APPENDIX A: Data Series

APPENDIX A: Data series

Data sources

Monthly water level series were calculated from relative mean daily water levels recorded at gauge stations by the Irish Environment Protection Agency ( accessed March 2012). Monthly series of the North Atlantic Oscillation (NAO) Indexare available fromthe National Center for Atmospheric Research( accessed March 2012). Environmental variables were extracted from available GIS data. Catchment human population density variables were based on electoral division censuses between 1979 and 2011available from the Irish Central Statistics Office( accessed March 2012). Mean catchment precipitation and temperature were calculated from 1-km resolution grids of long-term (1981-2010) total annual precipitation and mean annual temperature produced by the Irish Meteorological Agency,Met Éireann ( accessed September 2012). Catchment weather variability (CV_Temp and CV_Prec) was estimated from the E-OBS 0.25° gridded daily mean temperature and total precipitation datasets from the EU-FP6 project ENSEMBLES ( accessed December 2011) over the period of study (April 1979 to March 2009).

Water level series

Mean monthly water levels were calculated from daily values where a minimum of one week of daily data was available within a month. We based this criterion on the highly significant (α < 0.001) water level autocorrelations (Rlag-30; Table A1) found in all series as determined by the Dublin Watson test (Fox, 2008)under the null hypothesis of no temporal autocorrelation in the series at the 30-day lag (dlag-30). Otherwise,a month was considered as a missing observation in the final series (see missing values percentages in Table A1). Imputation of missing values was performed by fitting individual Bayesian harmonic regression models (not shown here) to each of the lake series similar to those used by Viana et al. (2011), comprising a combination of a linear trend component and up to threeharmonics to model the seasonal and cyclic components of the series. An autoregressive component was also added to the model structure to account for temporal autocorrelation.

Table A1. List ofstudied lakes, autocorrelation function (Rlag-30) and Dublin Watson test statistic (dlag-30) at the 30-day lag for daily water level series of studied lakes.All dlag-30were significant at the 0.001 level. The subsequent percentage of missing values in the resulting monthly water level series is also shown.

Lake / Latitude / Longitude
(decimal degrees) / Rlag-30 / dlag-30 / % missing values
Anure (An) / 55.007N -8.276W / 0.192 / 1.626 / 0
Bawn (Ba) / 54.047N -6.91W / 0.418 / 1.162 / 1.9
Cutra (Cu) / 53.028 N -8.772 W / 0.304 / 1.418 / 5.8
Derryclare (De) / 53.464N -9.803W / 0.154 / 1.732 / 1.4
Derrygooney (Der) / 54.042 N -6.942 W / 0.451 / 1.085 / 3.1
Dromore (Dr) / 54.082N -7.087W / 0.398 / 1.229 / 8.3
Egish (Eg) / 54.058N -6.774W / 0.658 / 0.737 / 2.5
Eske (Es) / 54.687N -8.052W / 0.204 / 1.606 / 0
Fad (Fa) / 55.234N -7.376W / 0.374 / 1.36 / 12.8
Feeagh (Fe) / 53.925N -9.572W / 0.181 / 1.674 / 3.1
Gill (Gi) / 54.249N -8.439W / 0.362 / 1.31 / 0
Gleincmurrin (Gl) / 53.308N -9.498W / 0.299 / 1.434 / 2.5
Gowna (Go) / 53.866N -7.544W / 0.669 / 0.678 / 3.9
Inchiquin (In) / 52.951N -9.083W / 0.256 / 1.521 / 3.1
Muckno (Mu) / 54.1N -6.682W / 0.467 / 1.09 / 3.9
Oughter (Ou) / 54.038N -7.433W / 0.554 / 0.924 / 0
Skeagh (Sk) / 53.951N -7.007W / 0.671 / 0.689 / 1.1
White (Wh) / 54.114N -6.972W / 0.383 / 1.232 / 1.7

Figure A1. Location of the study lakes.

FigureA2. Monthly water level time series of the studied lakes.

References

Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second ed. Sage, California.

