Frequency distributions and transformations of lake variables, catchment area and morphometric parameters in predictive regression models for small glacial lakes

There are more than 83 000 lakes in Sweden and about 81 000 of these can be characterized as small, glacial lakes. Similar proportions between small, glacial lakes and other lake types ought to exist also for lakes in other parts of the world influenced by the latest glaciation, e.g. North America, Russia and Finland. Most lakes on the earth belong to this population of lakes. All lakes from this population cannot be thoroughly investigated, only a sample of lakes. A key question then is: how will empirical models based on data from the sample of lakes predict for other lakes from the population? It is not possible to answer that question unless several sub-questions are first addressed. This work concerns one of those, does the frequency distribution of the sample represent the frequency distribution of the population? The work addresses this issue from the perspective of predictive empirical models for lake management and research. This work presents comprehensive data sets on a battery of practically useful standard lake variables from more than 900 lakes. All these lakes are Swedish, but they cover a wide range of geographical, geological and climatological characteristics and the results should be widely applicable for all lakes from this lake type. General recommendations on suitable transformations for empirical models are presented for 12 water variables (pH, total-P, colour, hardness, etc.), 13 catchment area characteristics (bedrocks, soils, etc.) and 17 lake morphometric features (size and form parameters). This paper also presents case studies demonstrating the importance of selecting the right transformations for predictive empirical models. New models for Secchi depth, lake pH, colour and total phosphorus are presented to illustrate the practical utility of the results concerning transformations. The effects of sample size on transformations choices are also evaluated.