Synthetic Weather Simulation for Characterization of Uncertainty in
Extension of Stage-Frequency Curves in a System of Flood Control Dams
Abstract
Extreme floods which overwhelm the capacity of a system of flood control
dams may result in overtopping one or more of those structures.
Traditional US Army Corps of Engineers analysis of hydrologic hazards
isolates the study area to a single dam. However, in watersheds where
flood hazard is managed by several dams, the estimate for the annual
probability of overtopping a dam may be influenced by the operation of
one or more other dams in that system. Evaluation and prioritization of
modifications for dam safety in a portfolio of structures requires a
sound estimate of overtopping probability for every structure. In an
effort to properly characterize the hydrologic hazard for five dams in
the Trinity River Basin above Dallas, Texas, synthetic weather
generation coupled with hydrologic and reservoir models is applied to
extend the stage-frequency curve for each dam beyond the observed
record. The synthetic weather model is comprised of processes which
typify floods most likely to result in overtopping the study dams: 1)
continuous, local-scale precipitation and temperature sampling to
characterize antecedent hydrologic conditions, 2) intermittent
(inhomogenous Poisson), synoptic-scale precipitation sampling based on
regional precipitation-frequency analysis to generate hazardous floods,
3) k-nearest-neighbor resampling of precipitation and temperature
spatiotemporal patterns and 4) temporal disaggregation of daily
precipitation to hourly using correlated Brownian processes.
Interrelations between local-scale precipitation, synoptic-scale
precipitation and temperature are preserved using a Gaussian copula.
Natural variability in annual maximum reservoir stage is described using
a stratified sampling scheme used to disproportionately represent
extreme floods in a fixed sample of 1,000 events, resulting in fewer
model events required to span the probability space from 0.5 to 10-8
annual exceedance probability. Knowledge uncertainty in model components
is estimated using a parametric bootstrap, resulting in multiple
realizations of synthetic weather. Each weather realization of 1,000
events generated using varying parameters is routed using hydrologic and
reservoir models for the system which produce a posterior distribution
of annual overtopping probability for each structure.