From a policy perspective, it is important to understand forestry effects on surface waters from a landscape perspective. The EU Water Framework Directive demands remedial actions if not achieving good ecological status. In Sweden, 44 % of the surface water bodies have moderate ecological status or worse. Many of these drain catchments with a mosaic of managed forests. It is important for the forestry sector and water authorities to be able to identify where, in the forested landscape, special precautions are necessary. The aim of this study was to quantify the relations between forestry parameters and headwater stream concentrations of nutrients, organic matter and acid-base chemistry. The results are put into the context of regional climate, sulphur and nitrogen deposition, as well as marine influences. Water chemistry was measured in 179 randomly selected headwater streams from two regions in southwest and central Sweden, corresponding to 10 % of the Swedish land area. Forest status was determined from satellite images and Swedish National Forest Inventory data using the probabilistic classifier method, which was used to model stream water chemistry with Bayesian model averaging. The results indicate that concentrations of e.g. nitrogen, phosphorus and organic matter are related to factors associated with forest production but that it is not forestry per se that causes the excess losses. Instead, factors simultaneously affecting forest production and stream water chemistry, such as climate, extensive soil pools and nitrogen deposition, are the most likely candidates The relationships with clear-felled and wetland areas are likely to be direct effects.
For independently and identically distributed (i.i.d.) univariate observations a new estimation method, the maximum spacing (MSP) method, was defined in Ranneby (Scand. J. Statist. 11 (1984) 93) and independently by Cheng and Amin (J. Roy. Statist. Soc. B 45 (1983) 394). The idea behind the method, as described by Ranneby (Scand. J. Statist. 11 (1984) 93), is to approximate the Kullback-Leibler information so each contribution is bounded from above. In the present paper the MSP-method is extended to multivariate observations. Since we do not have any natural order relation in R d when d > 1 the approach has to be modified. Essentially, there are two different approaches, the geometric or probabilistic counterpart to the univariate case. If we to each observation attach its Dirichlet cell, the geometrical correspondence is obtained. The probabilistic counterpart would be to use the nearest neighbor balls. This, as the random variable, giving the probability for the nearest neighbor ball, is distributed as the minimum of (n − 1) i.i.d. uniformly distributed variables on the interval (0, 1), regardless of the dimension d. Both approaches are discussed in the present paper.
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