Northeast Daily Stream Temperature

Daniel J Hocking
3/25/2016

Abstract

Coming Soon

Objectives

Our objective was to develop novel statistical model of daily stream temperature that incorporates features of stochastic models and extends the Letcher et al. (2016) framework to large geographic areas. The model needed to (1) handle time series data of widely varying duration from many sites accounting for autocorrelation at specific locations within watersheds, (2) while also including information about catchment, landscape, and meteorological conditions for explanatory and predictive purposes. (3) For a daily temperature model we needed to include an autoregressive function to account for temporal autocorrelation in the time series, a challenge with other statistical models at fine temporal resolution. (4) We also wanted to account for uncertainty at various levels and propagate this through to predictions.

We use the model to predict daily stream temperature across the northeastern United States over a 34-year time record.

Approach

Statistical models of stream temperature often rely on the close relationship between air temperature and water temperature. However, this relationship breaks down during the winter in temperature zones, particularly as streams freeze, thereby changing their thermal and properties. Many researchers and managers are interested in the non-winter effects of temperature. The winter period, when phase change and ice cover alter the air-water relationship, differs in both time (annually) and space. We developed an index of air-water synchrony ($Index_{sync}$) so we can model the portion of the year that it not affected by freezing properties. The index is the difference between air and observed water temperatures divided by the water temperature plus 0.000001 to avoid division by zero.

We calculate the $Index_{sync}$ for each day of the year at each reach for each year with observed data. We then calculate the 99.9% confidence interval of $Index_{sync}$ for days between the 125 and 275 days of the year (05 May and 02 October). Then moving from the middle of the year (day 180) to the beginning of the year, we searched for the first time when 10 consecutive days were not within the 99.9% CI. This was selected as the spring breakpoint. Similarly moving from the middle to the end of the year, the first event with fewer than 16 consecutive days within the 99.9% CI was assigned as the autumn breakpoint. Independent breakpoints were estimated for each reach-year combination. More details regarding the identification of the synchronized period can be found in Letcher et al. (2016). The portion of the year between the spring and autumn breakpoints was used for modeling the non-winter, approximately ice-free stream temperatures.

We used a generalized linear mixed model to account for correlation in space (stream reach nested within HUC8). This allowed us to incorporate short time series as well as long time series from different reaches and disjunct time series from the same reaches without risk of pseudoreplication (Hurlbert 1984). By limited stream drainage area to <200 $km^2$ and only modeling the synchronized period of the year, we were able to use a linear model, avoiding the non-linearities that occur at very high temperatures due to evaporative cooling and near 0 C due to phase change (Mohseni 1999).

Stream Temperature Data (Dependent Data)

Summary of data by states, contributors (agencies), and locations.

Predictor Variables

General Results

The model results are summarized in this coefficients table. More results will be added in the future.