4. Sonic Wind Calibration

Procedure

Another type of error which I did not attempt to analyze was that the sonic probes themselves can affect the airflow and hence the value of the u and v components. However, this type of error is impossible to detect from a comparison of two sensors because it would presumably affect them both similarly. This would require a comparison with a different type of wind sensor, ideally in a wind tunnel. If anyone has any information on how we should correct for these "probe distortion" errors let me know. There must be some papers or ATI company reports about this. It may even be in the owners manual, I didn't check.

So there were four effects to sort out and possible temporal changes in these effects, at least the calibration effects. It is theoretically possible to distinguish airflow effects and/or orientation effects from calibration errors, if the calibration errors do not have large temporal variability. Here was my procedure. To simplify matters, I assumed that the sensors were correctly orientated because small changes in orientation would have a relatively insignificant effect on sensor differences compared to what I actually observed. One would expect that the calibration errors would not be a function of RWD, for a given u or v value. I will use the level 1 vs. level 2 u-component as an example of my procedure. I would plot U1 - U2 vs. U1 during times they were at the same level (calibration periods). At the same time I would plot separately, but on the same screen U1 - U2 vs. RWD. The points would be color coded so I could identify the same point on each plot. If there were variations in U1 - U2 vs. U1 for the same RWD during the same calibration period, I would assume that this was due to a slope calibration error. If RWD changed while U1 - U2 changed, I would be suspicious that airflow effects had an influence. If I had the fortunate situation that U1 - U2 changed significantly, RWD changed significantly, but the absolute value of U1 and U2 changed by a much smaller percentage than U1 - U2, then I interpreted this a clue that RWD and hence airflow effects were causing the changes in U1 - U2 values. Usually there were not enough data points during a single calibration period to sort out the airflow effects, the slope errors and the bias errors. I had to do a sort of iterative procedure where I would attempt to distinguish tower airflow effects from calibration effects from one period and then test whether these made sense in other periods. When they did not make sense in other periods I would have to re-do my original assumptions and try again. This process had to be performed for each component of each sensor at every level. Fortunately, after analyzing the data for awhile, it became apparent that, in general, the bias and slope errors did not seem to change over the course of the experiment. Therefore I was able to look at plots of U1 - U2,4,5 vs. U1 and U1 - U2,4,5 vs. RWD (and the v-components) for the entire experiment and combine calibration periods. One obvious exemption was the level 3 sonic. The bias and slope characteristics of both u and v components showed an obvious change around JD 400. From the log I noted that there had been several problems with this sensor and it had been removed for repairs at this time. I'm not sure if a new sensor was installed, but whatever happened it was apparent that the calibration was different. But within these periods (before and after JD 400), the calibrations seemed consistent.

If the calibrations had shown significant temporal variations, such as with the scalars, I think the calibration procedure would have been a lost cause. But as it turned, I think I was able to detect differences between sonics that were truely due to calibration errors that could be corrected to result in more accurate measurements. For example check out the comparison of the Level 1 vs. Level 5 sonic u-component (Figure 9.). The slope and bias seemed quite consistent throughout the experiment. So in this case it was quite straightforward to deduce a slope and bias relationship between these two sensors that could be applied to the entire experiment. Effects related to RWD differences were usually consistent with what would be expected. For example when RWD was around 120 degrees U1 - U2,3,4 were relatively lower and V1 - V2,3,4 were relatively higher, which is consistent with the tower starting to block and slow the fixed level winds, but not the hazer. (The u-component is negative from this direction, hence the lower hazer - fixed difference.) Even more obvious were the changes in U1 - U2,3,4 and V1 - V2,3,4 that occurred when RWD was 200-300 degrees, a region where the hazer levels would be expected to be more affected by the tower than the fixed levels. I concluded that for the range 100 < RWD < 300 the airflow effects were significant enough that it was not possible to look at calibration effects. I excluded all points from this RWD region from the final analyses.

