Modeling the Dynamics of Long-Term Variability of Hydroclimatic Processes

Abstract

The stochastic analysis, modeling, and simulation of climatic and hydrologic processes such as precipitation, streamflow, and sea surface temperature have usually been based on assumed stationarity or randomness of the process under consideration. However, empirical evidence of many hydroclimatic data shows temporal variability involving trends, oscillatory behavior, and sudden shifts. While many studies have been made for detecting and testing the statistical significance of these special characteristics, the probabilistic framework for modeling the temporal dynamics of such processes appears to be lacking. In this paper a family of stochastic models that can be used to capture the dynamics of abrupt shifts in hydroclimatic time series is proposed. The applicability of such ''shifting mean models'' are illustrated by using time series data of annual Pacific decadal oscillation (PDO) indices and annual streamflows of the Niger River.

Nonlinearities, Feedbacks and Critical Thresholds within the Earth's Climate System

“…As depicted in Figure 5, the Niger River series is characterized by a slow decaying autocorrelation function, reflecting a long 'memory', yet there are occasional large rapid shifts in the annual flows. Sveinsson et al (2003) show that it is possible to simulate statistically similar time series patterns of streamflows that may occur in the future, and analyze the vulnerability of existing and projected water supply systems in this region. As evident in the time series outflows from the equatorial lakes measured at the Mongalla station for the period 1915-1983 (Figure 6), it is not necessary to employ any type of statistical analysis to recognize that something peculiar happened with the outflow time series around 1962.…”

“…Such shifting patterns illustrate the nonstationarity of the climate system, in that the assumption of the stability of socalled 'climate normals' does not adequately represent the real climate system. In comparison with ENSO, the physical dynamics associated with the PDO are not well understood, and the phase of the PDO is generally not predictable, although it is possible to create scenarios depicting similar shifting PDO patterns using stochastic methods (Sveinsson et al, 2003).…”

Regionalization of watersheds by hybrid-cluster analysis

“…Anthropogenic changes to global water and energy cycles and natural periodicity present in climate cause nonstationarity in the hydrologic time series (Rao and Hamed, 2003), which could alter the magnitude and frequency of flood events. However, the short historical records and the lack of mathematical framework for analyzing and modeling the dynamics of nonstationary processes have impaired studies in this direction (Sveinsson et al, 2003), especially on the river basin scale.…”

A simple method for effective multi-site generation of stochastic hydrologic time series

“…The reasons may be many, and they are certainly in part due to the complex nature of hydrologic processes, including discontinuities in the data in dry regions, the controversy regarding the Hurst phenomenon (Hurst 1957), or the uncertainty proposed by some researchers regarding the assumption that hydrologic phenomena are indeed stationary in the long term, prompting the efforts to include the concept of a ''sudden shift'' pattern into modeling (Sveinsson and Salas 2003). The current lack of universal approach may in part be due to the complexity of the methods rendered so far, which involve significant effort and knowledge to conduct identification of the appropriate model and estimation of its parameters, as well as the difficulties in assessing the shape of the multivariate probabilities and their transformations from normal to skewed distribution required to model hydrologic processes.…”