Teil C - Annex 
67 
before, during and after pile driving events. Based on experience, a resolution by hours (e. g. 
DPM hr 1 ) is helpful here. The parameter DP10M d~ 1 , which is a good measure for phenological 
descriptions, is too inaccurate for registering the influence of pile driving activities on harbour 
porpoises. 
Another value to be calculated is “waiting time”, defined as a time interval (minutes) between 
two harbour porpoise detections. Because of the chronologically possible autocorrelation 
between two detections, at least 10 minutes without detection must pass. Such related har 
bour porpoise-positive 10-minute periods are called “encounter” and gaps are called “waiting 
time”. Thus, the defined minimum value for “waiting time” is 10 minutes (definition in 
Carstensen et al. 2006 and Tougaard et al. 2009). 
For integrating the pile driving activities into the statistical modelling, the pile driving data per 
pile should be available as machine-readable ASCII file derived from the piledriver’s measure 
ment sensors. These files must provide clear identification of the pile, the date and time per 
single impact (documentation of time system) and the impact energy (kJ). If the pile driving 
data is not available in such detail, at least the total impact energy, total number of impacts as 
well as beginning and end (at least correct to 10 minutes) of the pile driving event must be in 
cluded in the evaluation. To include in statistical modelling the waterborne noise measured at 
the C-POD’s measuring position, the median value (50% percentile) of the single event level 
(SEL 50 ) should be available for each pile and measuring position in order to provide a measure 
for the volume [dB re 1 pPa 2 s] for the mainly used impact energy. 
Influence of pile driving on harbour porpoise activity and harbour porpoise activity re 
covery times 
To analyse the influence of pile driving on harbour porpoise activity, generalised additive mod 
els (GAM, Wood 2006) or generalised linear models (McCullagh & Nelder 1989) should be 
used due to the condition of the data (as a rule, not normally distributed data, over dispersion, 
heterogeneity of variance, temporal and spatial autocorrelation). Where necessary, these 
models can easily be extended to generalised additive mixed models (GAMM, Lin & Zhang 
1999) or generalised linear mixed models (GLMM) by inclusion of random factors. For these 
methods it is a priori not known over which functional form one or several explanatory varia 
bles impact on the dependent variable. Moreover, in addition to the parametric forms of gen 
eralised linear models (GLM), a GAM allows for the use of non-linear so-called smoothing 
terms to characterise the connection between the dependent (response) and the explanatory 
(predictor) variable. Flere, all parameters are included in a purely additive manner, as is the 
case also in the traditional linear models. 
The analyses can be carried out script-based in the R software (current version 2.15.2, R Devel 
opment Core Team 2012), which holds available several different GAM and GLM packages. 
Since there is no exactly delineated definition for what exactly is a GAM, these models can be 
very variable. The deriving diversity of models is reflected in the various implementations: “mgcv” 
(current version 1.7-22, Wood 2006) and “gam” (current version 1.06.2, Hastie & Tibshirani 
1990). Other uses include “VGAM” (current version 0.9-0, Yee 2012) and “gamlss” (current ver 
sion 4.2-0, Rigby & Stasinopoulos 2005). For GLM, the packages “Ime4” (Bates et al. 2012), 
“nlme” (Pinheiro et al. 2012) and “MCMCglm” (Hadfield 2010) and others are important. 
Statistical models are subject to ongoing further and new development, which can result in 
new or advanced methods being similarly efficient and adequate in answering the given is 
sues as are the ones described here. In so far, this method is to be understood as providing 
a basis, which may be extended to take into account recent developments.