2. Temperature Calibration
Procedure
I compared the temperature readings from the file Ola created for
each of the calibration periods and levels. I plotted
T1 - T2,3,4,5 vs. T1 and T5 - T4 vs. T5
Here is an example of one of these
plots (Figure 1.). I could not discern any change in the temperature differences
as a function of temperature (what I will call "slope" errors). But
there were systematic average differences (I call "bias" errors) that
seemed to be a function of time. I also plotted (not shown) the temperature differences
as a function of relative wind direction (RWD), wind speed (WS) and
shortwave radiation in order to look for any outside contamination effects.
In most cases the variations within each period were small. A few cases
had relatively large variations, often during low winds and at other times
for unknown reasons, perhaps frost blocking. These outliers were removed.
Then the median temperature difference for each level and each period
were calculated. Detailed notes for each period and level are
here.
In general the bias errors
were relatively small, less than 0.1 C absolute value. The level T5 vs. T1
bias (Red on Figure 1.) was the largest, 0.17 C.
I wanted to know whether these bias errors were at all realistic or just slow
random variations. I also wanted to see the temporal varibility of the bias
errors. I also wantd to try to "fill in" the bias errors during the large
wintertime gap. In order address these issues I created two data sets:
- A nearly-neutral stability (low flux) data set. This was when the absolute value of heat flux
at both levels of interest was less than 3 W/m2 and the wind speed was greater
than 5 m/s. I assumed that the sonic sound speed flux was the same as the true heat
flux.
- An extrapolated data set. This was when the absolute value of heat flux
at both levels of interest was less than 6 W/m2, the wind speed was greater
than 5 m/s and abs(Z/L) was less than 0.07. Using the heat and momentum fluxes
as measured from the tower, I assumed the existence of a constant flux layer and
used MO theory to extrapolate T1 to the level of interest. I used a bulk
humidity flux to determine the effect of humidity of density (it was small) and
I compared potential temperature values. Because flux data was not always available,
due to bad relative wind directions, frosting or other problems with the sonics, the number of available
points for this data set were quite small. I actually used two data sets,
one used tstar, zot and L based on the lower level flux measurements, another based
on the upper level tstar, zot and L. I used the surface temperature, To,
(required to determine zot) derived from the Epply. Using either method gave
essentially identical results;
the actual values used here are based on the zo, zot and L values derived from
the upper level.
Results
I have plotted the temperature biases from the calibration
periods and using the above two methods
(Figure 2, Figure 3, Figure 4, Figure 5).
I also plotted a summary of the median calibration period biases and the recommended
correction for all levels (Figure 6).
This comparison tells us the relative biases between the different levels. But it
does not tell the absolute values of the temperatures. I could look at the
surface temperature during zero or very low flux periods or use an extrapolation
method to extrapolate the surface temperature upward. But this would assume that
the surface temperature is exact, and I don't trust any of our surface temperature
methods the within the better than 0.1 C accuracy that would be needed to make this
useful. I also did not use the "wand" as an absolute calibration because I did not
think it was any more accurate than the tower instruments. Therefore, I simply took the mean of all the biases for each
period (defining the level 1 bias as zero) and subtracted this mean value from all
the biases shown above. I.e., I am assuming that the mean temperature of all the
levels was the correct temperature. I did not include the level 5 temperatures
for the periods 1 and period 2 because these were much cooler that the other
levels and considered outliers. If anyone has
any other ideas on how to determine the absolute values i.e. the overall bias,
please let me know.
Perhaps the laboratory calibrations could be used, but given the obvious temporal
variability I doubt this would be highly useful. The mean biases for each level
(compared to level 1) were:
| Period 1 |
Period 2 |
Period 2.5 |
Period 3 |
Period 4 |
Period 5 |
Period 6 |
| -0.0275
| -0.035
| -0.028
| 0.008
| -0.006
| 0.005
| 0.0175
|
I'm not claiming a temperature accuracy of one ten-thousandth of a degree, but I saw
no reason to eliminate digits.
Conclusions and Recommendations
All of the biases were quite small, which is good. Also the different methods
compared well. I estimate that after these corrections, the tower temperatures
were generally accurate (one standard deviation), relative to each other to within 0.03 C, except during
high frost periods. I'm not sure about the overall accuracy, but based on the
variation between sensors I would say about 0.05 C is reasonable for most periods.
For 95% confidence (about two standard deviations) I would double these estimates.
I recommend that the following MATLAB programs be used to correct the data in
the file that Ola created.
Click here to view and/or download
the temperature correction MATLAB program
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Introduction Page |
Relative Humidity Calibration |
Last update: 5/4/99
Please send all comments and suggestions to the author,
Peter Guest,