Calibration and Validation of an Empirical Dissolved Oxygen Model

A common difficulty in stream health assessments is the scarcity of real-time dissolved oxygen (DO) data. Discrete DO measurements, collected at times often imposed by sampling constraints, are difficult to use in assessments because of diurnal variations. An empirical model is developed here to adjust these discrete measurements to a common time-reference value using an extended stochastic harmonic analysis (ESHA) algorithm, which was originally formulated with a fraction of DO saturation model by the authors. The model was calibrated and validated for different stream sites across Minnesota, incorporating effects of different ecoregions and variable drainage areas. Data were normalized to increase the general applicability of the fitted parameters. Model calibration for five long record stations accurately represented observed diurnal variations in DO. The root-mean-square error (RMSE) for predicting hourly DO ranged from $0.53\text{to}0.80\mathrm{mg}∕\mathrm{L}$ and for predicting DO at a standard time ranged from $0.44\text{to}0.91\mathrm{mg}∕\mathrm{L}$ . Estimated model parameters were robust in terms of both spatial and temporal variations. Analytical as well as numerical analyses of parameter uncertainties were performed using sensitivity coefficients. Model validation with independent data for eight different Minnesota streams was performed using three different approaches for estimating parameters. The best approach considered both ecoregional location and watershed size to select representative model parameters. The RMSE for predicting hourly DO and standard DO respectively ranged from $0.53\text{to}1.65\mathrm{mg}∕\mathrm{L}$ and $0.00\text{to}1.83\mathrm{mg}∕\mathrm{L}$ . The developed model is a useful tool for total maximum daily load assessment of aquatic ecosystem health across a range of temporal and spatial scales. It is more elegant and simpler than the application of the ESHA algorithm for the fraction of DO saturation model.