On fitting the k-C* first order model to batch loaded sub-surface treatment wetlands

The k-C* first order model was fit to time-series COD data collected from batch-loaded model wetlands. Four replicates of four plant species treatments; Carex utriculata (sedge), Schoenoplectus acutus (bulrush), Typha latifolia (cattail) and unplanted controls were compared. Temperature was varied by 4 degrees C from 24 degrees C to 4 degrees C to 24 degrees C over a year-long period. One mathematical fit was made for each wetland replicate at each temperature setting (192 fits). Temperature effects on both parameters were subsequently estimated by fitting the Arrhenius relationship to the estimated coefficients. Inherent interactions between k and C* make values dependent on sample timing and statistical technique for either time series (batch load) or distance profile (plug flow) data. Coefficients calibrated using the Levenberg-Marquardt method are compared to values previously reported using a nonlinear mixed effect regression technique. Overall conclusions are similar across approaches: (a) the magnitude of the coefficients varies strongly by species; (b) the rate constant k decreases with increasing temperature; and (c) temperature and species variation in the residual concentration C* is greater than the variation in k, such that variation in k alone is a poor predictor of performance. However, the magnitudes of the coefficients, especially the rate parameter k, vary between the statistical techniques, highlighting the need to better document the statistical routines used to calibrate the k-C* model.