Predicting Daily Mean Stream Temperature with Daily MIN/MAX Temperatures
The initial stream temperature data used for this model has a total of 8462 observations.
There are 96 stations ranging in elevation from about 1707 to 2783 m.
The temperature data consist of the daily min, max and mean for the summer season.
These data came from continuously recording digital thermographs
and they allow establishing a relationship between the min/max data and the mean.
This relationship will then allow the use of the simple min/max thermometers to estimate "D".
In the graph below the thin, white line is the simple diagonal and the thick, green line
is the best linear regression.
The rough mean temperature is:
Rough Mean = (MIN + MAX) / 2.0
This equation is normally used for mean air temperature.
It is clear however, that this prediction is a little too high.
This is expected for the summer season because of the long days.
The regression equation with R-squared = 0.9862, is:
True Mean = 0.965 (Rough Mean) + 1.091°F
The station elevation is negatively correlated with these residuals as seen in the graph below.
The green line is the linear regression with R-squared = 0.08556:
RESIDUAL = 1.285°F - 0.000622 ELEVATION (m)
This regression is used to further improve the estimate of the daily mean
based on the min/max temperatures.
Combining all 3 equations:
MEAN = 2.3766°F + 0.965 ( (TMIN + TMAX) / 2.0 ) - 0.000622 ELEVATION (m)
As a final check, a seasonal plot of the improved model residuals is shown below.
There is little sign of any pattern or bias.
The mean error is 0.0004°F, the standard deviation is 0.5360°F
and the range is -2.9600°F to 2.8400°F.
The mean absolute error is 0.4070°F.
05 NOV 2001, updated on 06 NOV 2001
dlg@rapid.msu.montana.edu