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CADDIS Volume 3: Examples & Applications

Analytical Examples

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Analytical techniques used:

Type of evidence supported :

Spatial Co-occurrence with Regional Reference Sites


We would like to determine whether stream temperatures observed at a test site in Oregon are higher than those observed at comparable regional reference sites. If temperatures at the test site are higher than reference expectations, then we can conclude that increased temperature spatially co-occurs with the observed impairment. Conversely, temperatures at the test site that are comparable to temperatures at regional reference sites would suggest that increased temperature does not spatially co-occur with the observed impairment.


The Oregon Department of Environment Quality (ORDEQ) deployed continuous temperature monitors in streams from 1997-2002. These temperature monitors recorded hourly temperature measurement which were then summarized as seven day average maximum temperatures in degrees C (7DAMT). Sites were also characterized by the geographic location (latitude and longitude), elevation, and catchment area. Reference sites were designated in Oregon based on land use characteristics.

Analysis and results

scatter plots
Figure 1. Scatter plots comparing 7 day average maximum temperature (7DAMT) with elevation (top plot) and latitude (bottom plot).

Scatter plots are first used to examine the variation of stream temperature with different natural factors. The factors that are chosen (e.g., elevation, geographic location) must not be associated with local human activities. This initial data exploration suggests that stream temperature in reference sites are inversely related with both elevation and latitude (Figure 1). Next, regression analysis is used to model stream temperature as a function of elevation and latitude.

Both elevation and latitude are statistically significant (p < 0.05) predictors of stream temperature. The model explains approximately half of the overall variability in stream temperature. This model can be used to predict the reference expectations for stream temperature at other sites. That is, the reference expectation for temperature can be calculated as follows:

t = 76.6 - 0.0019E - 1.36L

where t is the stream temperature, E is the elevation of the site in feet, and L is the latitude of the site in decimal degrees.

Now, suppose a biologically impaired test site of interest is located at a latitude of 43 degrees N and an elevation of 1000 ft. We monitored stream temperature at this site and found that the seven day average maximum temperature at the site was 22 °C. Temperature is listed as a candidate cause of impairment at this site, and so we would like to know whether stream temperature at the site is elevated relative to the regional reference conditions. The reference expectation for stream temperature can be predicted as follows,

t = 76.6 - 0.0019(1000) - 1.36(43)

which gives a predicted reference temperature of 16.4 degrees. Most statistical software will also provide prediction intervals at a specified probability. For this case, 95% prediction intervals around the mean value are 11.4 and 21.4 degrees. Hence, the observed temperature is greater than temperatures we would expect for 95% of reference samples collected at the same elevation and latitude, suggesting that stream temperature is indeed elevated at the test site. We would conclude that at this test site, elevated stream temperature co-occurs with the biological impairment.

The CADStat Regression Prediction tool performs all of these calculations, and also determines whether conditions at test sites are within the range of experience of the set of reference sites.

How do I score this evidence?

Elevated temperatures co-occurs with the biological impairment so we would score this evidence as +.

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