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No. 393: Climate normalization of nitrogen runoff

Larsen, S.E., Thodsen, H., Tornbjerg, H. & Windolf, J. 2020. Klimanormalisering af kvælstofafstrømning. Aarhus Universitet, DCE – Nationalt Center for Miljø og Energi, 30 s. - Videnskabelig rapport nr. 393


Assessment of the annual total nitrogen load to the sea is reported in the annual NOVANA river report (Thodsen et al., 2019b), both as the actual annual load and as the normalized annual load. The normalization is done with the purpose of removing the variation of the time series caused by year-to-year variation in climate/weather.


The size of the annual runoff and the associated nitrogen load are coupled. Wet years with a relatively large runoff are usually associated with larger nitrogen loads than dryer years with less runoff. Thus, the year-to-year variation in runoff gives a substantial variation in the nitrogen load. This variation makes the single-year load difficult to use administratively and e.g. blurs the evaluation of effect of mitigation measures established to reduce nitrogen loads. The normalized nitrogen load is therefore calculated in order to be able to see the trend of the diffuse nitrogen load with a minimal influence of a given year’s climate/weather. The normalized nitrogen load is calculated both for calendar- and agro-hydrological years (April 1st – March 31st). In this report, a number of statistical methods to climate normalization of annual total nitrogen loads to the sea are evaluated. Both different time steps (month, year) and different geographical resolutions (entire Denmark, coastal area, river) are evaluated.


The evaluation shows that assessments done on monthly or annual data yield different results, the monthly step yielding the best results. Therefore, a monthly time step is used. Climate normalization performed on aggregated single river data, aggregated single coastal areas or for the entire country yields virtually the same results. Therefore, the entire country approach is used. The method also works on the river or coastal area level, but must be expected not to perform as well with decreasing scale (time as well as space).


The method is evaluated for total nitrogen, but there is no theoretical reason for not applying it to other substances/nutrients, for example nitrate or total phosphorus. However, this requires verification of the equations’ performance on such data and testing the need for the inclusion of climate/weather parameters other than runoff. In the latest NOVANA report (Thodsen et al., 2019b), the method was applied for nitrate loads.


Following the analysis of a range of methods, a method based on logarithmic transformed nitrogen loads and linear regression was chosen. The analysis is performed using logarithmically transformed runoff values as the explaining variable, with an associated slope coefficient modelled as a linear function of the year in the time series. Throughout this report, the term logarithm means the natural logarithm. It is recommended that normalization is performed on monthly data.


The normalization on monthly data makes it possible to sum up not only calendar years, but also e.g. different hydrological years. If only annual data are available, it is recommended to apply the same method for annual values.


Climate normalization is shown to perform best using runoff as the input parameter. Precipitation can be used with comparable success on annual data, but performs less well on monthly data. The main reason for this is that a large part of the precipitation falling in the late part of a month enters the river during the next calendar month, depending on the season and the geology of the catchment. No other climate parameters, such as temperature or the number of frost-days, were found to have a significant effect on the normalization.