A Nonparametric Approach to Generating Inseason Forecasts of Salmon Returns

Variations in the size and timing of salmon runs have frustrated attempts to develop models for updating forecasts of returns inseason. The relationship between run size and inseason predictor variables is often nonlinear and changes over time. The nature of these nonlinearities is generally not known and analysts have elected to approximate observed patterns in the data with ad hoc parametric models. Although conceptually attractive, the performance of these models is frequently degraded by their inflexibility and failure to satisfy key model assumptions. In this paper, nonparametric probability density estimation techniques are employed to calculate the total run size conditional on the observed inseason data. Unlike the parametric techniques, the nonparametric approach allows the data to speak for themselves instead of having to merely conform to some arbitrary mathematical model. The approach is easily adapted to handle information from either terminal or guantlet fisheries and can be generalized to compute conditional expectations of various quantities of interest including run size, run timing, or both. Weekly estimates of the number of sockeye salmon (Oncorhynchus nerka) returning to the Skeena River, British Columbia, are employed to demonstrate the performance of the model.