Combining temporally correlated environmental data from two measurement systems

摘要

We consider the problem of combining temporally correlated environmental data from two measurement systems. More specifically, we suppose that an environmental variable has been measured at regular intervals for a relatively long period of time using one measurement system and that a newer, possibly cheaper or more reliable measurement system has been in operation in tandem with the old system for a relatively short period of time. We suppose that, for purposes of detecting changes or trends in the variable over time, the time series corresponding to the new system only is too short so that it is desirable to somehow combine it with the longer time series from the old system. We present two methods for combining the data and for using the combined data to detect trend. The first is a frequentist analysis of an autoregressive moving-average time series model featuring a common time trend, measurement errors with system-specific biases and variances, and missing data. The second method is a Bayesian analysis of a similar model that is implemented by a Markov chain Monte Carlo procedure. We use the methodology to combine and analyze snow water equivalent data from manual snow surveys (an old measurement system) and snow telemetry (a newer system), which are both currently in use in the western United States.