Overcoming Equifinality: Leveraging Long Time Series for Stream Metabolism Estimation

Abstract

The foundational ecosystem processes of gross primary production (GPP) and ecosystem respiration (ER) cannot be measured directly but can be modeled in aquatic ecosystems from subdaily patterns of oxygen (O2) concentrations. Because rivers and streams constantly exchange O2 with the atmosphere, models must either use empirical estimates of the gas exchange rate coefficient (K600) or solve for all three parameters (GPP, ER, and K600) simultaneously. Empirical measurements of K600 require substantial field work and can still be inaccurate. Three‐parameter models have suffered from equifinality, where good fits to O2 data are achieved by many different parameter values, some unrealistic. We developed a new three‐parameter, multiday model that ensures similar values for K600 among days with similar physical conditions (e.g., discharge). Our new model overcomes the equifinality problem by (1) flexibly relating K600 to discharge while permitting moderate daily deviations and (2) avoiding the oft‐violated assumption that residuals in O2 predictions are uncorrelated. We implemented this hierarchical state‐space model and several competitor models in an open‐source R package, streamMetabolizer. We then tested the models against both simulated and field data. Our new model reduces error by as much as 70% in daily estimates of K600, GPP, and ER. Further, accuracy benefits of multiday data sets require as few as 3 days of data. This approach facilitates more accurate metabolism estimates for more streams and days, enabling researchers to better quantify carbon fluxes, compare streams by their metabolic regimes, and investigate controls on aquatic activity.

Hydrological pulses and burning of dissolved organic carbon by stream respiration

“…It remains to program the calculations more effectively, run more simulations (10,000) and explore the sensitivity of the parameters. Finally, the numerical method presented here should be compared to other recent approaches (e.g., Grace et al ; Hall et al , ; Schindler et al ; Appling et al ), bearing in mind underlying assumptions (Demars et al ; Holtgrieve et al ).…”

Stream metabolism controls diel patterns and evasion of CO2 in Arctic streams

“…This approach assumes that the concentration of O 2 in water is affected by three processes: (a) gross primary production (GPP) that produces O 2 , (b) ecosystem respiration (ER) that consumes O 2 and (c) stream water turbulence that affects the air–water exchange of O 2 . Recent advances in O 2 sensor technology, together with new modelling tools, make it possible to estimate daily GPP, ER and net ecosystem production (NEP; NEP = GPP − ER) using continuous time series of O 2 , light and hydrological parameters (Appling, Hall, Yackulic, & Arroita, ; Hall & Hotchkiss, ; Holtgrieve, Schindler, Branch, & A'mar, ). Importantly, GPP and ER also consume and produce CO 2 , respectively, and thus provide estimates of aquatic C processing rates that can be compared to independent measures of CO 2 .…”

Seeing the light: urban stream restoration affects stream metabolism and nitrate uptake via changes in canopy cover

“…Recent technological and analytical advances have allowed stream and river ecologists to overcome various logistical challenges inherent to estimating stream metabolism (Appling et al. , Bernhardt et al. ).…”