Viana, M., Graham, N., Wilson, J.G., Jackson, A.L. (2011) Fishery discards in the Irish Sea exhibit temporal oscillations and trends reflecting underlying processes at an annual scale. ICES Journal of Marine Science 68, 221-227.

APPENDIX B: Comparing time-frequency coherency patterns

Our approach to compare the time-frequency coherency patterns among lakes follows the method proposed by Rouyer et al. (2008) based on the Maximum Covariance Analysis (MCA). The following gives a brief description of the method. Interested readers are directed to the original source for more detailed information.

Given a pair of coherency spectra Wi and Wj, the singular vector decomposition on their covariance matrix Σij is calculated as

where the columns of U and V are orthonormal and contain the singular vectors for Wi and Wj respectively, and Sij is a diagonal matrix containing the nonzero singular values of the covariance matrix in decreasing order of magnitude which are proportional to the squared covariance accounted for each axis of the MCA. In this way, each axis of the MCA corresponds to a fraction of the covariance between the two spectra in decreasing order of importance. The singular value decomposition finds an orthonormal basis for each spectrum, determined by their respective singular vectors, that maximizes their mutual covariance. Where the singular vectors describe the spectrum frequency patterns, the projection of each spectrum over its corresponding singular vectors (i.e. the leading patterns), shows the evolution in time of these frequency patterns. The method thus extracts sequentially the k first axes to account for a specified amount of the total covariance (99% in our analysis). Each axis is associated to a pair of singular vectors and leading patterns; one for each spectrum.

The resulting singular vectors and leading patterns obtained by the MCA are then used to compute the distance between the pair of spectra. The lack of linearity between singular vectors and leading patterns precludes the use of simple correlation as a distance measure. Instead, given the kth pair of leading patterns , , and singular vectors , , each of length n, the angle between each pair of vector segments can be measured as:

Using the weighted mean of D for each of the retained pairs of singular vectors and leading patterns, the distance between the two spectra Wi, Wj is finally computed as

where wk is the vector of weights corresponding to the amount of covariance explained by each axis. The distances DT are then used to fill a distance matrix suitable for for traditional ordination analysis.

Figure B1.Flow-chart of the different steps followed to analyse the relationship between landscape environmental filters and the local time-frequency patterns of correlation between the NAO and the water levels in the study lakes.

References

Rouyer T, Fromentin J, Stenseth N, Cazelles B (2008) Analysing multiple time series and extending significance testing in wavelet analysis. Mar Ecol Prog Ser 359:11-23. doi:10.3354/meps07330

APPENDIX C: Relative importance of predictor variables

Based on the corrected Akaike Information Criterion (AICc; Burnham and Anderson, 2004), and starting with the full set of models (R)comprising all possible variable combinations, we calculated the Akaike weight (wi) of each model based on the differences between the AICc value of the models and that of the most parsimonious model (Δi = AICci- AICcmin) as

To estimate the relative importance of each predictor variable relative to the others, we first selected a subset of competitive models (as defined as having Δi≤ 4;Burnham et al., 2011). Based on the resulting competitive subset, comprising a total of 39 models (Table B1), we calculated the Akaike weight of each variable (w+(j))as the sum of the Akaike weights (wi) across all models where that variable appeared (Burnham and Anderson, 2002).

Table C1. List of the 39 competitive models (Δi ≤ 4) used to assess the relative importance of the different environmental variables(as defined by the corresponding first principal components) in explaining the NAO-water level coherency-based dissimilarities among lakes.

