must separate intervals of incision and/or deposition. While it has been argued that hiatuses may have a truncated power law distribution (reflecting the largely stochastic nature of processes in time and space), we (collectively) lack adequate data on magnitudes and temporal distributions of natural depositional and/or erosional events in many geologic systems to fully understand their relations. Abundantly available data on meteoric precipitation (rainfall), comprising precipitation amounts, precipitation durations, and drought durations at different timescales and from different climatic settings, are an attractive analogue for longer-term processes of deposition and erosion that can only be inferred from incomplete geologic data. Here, manifestations and reasons for the Sadler effect are examined in a region of relatively discontinuous meteoric sedimentation as recorded by 2,311 precipitation (and intervening hiatus) events over the past 63 yr in Las Vegas, Nevada. Collectively, these data suggest several conclusions. (1) Frequencies of rainfall magnitude, rainfall duration, and intervening hiatuses are closely approximated by exponential amount and duration frequency distributions; quantities and lengths of precipitation are more or less randomly partitioned in length-time space. (2) The negative power law dependence of precipitation rate on measurement interval is largely unrelated to the progressive inclusion or exclusion of longer or shorter intervals of precipitation or drought over longer or shorter durations of consideration. (3) Dependence of precipitation rate on total (rainfall plus hiatal) duration, manifested as positive covariance in total duration and amount, only becomes apparent among the Las Vegas data when durations span more than several years. Over shorter time spans, the stochastic nature of synoptic weather systems imparts steep negative power law covariance to duration versus rate relations; over longer durations, the influence of Las Vegas climate becomes increasingly apparent as variation in precipitation amounts is increasingly explained by total duration. (4) Actuality of the Sadler effect in Las Vegas rainfall data, manifested as the negative dependence of log-scaled rate on measurement duration, primarily reflects the degree of correspondence between amount and duration. These tenets are further examined in light of recently published data on cumulative durations and rates of bedrock incision. These degradational systems largely exhibit negative power law rate duration slopes, a trend previously interpreted as reflecting some sort of dependence of incision rate on measurement interval. However, when viewed in a context of precipitation as meteoric sediment, these erosional data are more readily understood as largely reflecting the degree of correlation between per-event durations and amounts of incision among the various river systems under consideration.