Functional data analysis: An approach for environmental ordination and matching discrete with continuous observations

Background/Question/Methods

Investigators are frequently confronted with data sets that include both discrete observations and extended time series of environmental data that had been collected by autonomous recorders.  Evaluating the relationships between these two kinds of data is challenging.  A common approach is to summarize the time or space series as a mean value that is then compared with the more limited discrete data.  This approach will be unsatisfactory when such data reduction obscures important attributes of the series, such as patterns in its intrinsic variability and differences in the rates of change of the parameter measured by the series.  An additional complication arises if multiple concurrent series of data have been collected, and the purpose is to examine their joint relationship to discrete observations.

Results/Conclusions

Functional data analysis is an approach that can be used to obtain a representation of one or more environmental series that can then be used to investigate relationships with discrete data.  The functional data analysis methodology will be described in detail together with an example drawn from the highly variable estuarine environment where the abundance of fishes in tidal channels is analyzed as a function of the co-occurring patterns of salinity, temperature, dissolved oxygen, and turbidity collected in the channel.   Functional data analysis also supports the ordination of multiparameter time series, allowing a full examination of the range of variation in conditions that occur over the time series, as well as an identification of common and exceptional conditions.