Model / Variable 1 / Variable 2 / Variable 3 / AICc / Δi / wi / R2
1 / Precipitation / -9.67 / 0.00 / 0.063 / 0.18
2 / Land use / -9.59 / 0.09 / 0.060 / 0.17
3 / Land use / Precipitation / -8.78 / 0.89 / 0.040 / 0.26
4 / Precipitation / Temperature / -8.78 / 0.90 / 0.040 / 0.26
5 / Anthropogenic / Precipitation / -8.62 / 1.06 / 0.037 / 0.26
6 / Land use / Anthropogenic / -8.54 / 1.13 / 0.036 / 0.25
7 / Land use / Temperature / -8.42 / 1.26 / 0.034 / 0.25
8 / Landscape / -8.37 / 1.30 / 0.033 / 0.11
9 / Landscape / Land use / -8.34 / 1.33 / 0.032 / 0.25
10 / Landscape / Precipitation / -8.24 / 1.44 / 0.031 / 0.24
11 / Morphology / Land use / -8.04 / 1.63 / 0.028 / 0.23
12 / Morphology / Precipitation / -8.04 / 1.63 / 0.028 / 0.23
13 / Temperature / -7.82 / 1.85 / 0.025 / 0.09
14 / Anthropogenic / -7.72 / 1.96 / 0.024 / 0.08
15 / Landscape / Temperature / -7.52 / 2.15 / 0.021 / 0.21
16 / Land use / Anthropogenic / Precipitation / -7.48 / 2.19 / 0.021 / 0.34
17 / Landscape / Anthropogenic / -7.45 / 2.22 / 0.021 / 0.21
18 / Anthropogenic / Precipitation / Temperature / -7.45 / 2.23 / 0.021 / 0.34
19 / Morphology / -7.39 / 2.28 / 0.020 / 0.06
20 / Landscape / Precipitation / Temperature / -7.18 / 2.49 / 0.018 / 0.33
21 / Landscape / Land use / Anthropogenic / -7.11 / 2.57 / 0.017 / 0.33
22 / Landscape / Land use / Precipitation / -7.08 / 2.59 / 0.017 / 0.33
23 / Land use / Anthropogenic / Temperature / -7.06 / 2.61 / 0.017 / 0.33
24 / Land use / Precipitation / Temperature / -7.05 / 2.62 / 0.017 / 0.33
25 / Morphology / Landscape / -6.92 / 2.75 / 0.016 / 0.18
26 / Landscape / Land use / Temperature / -6.92 / 2.75 / 0.016 / 0.32
27 / Morphology / Land use / Precipitation / -6.85 / 2.82 / 0.015 / 0.32
28 / Morphology / Precipitation / Temperature / -6.80 / 2.88 / 0.015 / 0.32
29 / Morphology / Land use / Anthropogenic / -6.65 / 3.02 / 0.014 / 0.31
30 / Morphology / Anthropogenic / Precipitation / -6.65 / 3.02 / 0.014 / 0.31
31 / Morphology / Landscape / Land use / -6.55 / 3.12 / 0.013 / 0.31
32 / Anthropogenic / Temperature / -6.55 / 3.12 / 0.013 / 0.17
33 / Morphology / Land use / Temperature / -6.54 / 3.13 / 0.013 / 0.31
34 / Landscape / Anthropogenic / Temperature / -6.49 / 3.19 / 0.013 / 0.31
35 / Landscape / Anthropogenic / Precipitation / -6.39 / 3.28 / 0.012 / 0.30
36 / Morphology / Landscape / Precipitation / -6.28 / 3.39 / 0.012 / 0.30
37 / Morphology / Temperature / -6.15 / 3.52 / 0.011 / 0.15
38 / Morphology / Anthropogenic / -6.08 / 3.60 / 0.010 / 0.14
39 / Morphology / Landscape / Temperature / -5.69 / 3.98 / 0.009 / 0.27

References

Burnham, K.P., Anderson, D.R. (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods and Research 33, 261-304.

Burnham, K.P., Anderson, D.R., Huyvaert, K.P. (2011) AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons Behavioral Ecology and Sociobioly 65, 23-35.

APPENDIX D: Global power spectra

Figure D1. Global power spectra for the 18 deseasonalized lake series illustrating the distribution of global power (i.e., variance) across periodicities in water levels. Red solid sections of the spectra correspond to statistically significant (P ≤ 0.05) peaks in the global wavelet spectrum (based on 1000 bootstrapped surrogates).