Alistair I McKerchar

Chaotic characteristics of the Southern Oscillation Index time series

Abstract The monthly time series of the Southern Oscillation Index (SOI) is analysed to examine its chaotic characteristics. Three schemes, moving average, low-pass filter and nonlinear smoothing, were used to reduce noise and enhance chaotic properties. Autocorrelation and spectral characteristics, as well as three chaos-oriented properties — phase space trajectory, the largest Lyapunov exponent and correlation dimension — were then examined. No significant signs of chaotic behaviour were found for either the noise-reduced SOI time series or the raw one. Although it contains long-term periodicity, the SOI time series is considered to be stochastic rather than chaotic from the viewpoint of dynamical systems theory.

Dependency of summer lake inflows and precipitation on spring SOI

Abstract Inflows to South Island, New Zealand lakes deriving from snowmelt are quantified using a water balance approach and are shown to be between 8% and 24% of annual inflow. A snow accumulation index calculated from climatological data using a snowpack simulation model confirms the general pattern of the year-to-year variability of these estimates. Previous work has shown that summer inflows tend to be relatively low in years when the El Nino Southern Oscillation phenomenon is in a positive phase (i.e. La Nina). We show that this patter is also evident in records of precipitation around the catchments, particularly where precipitation exceeds 1000 mm/yr. Variance of inflows and precipitation appears to be dependent on the magnitude of the SOI. Snowmelt increases somewhat in La Nina years, and this may relate to a general trend for warmer temperatures in these years. A relative absence of La Nina conditions for 1976–1994 may be partially responsible for a significant increase in mean lake inflows over the period 1978–1994.

Prediction of summer inflows to lakes in the Southern Alps, New Zealand, using the spring Southern Oscillation Index

The relationship between the austral spring Southern Oscillation Index (SOI) and the austral summer runoff is investigated for a broad, contiguous region (20 000 km2) of the Southern Alps, New Zealand, representing 70% of the length of the Alps. Using a Bayesian method developed in an earlier study (Moss et al., 1994, Water Resour. Res., 30(10): 2717–2723), probabilities of summer inflows to alpine lakes when the spring Sol is positive (La Nina conditions) are shown to be significantly larger than in springs when SOI is neutral or negative (El Nino conditions). This has major economic significance because the lakes feed hydroelectric power plants that produce typically 43% of the electrical energy used in New Zealand. The lake inflows peak in spring and summer, and use of the available controlled storage must be scheduled carefully to meet power demands that peak in winter. We hypothesise that this occurs because in springs with La Nina conditions, there is a relative absence of snow accumulation, and hence less summer snowmelt.

Temporal patterns for design hyetographs in New Zealand

ABSTRACT Temporal patterns for design hyetographs are estimated by the average variability method for the main regions of New Zealand based on the records from regional clusters of at least five rain gauges with 30 year records. An asymmetric hyperbolic tangent function is used to model non-dimensional cumulative hyetographs for durations from one to 72 h. Results from this reconnaissance study indicate that the largest hyetograph peaks occur near the middle of a storm of 12 or 24 h duration. Slightly lower peaks occur marginally earlier for 1, 6 and 48 h duration peak. Both the 48 and 72 h durations have the lowest but similar peak sizes and the latter occurs latest in a storm for all durations. There is little difference between the cumulative hyetographs for all durations and regions between the North and South Islands and no apparent influence of return period on the results. Considerably more data from more locations are required to make substantive progress in empirical estimation of temporal rainfall patterns, to better understand the influence of return period and to define patterns for durations less than one hour. Hyetographs presented in this study should only be used as a guideline in design.