Reducing bias and quantifying uncertainty in watershed flux estimates: the R package loadflex

Abstract

Many ecological insights into the function of rivers and watersheds emerge from quantifying the flux of solutes or suspended materials in rivers. Numerous methods for flux estimation have been described, and each has its strengths and weaknesses. Currently, the largest practical challenges in flux estimation are to select among these methods and to implement or apply whichever method is chosen. To ease this process of method selection and application, we have written an R software package called loadflex that implements several of the most popular methods for flux estimation, including regressions, interpolations, and the special case of interpolation known as the period‐weighted approach. Our package also implements a lesser‐known and empirically promising approach called the “composite method,” to which we have added an algorithm for estimating prediction uncertainty. Here we describe the structure and key features of loadflex, with a special emphasis on the rationale and details of our composite method implementation. We then demonstrate the use of loadflex by fitting four different models to nitrate data from the Lamprey River in southeastern New Hampshire, where two large floods in 2006–2007 are hypothesized to have driven a long‐term shift in nitrate concentrations and fluxes from the watershed. The models each give believable estimates, and yet they yield different answers for whether and how the floods altered nitrate loads. In general, the best modeling approach for each new dataset will depend on the specific site and solute of interest, and researchers need to make an informed choice among the many possible models. Our package addresses this need by making it simple to apply and compare multiple load estimation models, ultimately allowing researchers to estimate riverine concentrations and fluxes with greater ease and accuracy.

Quantification of Phosphorus Exports from a Small Forested Headwater-Catchment in the Eastern Ore Mountains, Germany

“…Using this relationship, the solute concentration for the times without samples is estimated based on the measured discharge. The extrapolation methods differ in the method used to establish the discharge-solute relationship [9,20]. The interpolation models shown in Table 1 were applied using the R-package loadflex [20].…”

“…The extrapolation methods differ in the method used to establish the discharge-solute relationship [9,20]. The interpolation models shown in Table 1 were applied using the R-package loadflex [20]. Here, the discharge-solute concentration relationship is established by connecting the measured solute concentration using different means of interpolation (e.g., rectangular, triangular, spline, distance-weighted, etc.)…”

“…Here, the discharge-solute concentration relationship is established by connecting the measured solute concentration using different means of interpolation (e.g., rectangular, triangular, spline, distance-weighted, etc.) [20]. For the linear model, a linear regression is fitted with the log-discharge and log-solute concentration [20].…”

“…[20]. For the linear model, a linear regression is fitted with the log-discharge and log-solute concentration [20]. For the Loadest regression models (Table 1), non-linear regression functions between measured discharge and solute concentrations were established [22][23][24].…”

“…For the period from December 2009 to December 2011, weekly samples were available, while bi-weekly samples were available during 2012. The finest temporal resolution available for the entire data period was therefore bi-weekly, which was then used to establish the discharge-solute concentration relationships for all methods listed in Table 1, using the R-package loadflex [20]. After the establishment of the load calculation models, loadflex was used to predict the P fluxes for the time steps without TP-P measurements using the measured discharge as a predictor.…”