Statistical modeling of total phosphorus concentrations measured in south Florida rainfall

Atmospheric deposition can be a significant source of phosphorus to South Florida’s aquatic system. The weekly total phosphorus (TP) concentrations in rainfall have been measured routinely in the region since 1974, but the historical data set has significant gaps due to instrumental failures and sample contamination. This study attempts to develop a statistical model of rainfall-borne TP concentration to estimate missing data. The model is based on a multivariate stochastic time-series theory. The model parameters and noise covariances were calibrated using the expectation–maximization algorithm which is known to be efficient for data sets with many gaps. Model verification demonstrates that the calibrated model provides unbiased data estimates while preserving the statistics of the raw data. The data with gaps filled in are useful for computing the weekly TP loads.