The Southern Oscillation index as a predictor of the probability of low streamflows in New Zealand

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Abstract
The Southern Oscillation index (SOI) can yield information about subsequent streamflows on the South Island of New Zealand; however, the relationship between streamflow and SOI may be nonlinear and heteroscedastic. To deal with such difficulties, the conditional probability of streamflow's being below a critical magnitude, given a prior observation of SOI, can be considered a random variable, with its probability density function (pdf) estimated by Bayesian analysis of existing observations of streamflow and SOI. The conditional pdf can yield a probabilistic forecast of critically low streamflows given a precursor value of SOI. In the Clutha River basin of New Zealand, average austral summer inflow to the headwater lakes has an unconditional probability of nonexceedance of 360 m3/s of approximately 17%. However, during a moderate La Niña, average austral spring SOI = 12, the conditional probability of nonexceedance has an expected value of 55%. For an El Niño with a spring SOI of −12, the expected probability of nonexceedance is 18%; for a neutral SOI of 0, the expected probability is 10%. Thus, the probability of nonexceedance of seasonal streamflow can be seen to vary by a factor of more than 5 as a function of the SOI.