A lagged variable model for characterizing temporally dynamic export of legacy anthropogenic nitrogen from watersheds to rivers

Legacy nitrogen (N) sources originating from anthropogenic N inputs (NANI) may be a major cause of increasing riverine N exports in many regions, despite a significant decline in NANI. However, little quantitative knowledge exists concerning the lag effect of NANI on riverine N export. As a result, the N leaching lag effect is not well represented in most current watershed models. This study developed a lagged variable model (LVM) to address temporally dynamic export of watershed NANI to rivers. Employing a Koyck transformation approach used in economic analyses, the LVM expresses the indefinite number of lag terms from previous years' NANI with a lag term that incorporates the previous year's riverine N flux, enabling us to inversely calibrate model parameters from measurable variables using Bayesian statistics. Applying the LVM to the upper Jiaojiang watershed in eastern China for 1980-2010 indicated that similar to 97 % of riverine export of annual NANI occurred in the current year and succeeding 10 years (similar to 11 years lag time) and similar to 72 % of annual riverine N flux was derived from previous years' NANI. Existing NANI over the 1993-2010 period would have required a 22 % reduction to attain the target TN level (1.0 mg N L-1), guiding watershed N source controls considering the lag effect. The LVM was developed with parsimony of model structure and parameters (only four parameters in this study); thus, it is easy to develop and apply in other watersheds. The LVM provides a simple and effective tool for quantifying the lag effect of anthropogenic N input on riverine export in support of efficient development and evaluation of watershed N control strategies.