Missing data imputation for paired stream and air temperature sensor data

Abstract

Stream water temperature is an important factor in determining the impact of climate change on hydrologic systems. Near continuous monitoring of air and stream temperatures over large spatial scales is possible due to inexpensive temperature recorders. However, missing water temperature data commonly occur due to the failure or loss of equipment. Missing data creates difficulties in modeling relationships between air and stream water temperatures. It also imposes challenges if the objective is an analysis, for example, clustering streams in terms of the effect of changes in water temperature. In this work, we propose to use a novel spatial–temporal varying coefficient model to impute missing water temperatures. Modeling the relationship between air and water temperature over time and space increases the effectiveness of imputing the missing water temperatures. A parameter estimation method is developed, which utilizes the temporal covariation in the relationship, borrows strength from neighboring stream sites, and is useful for imputing sequences of missing data. A simulation study is conducted to examine the performance of the proposed method in comparison with several existing imputation methods. The proposed method is applied to cluster streams with missing water temperatures into groups from 156 streams with meaningful interpretations.