Scaling has long been used to develop robust modeling, prediction and application tools in many physical science and engineering disciplines. Although a considerable scaling research has been conducted in ecology and biology, it is unclear whether scaling can lead to useful tools for Ecological Engineering. Taking dissolved oxygen (DO) as an ecological health indicator, we present a unique application of scaling for robust predictions and assessments in stream ecological engineering. A reference time, single observations of different 24-hr diurnal cycles (of the same site or different sites) were used to scale the corresponding cycles and collapse them onto a general diurnal cycle. The normalized cycles were parameterized by forcing them to pass through the scaled, reference observations of 1.0 by using an extended stochastic harmonic analysis (ESHA), which was previously developed and published by the authors. Estimated parameters and the scaled model were then applied to simulate/predict different diurnal DO cycles from their corresponding single reference observations. The scaling concept was tested for spatio-temporal robustness with hourly DO data for four Minnesota streams of comparable watershed sizes, representing four distinct Level III Ecoregions.
Results/Conclusions
Estimated model parameters demonstrated notable robustness in time and space. Modeled DO with temporal (May-August) averages of site-specific parameters remarkably resembled the observed diurnal DO cycles. The root-mean-square error (RMSE) ranged from 0.48 to 0.80 mg/L, the correlation coefficient (r) between observations and predictions ranged from 0.87 to 0.96, and the Nash-Sutcliffe Efficiency (NSE) ranged from 0.58 to 0.74. Use of monthly averages of estimated parameters resulted in nearly equivalent modeling performance, reemphasizing the temporal robustness of the scaled model. Site-specific predictions using parameters of independent sites, as well as a set of regional parameters, demonstrated spatio-temporally robust modeling performance. The data driven DO model can be a handy tool to simulate continuous DO time-series from limited observations at different stream sites of comparable watershed sizes without requiring site or day specific calibrations. The estimated continuous DO will facilitate a dynamic assessment of stream and river health.