By K. Nowak, B. Rajagopalan and E. Zagona (2011), Wavelet Auto-Regressive Method (WARM) for multi-site streamflow simulation of data with non-stationary spectra, Journal of Hydrology, 410 (1-2) 1-12.
Abstract: Traditional stochastic simulation methods that are crafted to capture measures such as mean, variance and skew fail to reproduce significant spectral properties of the observed data. A growing body of literature indicates that many geo-physical data, especially streamflow, exhibit quasi-periodic and non-stationary variability driven by large scale climate features. Thus, methods which accurately model this behavior, in particular, the time evolution of variability, frequency of wet/dry epochs, etc. are crucial for risk assessment and management of water resources. In this paper, a Wavelet based Auto Regression Modeling (WARM) framework is proposed for data with significant non-stationary spectral features. This approach has four broad steps – (i) the wavelet transform of a time series is reconstructed as several periodic components based on dominant variability frequencies, (ii) scale averaged wavelet power (SAWP) is computed for each band to capture the time varying power and the components are scaled by this, (iii) Auto Regressive (AR) models fit to the scaled components and, (iv) simulations are performed from the AR models, rescaled and combined to obtain simulations of the original time series. Step (ii) is a new and unique departure from the WARM proposed by Kwon et al. (2007). We demonstrate this approach on annual streamflow at the Lee’s Ferry gauge on the Colorado River. Furthermore, this is coupled with a spatial disaggregation method to generate streamflow ensembles at multiple locations upstream. We also show that this combination captures the spectral properties at several locations in a parsimonious manner.