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Valid mass load predictions of nutrients, in particular nitrogen (N) andphosphorus (P), are needed for the limnological understanding of single lakeecosystems as well as larger river/lake ecosystems. The mass of N and P thatenters a lake will determine the ecological state of the lake, and the massrelease from the lake will determine the ecological state of downstreamecosystems. Hence, establishing sound quantifications of the external load iscrucial and e.g. contributes to the foundation of assessments of necessarymanagement interventions to improve or preserve the ecological integrity oflakes. The external load of N and P is an integral of several pathways, eachhaving different contributions to the total mass load. Around the world,balances of N and P have been derived for decades to support both lake waterquality monitoring and research, but it can be difficult and, thus, costly tomake detailed and sufficiently covering measurement campaigns in alltributaries (surface as well as groundwater) in the watershed of the N and Pload including seasonality and temporal change from year to year. Thus, loadprediction is facing challenge of uncertainty due to unmeasured loads, whichcan be a consequence of limited resources available for the water flowrecordings and water concentration measurements in inlets around the lake, orsimply due to invisible water flow taking place through the lake bottom. Thelake outlet will typically take place in one single river, so the outletrecording seems easier to measure than inlets, however, the outlet may alsohave unmeasured parts in cases where water is leaching out though the lakebottom. In this paper, we propose a method that applies incomplete data sets(incomplete in the sense of temporal frequency and percentage of gaugedwatershed) to generate time series that predict the N and P loads entering andleaving the lake.

Statistical model concept to quantify input and output of water, nitrogen and phosphorus for lakes with partly gauged watersheds