A refined lack-of-fit statistic to calibrate pesticide fate models for responsive systems.

Background: Calibration by inverse modelling was performed with the MACRO transport and fate model using long-term (>10 years) drainflow and isoproturon (IPU) data from western France. Two lack-of-fit (LOF) indices were used to control the inverse modelling: sum of squares (SS) and an alternative statistic called the vertical-horizontal distance integrator (VHDI), which is designed to account for offsets in observed and predicted arrival times of peak IPU concentration. With these data, SS was artificially inflated because it is limited to comparison of predicted and observed IPU concentrations that are concurrent in time. The LOFs were used along with the index of agreement (d) and the correlation coefficient (r) to ascertain the fit of the calibrated models.

Results: Predicted arrival times of peak IPU concentration differed somewhat from observed times. All four indices indicated better model fit for the second of two validation periods when inverse modelling was controlled by VHDI rather than SS (SS = 26.4, d = 0.660, r = 0.606 and VHDI = 1.25). The VHDI statistic was markedly lower compared with the uncalibrated model (38.0) and SS calibration results (24.5). The final maximum predicted IPU concentration (44.5 microg L(-1)) for the calibration period was very similar to the observed value (44 microg L(-1)).

Conclusion: VHDI is seen as an effective alternative to SS for calibration and validation of pesticide fate models applied to responsive systems. VHDI provided a more realistic assessment of model performance for the transient flows and short-lived concentrations observed here, and also effectively substituted for the objective function in inverse modelling.