Modeling and Clustering Time Series Pairs: Evaluating Temperature Patterns in Southeastern U.S. Brook Trout Streams

• Activity Number: 332
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Eric P. Smith* and Xinwei Deng and Han P. Li
• Companies: Virginia Tech and Virginia Tech and Virginia Tech
• Keywords: time series ; clustering ; temperature ; climate change ; time varying coefficient modells ; spatial correlation

Abstract

Stream temperature is a critical factor for aquatic species such as brook trout. To study potential changes in stream temperature associated with changes in air temperature, paired air-water sensors were placed in streams in southeastern U.S. and resulted in measurements every 30 minutes over a year. To model the data, a time-varying coefficient model is used to quantify the air-water temperature relationship. The method performs better than other approaches in describing the relationship and how it varies over time. A novel clustering method for bivariate functional data is proposed to group streams based on their water-air temperature relationship that will aid in regional management. 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. The proposed clustering method is applied to 62 brook trout streams in southeastern US.