Modelling Total Organic Nitrogen Concentrations in Danish Streams using Machine Learning

Total organic nitrogen (TON) constitutes almost 20% of the total nitrogen (TN) riverine loadings to Danish coastal waters. Thus, knowledge about the TON concentrations in streams and its spatial variation is essential to accurately assess the importance of TON for TN loadings to coastal waters and thereby achieving a more precise basis for calculation of the sources of TON in catchments.

We used environmental monitoring data from 390 stream stations across Denmark for the period 2018-2021to calculate indirectly measured annual and seasonal average TON concentrations (~1,500 samples) along with a wide range of predictor variables. TON samples showed a mean annual TON concentration in Danish streams amounting to 0.70 mg L^-1 with a standard deviation of 0.31 mg L^-1 and revealed a relatively high spatial variability.

We trained a machine learning model to learn spatial and temporal patterns in our TON data set for prediction of spatially distributed annual and seasonal average TON concentrations in Danish streams in ungauged basins. Furthermore, we utilized quantile regression to estimate the uncertainty on model predictions, and we utilized quantile regression in combination with the Shapley additive explanations (SHAP) approach to investigate how the importance and influence of predictor variables vary across TON’s entire distribution.

The annual TON concentration is modelled with a root-mean-squared error of 0.20 mg L^-1. The new national annual average TON concentration model is largely driven by the mean elevation (negative), the percentage of agricultural land (positive), the percentage of tile drained areas (positive), and the percentage of lakes (positive).

The predicted annual average TON concentrations were generally higher than the measured average annual TON concentrations, with an overall mean of 0.84 mg L^-1, probably because catchments in the training data generally had higher mean elevations (DEM) than the prediction catchments as many ungauged catchments are located near the coast

The developed model and national TON maps contribute to our understanding of annual TON concentrations in streams supporting national-scale land-use and water management.