Bivariate functional data clustering: grouping streams based on a varying coefficient model of the stream water and air temperature relationship

A novel clustering method for bivariate functional data is proposed to group streams based on their water–air temperature relationship. A distance measure is developed for bivariate curves by using a time-varying coefficient model and a weighting scheme. This distance is also adjusted by spatial correlation of streams via the variogram. Therefore, the proposed distance not only measures the difference among the streams with respect to their water–air temperature relationship but also accounts for spatial correlation among the streams. The proposed clustering method is applied to 62 streams in Southeast US that have paired air–water temperature measured over a ten-month period. The results show that streams in the same cluster reflect common characteristics such as solar radiation, percent forest and elevation. Copyright © 2015 John Wiley & Sons, Ltd