Appendix 1. Location and Relative Size of Lakes Mendota and Monona, in Madison,Wisconsin

Appendix 1. Record length and source of data acquired for time-series analyses. Terms in italics represent variable names used in the analyses.

Appendix 1. Location and relative size of Lakes Mendota and Monona, in Madison,Wisconsin.

Appendix 2. Record length and source of data acquired for time-series analyses. Terms in italics represent variable names used in the analyses.

Appendix 3. Statistical framework used to determine the relative importance of temporal processes, large-scale climatic drivers, and local weather on the 100 year ice record for Lakes Mendota and Monona.

Appendix 4. Specifics of the Moran Eigenvector Maps (MEM) analysis used in the study.

Details of the MEM analyses follow. First, a linear regression is performed on the response variable over time. If the linear regression is significant, the response variable is detrended to remove the linear trend in the response data. A linear trend is an indication of temporal structure acting at a longer interval than the extent of observations. A trend can obscure other structure in the dataset that could be more optimally modelled by MEM variables. The residuals of the linear regression are retained for subsequent analyses. Second, MEM eigenfunctions are constructed by computing the Euclidean distance among the sampling times, which here were years. A Principal Coordinates Analysis (PCoA) is conducted on the modified Euclidean distance matrix and generates eigenfunctions representing the temporal structure in the dataset. The MEM variables are a series of sine waves with decreasing periods. A forward selection procedure with 1000 permutations was used because the number of MEM variables produced was large (Blanchet et al. 2008). Only predictor variables with p< 0.05 were retained in the model (Blanchet et al. 2008). These significant MEM variables are used as predictor variables representing temporal structure in the response data. Finally, a linear analysis (such as redundancy analysis if the response data are multivariate and multiple linear regression if response data are univariate) is performed on the response data (ice breakup dates) with a set of predictor variables (local daily weather, local winter weather, indices of sunspot numbers and large-scale climatic drivers, and cyclic temporal dynamics as modelled by MEM variables); see Figure 1 (this study); Borcard and Legendre 2002; and Borcard et al. 2004 for details).

Appendix 5. Autocorrelation function (ACF) plots of ice breakup dates for Lakes a) Mendota and b) Monona between 1905-2004.

Appendix 6. Partial autocorrelation function (PACF) plots of ice breakup dates for Lakes a) Mendota and b) Monona between 1905-2004.

Appendix 7. Unique and shared contributions of local daily weather (Daily), local winter weather (Winter) and temporal oscillatory cycles (Cycles) on ice breakup for a) Lake Mendota and b) Lake Monona. Adjusted percent variation (R2adj) is summarized. Unique contributions of variables explaining ice breakup date are the areas of the circles that do not overlap with any other circle. The shared contributions are within the overlapping areas of the circles. For example in Lake Mendota, 14% of variation in ice breakup date is explained uniquely by daily weather and 8% of variation in ice breakup date is explained uniquely by winter weather. The shared contribution of daily and winter weather is 2 % (as represented in the region that overlaps the daily and winter weather circles).