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 (http://hydronet.epa.ie/conditions.htm; accessed March 2012).
Monthly series of the North Atlantic Oscillation (NAO) Index are available from the National Center for
Atmospheric Research (http://climatedataguide.ucar.edu/guidance/hurrell-north-atlantic-oscillation-naoindex-pc-based; 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
2011 available from the Irish Central Statistics Office (http://www.cso.ie/en/databases/index.html; 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 (http://www.met.ie/climate-ireland/30year-averages.asp; 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 (http://eca.knmi.nl; 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 three harmonics 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 of studied 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-30 were 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
Rlag-30
dlag-30
(decimal degrees)
% 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.
Figure A2. 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
𝛴𝑖𝑗 = 𝑈𝑖𝑖 × 𝑆𝑖𝑗 × 𝑉𝑗𝑗𝑇
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
𝐿𝑘𝑖 , 𝐿𝑗𝑘 , and singular vectors 𝑈𝑖𝑘 , 𝑉𝑗𝑘 , each of length n, the angle between each pair of vector segments can be
measured as:
𝑛−1
𝐷(𝐿𝑘𝑖 , 𝐿𝑗𝑘 ) = ∑ atan[(𝐿𝑘𝑖 (𝑡) − 𝐿𝑗𝑘 (𝑡)) − (𝐿𝑘𝑖 (𝑡 + 1) − 𝐿𝑗𝑘 (𝑡 + 1))]
𝑡=1
𝑛−1
𝐷(𝑈𝑖𝑘 , 𝑉𝑗𝑘 ) = ∑ atan[(𝑈𝑖𝑘 (𝑡) − 𝑉𝑗𝑘 (𝑡)) − (𝑈𝑖𝑘 (𝑡 + 1) − 𝑉𝑗𝑘 (𝑡 + 1))]
𝑡=1
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
𝐷𝑇(𝑖,𝑗) =
𝑘
𝑘
𝑘
𝑘
∑𝑘=𝐾
𝑘=1 𝑤𝑘 × (D(𝐿𝑖 − 𝐿𝑗 ) + D(𝑈𝑖 − 𝑉𝑗 )
∑𝑘=𝐾
𝑘=1 𝑤𝑘
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
1
𝑤𝑖 =
𝑒 −2Δ𝑖
1
∑𝑅𝑟=1 𝑒 −2Δ𝑟
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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Variable 1
Variable 2
Precipitation
Land use
Land use
Precipitation
Precipitation
Temperature
Anthropogenic Precipitation
Land use
Anthropogenic
Land use
Temperature
Landscape
Landscape
Land use
Landscape
Precipitation
Morphology
Land use
Morphology
Precipitation
Temperature
Anthropogenic
Landscape
Temperature
Land use
Anthropogenic
Landscape
Anthropogenic
Anthropogenic Precipitation
Variable 3
Precipitation
Temperature
AICc
Δi
wi
R2
-9.67
-9.59
-8.78
-8.78
-8.62
-8.54
-8.42
-8.37
-8.34
-8.24
-8.04
-8.04
-7.82
-7.72
-7.52
-7.48
-7.45
-7.45
0.00
0.09
0.89
0.90
1.06
1.13
1.26
1.30
1.33
1.44
1.63
1.63
1.85
1.96
2.15
2.19
2.22
2.23
0.063
0.060
0.040
0.040
0.037
0.036
0.034
0.033
0.032
0.031
0.028
0.028
0.025
0.024
0.021
0.021
0.021
0.021
0.18
0.17
0.26
0.26
0.26
0.25
0.25
0.11
0.25
0.24
0.23
0.23
0.09
0.08
0.21
0.34
0.21
0.34
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Morphology
Landscape
Landscape
Landscape
Land use
Land use
Morphology
Landscape
Morphology
Morphology
Morphology
Morphology
Morphology
Anthropogenic
Morphology
Landscape
Landscape
Morphology
Morphology
Morphology
Morphology
Precipitation
Temperature
Land use
Anthropogenic
Land use
Precipitation
Anthropogenic Temperature
Precipitation
Temperature
Landscape
Land use
Temperature
Land use
Precipitation
Precipitation
Temperature
Land use
Anthropogenic
Anthropogenic Precipitation
Landscape
Land use
Temperature
Land use
Temperature
Anthropogenic Temperature
Anthropogenic Precipitation
Landscape
Precipitation
Temperature
Anthropogenic
Landscape
Temperature
-7.39
-7.18
-7.11
-7.08
-7.06
-7.05
-6.92
-6.92
-6.85
-6.80
-6.65
-6.65
-6.55
-6.55
-6.54
-6.49
-6.39
-6.28
-6.15
-6.08
-5.69
2.28
2.49
2.57
2.59
2.61
2.62
2.75
2.75
2.82
2.88
3.02
3.02
3.12
3.12
3.13
3.19
3.28
3.39
3.52
3.60
3.98
0.020
0.018
0.017
0.017
0.017
0.017
0.016
0.016
0.015
0.015
0.014
0.014
0.013
0.013
0.013
0.013
0.012
0.012
0.011
0.010
0.009
0.06
0.33
0.33
0.33
0.33
0.33
0.18
0.32
0.32
0.32
0.31
0.31
0.31
0.17
0.31
0.31
0.30
0.30
0.15
0.14
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).
Lough Anure (An)
Lough Bawn (Ba)
Lough Cutra (Cu)
Lough Derryclare (De)
Lough Derrygooney (Der)
Lough Dromore (Dr)
Lough Egish (Eg)
Lough Eske (Es)
Lough Fad (Fad)
Lough Feeagh (Fe)
Lough Gill (Gi)
Lough Gleincmurrin (Gle)
Lough Gowna (Go)
Lough Inchiquin (In)
Lough Muckno (Mu)
Lough Skeagh (Ske)
Lough Oughter (Ou)
Lough White (Whi)
6
4
2
6
4
2
6
Power (σ2)
4
2
6
4
2
6
4
2
6
4
2
1
2
4 6 8 14
1
2
4 6 8 14
Period (year)
1
2 4 6 8 14