Regression alchemy for temporal disaggregation of mean annual loads

Mean annual budget-based watershed models offer benefits of robustness and simplicity, but they do not provide information on seasonal or storm event loadings that are of more ecological relevance.

Mean annual budget-based watershed models offer benefits of robustness and simplicity, but they do not provide information on seasonal or storm event loadings that are of more ecological relevance. We have therefore investigated methods for temporal disaggregation of loads, with emphasis on ungauged sites.

For seasonal analysis, rating curve methods were used to determine summer loads as a fraction of mean annual nutrient loads for approximately 200 sites in New Zealand. The fractions were then regressed against catchment and stream attributes that are available over the REC stream network, using Boosted Regression Trees. The resulting models provided satisfactory predictions for TN and TP, but not for dissolved nutrients. The simpler MARS regression methods were also applied, with similar model performance and additional benefits of improved model interpretability and easier predictions.

We also developed methods for disaggregating sediment loads into event loads, based on determining the probability distribution of event loads at monitoring sites, normalising to mean annual load, then regression parameters as a function of catchment characteristics using regression forests. The probability distribution was characterised with a two-part empirical-Pareto distribution, because single parametric distributions did not provide a suitable fit to site data. It was found that normalisation reduced site variations considerably, various generalisation errors were taken into account through cross-validation, and we were unable to satisfactorily resolve spatial variations in the normalised probability distribution. Hence a simple master curve of normalised probability distribution, along with characterisation of errors, was appropriate for event sediment loads.

Future work will investigate regionalisation of rating curves and other methods, such as catchment similarity indices, as alternative approaches to derive event loads.