Statistical distribution of series of 12 monthly concentration samples for environmental classification of rivers

Abstract. Environmental monitoring and classification of rivers in the northern hemisphere is frequently hampered by lack of infrastructure in the scarcely populated areas of the north. Carefully designed economical methods are important. Analysis of 15 constituents in 14 rivers in Iceland show that monthly samples for a period of 1 year are sufficient for classification provided that the correct statistical distribution is known. Normalizing and plotting all the constituents in each river by rank shows systematic deviations from both the normal and lognormal distributions. When the constituents are pooled by river the result is one distribution for each river, all very similar. A new cumulative distribution function (DoC) is formed as the average of these. It has a long tail similar to that of the lognormal distribution but below the 60% quantile, the DoC differs a lot from the lognormal so if it is to be used, an unbiased estimate of the scale and location parameters will in most cases be difficult to obtain if more than 30–40% of the highest points is used. The influence of the DoC on the classification result is very strong when the 90% quantile is used for classification, but fades out at the 60% quantile. It is shown that the storage effect in rivers with a lake that holds some weeks flow in storage, can have a great influence on the classification result.