Uncertainties associated with the use of erosional cave scallop lengths to calculate stream discharges

Abstract

Scallops are extremely valuable indicators of past water flows in caves because they often record events that cannot be safely witnessed nor measured. Qualitatively, the inverse relationship between their lengths and formative water velocities is useful for determining how flow changes along a cave passage, but they are most valuable because they can be used to directly estimate actual water velocities and discharges. We explore the effects of sample size, measurement choices, and other methods commonly applied to the use of cave scallops in estimating cave stream velocities and discharges. We measured 100 scallops on a cave wall and find them to be log-normally distributed. We used Monte Carlo simulations to sub-sample the 100 scallops for sample sizes of 10 to 30. As expected, smaller sample sizes yield widely varying means with precision increasing slowly with sample size. A sample size of 30 results in greater than 50% of simulated means falling within one standard deviation of the mean for all 100 scallops. This is also true of sample sizes as small as 20, so we recommend a minimum of 20 to 30 scallop measurements in the field. The formulas we use to estimate water velocities and discharges explicitly use the Sauter mean of scallop lengths, but some authors use the arithmetic mean. We simulated the use of both the Sauter and arithmetic means and find that the latter yields substantially larger velocities and discharges. We recommend use of the Sauter mean because that is consistent with the original formulations and the arithmetic mean may cause significant overestimation of velocity and discharge.

Keywords

• cave
• scallops
• karst hydrology
• stream
• water