Estimating stocks and flows of nitrogen: Application of dynamic nutrient balance to European agriculture

•Analyzing stocks and flows of nutrients requires dynamic modeling.•This study elaborates the dynamic model of N balance.•The model is applied to the data of 14 European countries in years 1961-2009.•Nutrient efficiency is calculated based on the N outflow.•N outflow provides a more robust environmental indicator than the N balance.

This study elaborates the dynamic nutrient balance model and applies it to analyze nitrogen use and nitrogen efficiency in agriculture. We use publicly available agricultural production data to estimate the net inflows, stocks and outflows of nitrogen for 14 European countries in years 1961-2009. The dynamic model allows us to analyze the trends in the nitrogen stocks and flows over time, and break down the total outflow of nitrogen into flows to water, air and soil. We argue that the nitrogen outflow, modeled as the decay of nitrogen stock, provides a more reliable and robust agri-environmental indicator than the conventional nutrient balance. Mathematically, the nutrient balance is an interval scale measure, whereas the nitrogen stock and the outflow from stock are ratio scale measures. Nitrogen efficiencies, calculated based on the nitrogen stocks, provide useful and insightful information beyond the conventional eco-efficiency measures defined from the nitrogen balances. The results of this paper can be used as input data for more comprehensive eco-efficiency or productivity analysis and for the evaluation and design of agri-environmental policies in Europe.