Modeling River Water Temperature Using Clustered Data Collected at Haphazard Times and Random Spatial Locations

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Brian Gray*+ and Jim Rogala
• Companies: U.S. Geological Survey and U.S. Geological Survey
• Keywords: hierarchical model ; location-scale models ; multilevel models ; water temperature

Abstract

We develop a three-level linear model of water temperature for use with data obtained from single visits to spatial random samples of locations and where sampling recurs annually. The study was motivated by data from the Illinois River, in which observations per day and days sampled in each of 16 two-week annual sampling periods were few (1 - 7 and 5 - 12, respectively). Solar radiation ("time") associations were permitted to vary by day-to address that sampling occurred earlier in the day in later study years, that observations were obtained at haphazard times within days, and that temperature varied with time of day. Day and year effects on the mean were also treated as random. The log of sampling-scale variation was permitted to vary as a function of random year. The proposed model yielded improved fit over a reference model without time effects and heterogeneous sampling variances (LRT X2(2) = 128); point estimates of multi-year temporal trends (95% CI) under the proposed and base models were 0.10 (-0.11, 0.30) and 0.07 (-0.13, 0.27) °C yr-1, respectively. Efforts to distinguish temporal from spatial components are ongoing.