Robust empirical modeling of dissolved oxygen in small rivers and streams: Scaling by a single reference observation

- We developed a scaling based, empirical model for stream dissolved oxygen (DO).
- Dynamic measures of model sensitivity and uncertainty were analytically derived.
- Model parameters showed impressive robustness both in time and space.
- Model provided spatiotemporally robust predictions of different diurnal DO cycles.
- A tool to predict stream DO cycles from their single reference observations.

SummaryA scaling-based, data-driven empirical model was developed for robust predictions of the diurnal cycle of stream dissolved oxygen (DO) by utilizing a single reference observation as the scaling parameter. The scaling concept was investigated by predicting hourly DO time-series of May to August from different streams representing four distinct US EPA Level III Ecoregions of Minnesota. Absence of any clear temporal trends or site-specific groupings of model parameters suggested a useful generalization and robustness of the scaled, dimensionless DO model over time and space. DO predicted using seasonal (May-August) averages of site-specific parameters simulated the observed diurnal DO cycles with high accuracy (root-mean-square error based coefficient of variation, CV(RMSE) = 0.07-0.11), superior linear correspondence (correlation coefficient, r = 0.87-0.96), and acceptable efficiency (Nash-Sutcliffe Efficiency, NSE = 0.58-0.74); the high accuracy predictions of hourly DO for different days with a single set of dimensionless parameters for the entire season underscore the temporal robustness of the scaled DO model. Nearly equivalent predictions were obtained using monthly averages of parameters, reaffirming the temporal robustness of the dimensionless model. Impressive predictions using parameters of independent sites, as well as a set of spatially averaged (i.e., quasi-regional) seasonal parameters, demonstrated spatiotemporally robust model performance. Model robustness was further demonstrated by deriving and quantifying analytical, dynamic sensitivity and uncertainty measures. The research is an example of useful scaling applications in ecohydrological engineering. The relatively robust, empirical DO model can be applied for simulating continuous (e.g., hourly) DO time-series from a single observation (or a set of limited observations) at different stream sites of comparable watershed sizes. The method can also be used to fill-in missing data in observed sub-daily time-series of periodic water quality variables. High resolution, continuous DO time-series will facilitate a dynamic assessment of the general health of streams and river ecosystems.