Comparative parameterization of dissolved oxygen by an extended stochastic harmonic analysis (ESHA) algorithm

Traditional assessment of surface water quality based on gap samples of discrete dissolved oxygen (DO) is often limited by large diurnal fluctuations. A common reference time for DO measurements is needed for better assessments of differences among water bodies and for identifying changes with time. Two different models have been developed by the authors to convert a DO measurement at any diurnal time to a DO value at a reference time. Both models are based on an extended stochastic harmonic analysis (ESHA). One of the models is formulated using the fraction of DO saturation. It requires real-time (continuous) and discrete data for both DO and water temperature for parameter estimation and an observed DO value with water temperature data in its application. The other model is formulated using only DO and, therefore, does not require water temperature data in estimating parameters as well as in application. Both models were evaluated for the same network of different stream sites across Minnesota, incorporating effects of different ecoregions and variable drainage areas. This paper draws contrasts between the frameworks and performances of the two models. Data were normalized in both cases to increase the general applicability of the fitted parameters. Each of the algorithms revealed good performance in representing observed diurnal variations in DO. For the fraction of DO saturation model, the root mean square error (RMSE) of predicting hourly DO and standard DO ranged from 0.43 to 0.77 mg/L and 0.37 to 0.90 mg/L among the five streams, respectively. In contrast, the RMSE for predicting hourly DO and standard DO respectively ranged from 0.53 to 0.80 mg/L and 0.44 to 0.91 mg/L with the DO only model. While the two models showed nearly equivalent modeling accuracy and consistency, the DO only model added to the elegance of ESHA algorithm for its simpler framework and single parameter (i.e., DO) input data requirement. Both models are useful tools for total maximum daily load (TMDL) assessment of aquatic ecosystem health across a range of temporal and spatial scales.