We are trying to quantify synchrony in water chemistry variation among several thousand sites. For each site we have a time-series of concentration. We'd like to quantify the overall temporal covariance (are concentrations going up and down at the same time) among the sites and are interested in different statistical approaches to to do this. The different chemistry parameters have very different absolute concentrations (e.g. 1-100 ppm for carbon, 0.001 to 1 ppm for phosphorus) so a relative metric is necessary. We have done this previously with the mean of pairwise scaled covariances (https://onlinelibrary.wiley.com/doi/abs/10.1111/ele.12897), but there surely is a more elegant method . . . We are happy to use R, Pyton, or Matlab. Thanks!
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What is the temporal frequency of which you collected the data at each site (e.g., every year, every month, etc.)? Also, do you care about whether or not concentrations at two sites tend to go up or down in tandem over the entire study period? (How long is the study period?) Or from one time point to another? – Isabella Ghement May 07 '18 at 15:51
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1The samples were collected monthly for 10 years. It would be great to know the overall covariance over the study time period (whether they go up or down in tandem) and for different subsets of time. For example, maybe the concentrations covary during the summertime when river discharge is lower but they have different behaviors during the winter. – benjabiker May 09 '18 at 20:45