2013 Lakes Monitoring Report

Technical Memo Statistical Analysis of Lake Data in the Capitol Region Watershed District Capitol Region Watershed District September 18, 2013

Before evaluating trends in a lake data set, exogenous variables that may be causing a pattern in the data must be evaluated and removed if present. An exogenous variable is a variable other than time that may have considerable influence on the response variable. These variables are usually natural such as rainfall, temperature or stream flow. For lakes, especially those with long residence times such as Lake McCarron, the most common potential exogenous variable is rainfall.

To test for rainfall as a factor, monthly total precipitation was regressed against monthly average TP concentrations for the period of record (Figure 3). No relationship between TP and monthly precipitation totals was found for the data or the logs of the data. Consequently, it was concluded that rainfall totals does not need to be accounted for in the trend analysis.

Seasonality and Autocorrelation

Two other factors that need to be accounted for in any trend analysis including serial autocorrelation and seasonality. Seasonality is important in lakes since they demonstrate a clear growing season along with a dormant season. However, most of the monitoring data were collected during the growing season meaning that years to year comparisons are not likely to include much seasonality in the data.

Monthly notched box plots confirm this assumption (Figure 4). Only Secchi depth for one month (August) demonstrated a significant difference among the months. Based on this assessment, using the seasonally adjusted Kendall Tau trend test is not necessary.

Lake data tend to be serially autocorrelated due to long residence times. To evaluate serial autocorrelation, correlograms were developed for each of the three parameters (Figure 5).

Autocorrelograms evaluate autocorrelation using time lags in the data. For our analysis, we chose a lag period of 12 to account for annual data. Typical sampling in Lake McCarrons was 7 samples over the summer growing season. However, a lag period of 12 allows for evaluation of autocorrelation within a sampling year and between years. All three parameters demonstrated autocorrelation within any given year but not between years. Consequently, autocorrelation must be accounted for in the trend analysis.

Trend Assessment

Because a major event (alum treatment) occurred in Lake McCarron, the trend assessment must account for both the pre‐ and post‐alum conditions. Total phosphorus conditions before and after the alum treatment were statistically different (Figure 6).

No trends were detected in either the pre‐ or post‐alum treatment data sets using the Mann‐Kendall trend test with a significance value of 0.05. Trends tests on the overall data set do demonstrate an improving trend in water quality although this is solely a result of the alum treatment conducted in 2004.

Multi‐Variate Assessment

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