Characterising river temperatures
River temperatures are highly variable in time and heterogeneous in space. Consequently, it is difficult to characterise the temperature of a river using absolute values, such as a maximum or average temperature, as this only gives information about relative temperatures, e.g., that one one site was warmer than a different site on a particular day. Such information is highly dependent on prevailing weather and hydrological conditions and is, consequently, difficult to generalise. 

Rather than use absolute values, we quantify the thermal regime at our monitoring sites by relating water temperature to air temperature. This provides information about how responsive water temperature is to changing air temperature, which acts as a surrogate measure for solar inputs.  

Regression modelling and statistical parameters

Daily maximum water temperature is strongly related to concurrently measured air temperature, because air and water are both heated and cooled by solar forcing. Following the work of others, we have used logistic regression models to predict river water temperature at LUTEN sites from air temperature. Our models demonstrate that 84 to 94% of variance in daily water temperature can be explained by air temperature (see Johnson et al. 2013).

Logistic regressions have three parameters (see graph to the right) that can be physically interpreted, so:

River Dove valley looking towards site D5 and D6 (October 2012)Looking across the Dove valley towards Chrome Hill
A logistic regression model showing the three parameters 
  • the alpha parameter indicates the maximum water temperature that the model can predict (i.e. the models upper asymptote).
  • the beta parameter is the air temperature at which the gradient of the regression is greatest
  • the gamma parameter is the gradient at beta, giving an indication of the gradient of the relationship between air and water temperature.
These parameters have been used to identify LUTEN sites that are particularly susceptible to warming, for example, because they can attain very high water temperatures (high alpha values) or because water temperature rises steeply with air temperature (high gamma values) (see Johnson et al. 2013).

Regressions curves from a 'hot spot' (site D21 - Milldale) and from a cool spot (site D23 - Dovedale)

Site D23Looking downstream towards site D23 in Dovedale

Catchment controls on regression parameters

We have related logistic regression parameters to catchment characteristics in order to identify the controls on thermal characteristics of rivers. Of particular significance to the thermal regime of the River Dove and Manifold are groundwater inputs and cumulative upstream tree shade. 

Groundwater altered all regression parameters. In particular, groundwater limited the maximum achievable water temperature and lowered the regression gradient. As a result, areas of groundwater had a relatively consistent water temperature that did not change substantially as solar inputs changed. As a result, such areas may provide important refuge for organisms during periods of temperature stress elsewhere (see Everall et al. in review).

Regression models constructed at sites with substantial cumulative upstream shade had lower gradients than those with minimal shade. In other words, sites with relatively little shade were more responsive to changing solar inputs (see Johnson et al. 2013 and Wilby et al. 2014). 

Predicting nocturnal temperatures
Nocturnal temperatures are of great significance to nocturnal organisms but research has predominantly focused on daytime temperatures. We have adapted logistic regression models for use with nocturnal water temperatures. It was found that the addition of a multiplier, which accounts for the inertia in water temperature change and that is seasonally and site dependent, results in daytime air temperature explaining 80 - 94% of the variance in nocturnal water temperatures (see Wilby et al. 2014 for more information).