Modeling maximum daily temperature using a varying coefficient regression model

Relationships between stream water and air temperatures are often modeled using linear or nonlinear regression methods. Despite a strong relationship between water and air temperatures and a variety of models that are effective for data summarized on a weekly basis, such models did not yield consistently good predictions for summaries such as daily maximum temperature. A good predictive model for daily maximum temperature is required because daily maximum temperature is an important measure for predicting survival of temperature sensitive fish. To appropriately model the strong relationship between water and air temperatures at a daily time step, it is important to incorporate information related to the time of the year into the modeling. In this work, a time-varying coefficient model is used to study the relationship between air temperature and water temperature. The time-varying coefficient model enables dynamic modeling of the relationship, and can be used to understand how the air-water temperature relationship varies over time. The proposed model is applied to 10 streams in Maryland, West Virginia, Virginia, North Carolina, and Georgia using daily maximum temperatures. It provides a better fit and better predictions than those produced by a simple linear regression model or a nonlinear logistic model.