Wavelet‐based time series bootstrap model for multidecadal streamflow simulation using climate indicators

Abstract

A model to generate stochastic streamflow projections conditioned on quasi‐oscillatory climate indices such as Pacific Decadal Oscillation (PDO) and Atlantic Multi‐decadal Oscillation (AMO) is presented. Recognizing that each climate index has underlying band‐limited components that contribute most of the energy of the signals, we first pursue a wavelet decomposition of the signals to identify and reconstruct these features from annually resolved historical data and proxy based paleoreconstructions of each climate index covering the period from 1650 to 2012. A K‐Nearest Neighbor block bootstrap approach is then developed to simulate the total signal of each of these climate index series while preserving its time‐frequency structure and marginal distributions. Finally, given the simulated climate signal time series, a K‐Nearest Neighbor bootstrap is used to simulate annual streamflow series conditional on the joint state space defined by the simulated climate index for each year. We demonstrate this method by applying it to simulation of streamflow at Lees Ferry gauge on the Colorado River using indices of two large scale climate forcings: Pacific Decadal Oscillation (PDO) and Atlantic Multi‐decadal Oscillation (AMO), which are known to modulate the Colorado River Basin (CRB) hydrology at multidecadal time scales. Skill in stochastic simulation of multidecadal projections of flow using this approach is demonstrated.

A Nonlinear Dynamical Systems‐Based Modeling Approach for Stochastic Simulation of Streamflow and Understanding Predictability

“…We tested the epochal nature of the projection skills on four selected 20‐year epochs mentioned above—high‐predictability epochs, 1731–1750 and 1820–1839, and low‐predictability epochs, 1681–1700 and 1841–1860. Blind projections were made for these 20‐year periods using the block bootstrap method (Erkyihun et al, ) and as described in the previous section. The PDFs of the flow simulations are shown as gray along with their median PDF and that of the historic flows for the four epochs in Figure .…”

“…The Atlantic Multidecadal Oscillation (AMO) and the Pacific Decadal Oscillation (PDO) have been shown to influence the low‐frequency variability of the Colorado River flow (e.g., Bracken et al, ; Erkyihun et al, ; Nowak et al, ). We use these two climate indices to understand the predictability of the Lees Ferry flow.…”

“…We used this wavelet to decompose the streamflow time series and for signal extraction. This approach for signal extraction has been applied to modeling and simulating the Colorado River flow series (Erkyihun et al, ; Nowak et al, ) and for rainfall and temperature in Florida (Kwon et al, ). We refer the reader to these papers and the review paper by Torrence and Compo () for details on wavelet analysis and signal extraction.…”

Technical note: Stochastic simulation of streamflow time series using phase randomization

“…An example of a new simulation procedure is the SMARTA model by Tsoukalas et al (2018), which employs Nataf's joint distribution model for the 25 simulation of stochastic time series, representing both short-and long-range dependence. In addition, simulation schemes based on wavelet decomposition, which avoid assumptions about the temporal dependence structure, have been proposed by Kwon et al (2007); Wang et al (2010) and Erkyihun et al (2016). Borgomeo et al (2015) have shown how simulated annealing can be used to generate synthetic streamflow time sequences that represent possible climate-induced changes in user-specified streamflow properties.…”

Analysing the influences of ENSO and PDO on water discharge from the Yangtze River into the sea

“…Therefore, changes in riverine discharge have been used as a type of climatic indicator to identify climate changes at different timescales (Restrepo et al, ). Two of the most important climatic oscillations are the El Niño Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO), which are usually used as predictors for precipitation and streamflow (Erkyihun, Rajagopalan, Zagona, Lall, & Nowak, ; Sankarasubramanian, Lall, & Espinueva, ; Switanek, Troch, & Castro, ). The ENSO, a coupled oceanic–atmospheric phenomenon occurring in the tropical Pacific Ocean, is the largest source of interannual climate variations in several parts of the globe (F. Liu et al, ; Shrestha & Kostaschuk, ; Ward, Beets, Bouwer, Aerts, & Renssen, ).…”