Methods of approximation influence aquatic ecosystem metabolism estimates

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Aquatic ecologists have recently employed dynamic models to estimate aquatic ecosystem metabolism. All approaches involve numerically solving a differential equation describing dissolved oxygen (DO) dynamics. Although the DO differential equation can be solved accurately with linear multistep or Runge–Kutta methods, less accurate methods, such as the Euler method, have been applied. The methods also differ in how discrete temperature and light measurements are used to drive DO dynamics. Here, we used a representative stream DO data set to compare the metabolism estimates generated by multiple Euler based methods and an accurate numerical method. We also compared metabolism estimates using linear, piecewise constant and smoothing spline interpolation of light and temperature. Using observed DO to calculate DO saturation deficit in the Euler method results in a substantial difference in metabolism estimates compared to all other methods. If modeled DO is used to calculate DO saturation deficit, the Euler method introduces smaller error in metabolism estimates, which diminishes as logging interval decreases. Linear and smoothing spline interpolation result in similar metabolism estimates, but differ from estimates based on piecewise constant interpolation. We demonstrate how different computational methods imply distinct assumptions about process and observation error, and conclude that under the assumption of observation error, the best practice is to use the accurate numerical method of solving differential equation with a continuous interpolation of light and temperature. The Euler method will introduce minimal error if it is paired with frequently logged data and DO saturation deficit is computed using modeled DO.