Unfortunately the slope and bias relationships were always not as apparent as the example shown above, even outside this RWD range. For example check out the Level 1 vs. Level 4 v-component comparisons (Figure 10.). It is obvious that there will be considerable uncertainty in any calibration correction based on this data.

In order to independently check the calibration corrections and try to make some sense of the ambiguous comparisons, I used two methods, both of which were based on data not in the calibration periods. For the first method, which I call the "zero wind" check, I chose data from periods when the wind speed was less than 1 m/s at level 4. I determined the median U1 - U2,3,4,5 and V1 - V2,3,4,5 differences for the zero wind data set. I then compared this with the biases determined from the calibration periods. Here are the results:

The correlation between the methods is pretty good for the u-component, and not too bad for the v-component. The correlation coefficient was 0.89. There was probably real variability in winds during these "zero wind" periods, which, were not truly zero. I believe this independent comparison shows there is considerable skill in the calibration biases.

As another check I used the measurements of wind stress and heat flux to extrapolate the wind vector from level 1 to the upper levels, similar to what was done for temperature. I used only cases when abs(z/L) was < 0.07 and RWD < 100 or RWD > 300. I kept the lower level RWD for the extrapolation to the upper level. I used zo, zot, ustar and tstar from the upper level (using the lower level produced almost identical results) and MO theory for the extrapolation. These were called the "original data" extrapolations. I then performed the "corrected" data extrapolation. This was done by converting the lower level WS and RWD to u and v components, making the corrections, converting back to WS and RWD and extrapolating up to the higher levels using MO theory. The ustar (and therefore, L) that I used for the extrapolation was corrected by the same amount as the wind speed because I assumed that fluctuations were affected in the same way as mean wind. I then converted the extrapolated WS and RWD to u and v components and compared them with the measured u and v components at that level. If it was obvious that some of the calibrations were based on points that were clear outliers from all the data, I then removed these points, performed the calibration all over again and cycled through the procedure once again. Because there were so many more data points available from the extrapolated data, it was tempting to base the corrections on this data only. But the problem with this was that I would be adjusting the data to fit my MO theory expectations, which included k = 0.4, and when we later try to evaluate the value of k, the constant flux assumption and the dimensionless stability functions, we would find that they matched what I used, because they were forced to by my calibration procedure. For this reason I tried not to put to much weight on the extrapolated data, unless the calibrations period results were really ambiguous. This extrapolation procedure was primarily done as a check to see if the calibration corrections had any skill at all or were just based on random fluctuations due to tower effects or other factors. There was considerable subjectivity in the final specification of the calibration biases and slopes. The procedure was so complicated, I think it would have taken me months to develop an objective procedure and even this would require some subjectivity in removing outliers. Detailed notes on the comparisons are here.

Similar to temperature and RH I used the mean biases and slopes from all the levels to determine the "true" u and v calibrations, i.e. the corrections applied to level 1 (and the other levels in addition to the above values). In this case the same values were assumed for the entire experiment.

Component	Mean Bias	Mean Slope
U	0.224	-0.0365
V	-0.078	-0.0372

Here are plots comparing the original and corrected differences in winds between the lower hazer and upper levels. For simplicity I just show the WS differences, not the individual components.

• Figure 11. WS1 - WS2
• Figure 12. WS1 - WS3
• Figure 13. WS1 - WS4
• Figure 14. WS1 - WS5

As you can see from the above figures, the suggested calibrations did improve the comparisons for the extrapolated data set. Most of the cases where the intercomparison calibration periods were way off occurred when the tower was probably affecting the the comparisons. In addition to plotting the level 1 u,v and total WS components minus the same at a particular level, I also plotted the differences vs. RWD in order to identify tower airflow effects. An example which includes extrapolated data is shown in Figure 15. Another figure shows the the same type of plot, but in this case the differences between sensors are divided by the WS1 so that a relative difference is shown. This one shows all the calibration periods at once, without the interpolated data set Figure 16.

Click here to view and/or download the sonic wind correction MATLAB program that I recommend.

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Last update: 5/4/99

Please send all comments and suggestions to the author, Peter Guest,