Uncertainty assessments. The WISER lake macrophyte data was used to examine variability associated with the varying levels of the hierarchical sampling scheme: transects within stations within waterbodies within countries. We assessed this for several response metrics, including: • Lake Macrophyte Intercalibration Metric for lake macrophytes (ICM-LM), • modified Xxxxxxxxx score, • maximum growing depth (C_max), • species richness. Each metric was calculated for each transect. We used lake level alkalinity and total phosphorus concentration as covariates in the analyses for two reasons. Firstly, these variables define strong gradients in the dataset. Secondly, the response of the macrophyte metrics to lake- level TP, accounting for variations in alkalinity, and for uncertainty in surveying lakes, is of considerable interest in itself. As these covariates were measured at the waterbody level they explain variance between waterbodies and countries, but not within waterbodies. We examined correlation between metrics at the various levels in the sampling hierarchy, and correlations between explanatory variables. Alkalinity information for Étang des Aulnes (France) was not available. Data from this lake were excluded from further analyses. We undertook the uncertainty analyses using linear mixed effects models, fitted using the nlme package in the R environment for statistical computing (R Development Core Team, 2008). The levels of the sampling hierarchy were specified as nested random effects, with the lowest level, variation between transects, forming the residual. We used TP and alkalinity, measured at the lake level, as explanatory variables in all analyses because of their strong relationship to the metrics studied. Depending on the focus of the analysis, we used additional explanatory variables. For example when looking at metric values for different depth zones, an indicator variable for depth zone was used. TP and alkalinity were log transformed, and richness was square root transformed prior to model fitting. Correlations between metrics were examined by first creating a data matrix with a single column for metric value and second column containing an indicator variable for the metric name. Analysis then considered the responses of pairs of metrics modelled as a bivariate normal distribution which can consider correlations between metrics at each of the levels of the sampling hierarchy. Models were fitted using Residual Maximum Likelihood Estimation (REML) to produce unbiased ...
