EP21C-0919
A Stochastic Model For Extracting Sediment Delivery Timescales From Sediment Budgets
Tuesday, 15 December 2015
Poster Hall (Moscone South)
James Eugene Pizzuto, Univ Delaware, Newark, DE, United States, Adam Benthem, U.S. Geological Survey, Reston, VA, United States, Diana L Karwan, University of Minnesota Twin Cities, Minneapolis, MN, United States, Jeremy J Keeler, University of Delaware, Newark, DE, United States and Katherine Skalak, USGS Headquarters, Reston, VA, United States
Abstract:
Watershed managers need to quantify sediment storage and delivery timescales to understand the time required for best management practices to improve downstream water quality. To address this need, we route sediment downstream using a random walk through a series of valley compartments spaced at 1 km intervals. The probability of storage within each compartment, q, is specified from a sediment budget and is defined as the ratio of the volume deposited to the annual sediment flux. Within each compartment, the probability of sediment moving directly downstream without being stored is p=1-q. If sediment is stored within a compartment, its “resting time” is specified by a stochastic exponential waiting time distribution with a mean of 10 years. After a particle’s waiting time is over, it moves downstream to the next compartment by fluvial transport. Over a distance of “n” compartments, a sediment particle may be stored from 0 to n times with the probability of each outcome (store or not store) specified by the binomial distribution. We assign q = 0.02, a stream velocity of 0.5 m/s, an event “intermittency “of 0.01, and assume a balanced sediment budget. Travel time probability density functions have a steep peak at the shortest times, representing rapid transport in the channel of the fraction of sediment that moves downstream without being stored. However, the probability of moving downstream “n” km without storage is pn (0.90 for 5 km, 0.36 for 50 km, 0.006 for 250 km), so travel times are increasingly dominated by storage with increasing distance. Median travel times for 5, 50, and 250 km are 0.03, 4.4, and 46.5 years. After a distance of approximately 2/q or 100 km (2/0.02/km), the median travel time is determined by storage timescales, and active fluvial transport is irrelevant. Our model extracts travel time statistics from sediment budgets, and can be cast as a differential equation and solved numerically for more complex systems.
