Optimal development of calibration equations for paired catchment projects

- Shows the rapid build-up of calibration information in a paired catchment study.
- Shows that the most information is gained by using the shortest-time units.
- Shows that autocorrelation of residuals and non-normal distributions can be a problem, but that the former can be removed.
- Shows that calibrations of >5 years unlikely to be beneficial.
- Lays out a technique for monitoring the quality of calibration of a paired catchment experiment.

SummaryData from two Australian paired-catchment projects were used to assess the effect of length of the calibration period on the quality of calibration achieved. The data were divided into a “calibration” and a “verification” set. The Nash-Sutcliffe (N-S) coefficient of efficiency was used to assess the quality of prediction of the verification set as a function of the length of the calibration set. The results showed a rapid initial increase in quality of calibration with increasing calibration length. This then “plateaued”. With simple linear regression models, reasonable calibration (N-S > 0.7) was achieved in 60 days and good calibration (N-S > 0.8) in 100 days. More complex models achieved good calibration after 300 days of data. In general, there were no increases in the N-S value achieved after 3 years - the main advantage of longer calibrations appeared to be lower mean errors. Similar results were obtained with daily, monthly, quarterly, or annual subdivisions of flows. All residuals suffered from autocorrelation and non-normality; the former was removed by an autoregressive technique, but the latter appears implicit in the technique. Simulation of the use of an n-fold data examination technique to monitor the development of calibration as data flowed in substantially reproduced this result. This appears to be a good strategy for hydrologists monitoring development of calibration in a continuing project. Paired-catchment experimentation is a robust experimental technique but would benefit from application of a set of protocols prescribing techniques.