Hereafter, "FG" refers to the flux gate compass. For all mobile mesonet data from VORTEX-95, whenever the vehicle was moving faster than 4 m/s the following pairs were recorded: {FG direction, FG-GPS direction}. Thus, a value >0 in the second position means the FG reads too high near that azimuth. Only pairs more than 5 degrees removed from the compass cardinal points (n, E, S, and W) were retained. This is because the vehicles were usually moving in one of those four directions, and the huge number of data points could bias the calibration.
The data were plotted using SciPlot (a freeware scientific graphing application for NeXTStep), and then the following equation was fit to the data:
y = A+Bsin(x)+Ccos(x)+Dsin(2x)+Ecos(2x) where y = FG-GPS, and x = FG.
This is simply the first two terms of a Fourier series, and was chosen because it is easy to fit, and recognizes the periodic nature of compass directions.
Note that this calibration procedure negates the need to adjust the FG compasses to true vs. magnetic north. We are calibrating them against GPS, which is a true system. Thus, the calibration coefficients inherently contain the offset for the average declination. The application, or lack thereof, of FG corrections in the MM software itself becomes totally irrelevant. The wind directions are derived from RMY directions and FG pointing angles. If we can be confident of the FG pointing angles (through this calibration), we can be confident of the wind directions.
This example is a plot of calibration points and the derived calibration curve for the vehicle PROBE1 (P1). It can be seen that the error in the flux gate compass, primarily caused by the vehicle's magnetic field, is about 12 degrees when the vehicle heading is roughly southwest, and generally less than this amount for other headings. Visual inspection shows that most points cluster within about 5 degrees of the fitted curve.
The notes that follow are mainly unedited notes composed while the calbrations were being performed. If any of this requires elaboration, email rasmussen@nssl.uoknor.edu, and hope that my memory contains something useful.
The PROBE1 laptop was apparently used by some other vehicle on 8-9 June. By that time, P1 was supposedly decommissioned. However, the P1 laptop has data on those dates, with a radically different calibration of the FG on 8-9 June. Calbiration curves will be obtained for the period through 4 June only. If the P1 data are to be used on 6/8, whichever vehicle it was, we will need to do a special FG calibration as well as determine the RMY pointing error for that day alone.
Number of samples: 15,766 Average absolute error prior to calibration: 6.45 degrees Average absolute error after calibration: 2.91 degrees
PROBE2 had consistent errors through the whole season. Number of samples: 17,653 Average absolute error prior to calibration: 8.42 degrees Average absolute error after calibration: 2.61 degrees
PROBE3 had consistent errors through the whole season. Number of samples: 16,380 Average absolute error prior to calibration: 5.83 degrees Average absolute error after calibration: 3.02 degrees
PROBE4 had consistent errors through the whole season. Number of samples: 15,361 Average absolute error prior to calibration: 4.29 degrees Average absolute error after calibration: 3.28 degrees
PROBE5 had consistent errors through the whole season. Number of samples: 21,268 Average absolute error prior to calibration: 8.28 degrees Average absolute error after calibration: 2.72 degrees
PROBE6 had consistent errors through the whole season. The initial graphing appears to have a lot more scatter than some of the other platforms. Number of samples: 19,579 Average absolute error prior to calibration: 10.94 degrees Average absolute error after calibration: 2.90 degrees
The PROBE7 FG calibration changed after the 4/30/95 mission. So the calibration must be performed in two separate runs. First group; P7a: Cases prior to 5/1/95. Number of samples: 5,450 Average absolute error prior to calibration: 40.41 degrees Average absolute error after calibration: 2.90 degrees First group; P7a: Cases after 5/1/95. Number of samples: 10,626 Average absolute error prior to calibration: 5.17 degrees Average absolute error after calibration: 2.63 degrees
PROBE8 had consistent errors through the whole season. Number of samples: 18,122 Average absolute error prior to calibration: 8.97 degrees Average absolute error after calibration: 2.77 degrees
PROBE9 had consistent errors through the whole season. Number of samples: 12,403 Average absolute error prior to calibration: 7.77 degrees Average absolute error after calibration: 2.56 degrees
TURTLE1 had consistent errors through the whole season. Number of samples: 12,011 Average absolute error prior to calibration: 7.66 degrees Average absolute error after calibration: 2.67 degrees
TURTLE2 had consistent errors through the whole season. Number of samples: 19,133 Average absolute error prior to calibration: 8.11 degrees Average absolute error after calibration: 2.75 degrees
NSSL1 had consistent errors through the whole season. The scatter plot shows that the N1 sensor had a significantly larger-amplitude error than the units on the sedans. Number of samples: 20,136 Average absolute error prior to calibration: 15.25 degrees Average absolute error after calibration: 3.54 degrees
NSSL2 had consistent errors through the whole season. Number of samples: 20,285 Average absolute error prior to calibration: 9.13 degrees Average absolute error after calibration: 4.59 degrees
NSSL4 FG had an equipment change or a calbration after the 4/26/95 mission. On that mission and prior, the average FG errors were around 80 degrees. After that date, they were around -10 degrees. Therefore, two different calibrations must be used for this vehicle. First group; N4a: Cases prior to 4/29/95. Number of samples: 2,473 Average absolute error prior to calibration: 81.32 degrees Average absolute error after calibration: 4.58 degrees First group; N4b: Cases after 4/28/95. Number of samples: 17,515 Average absolute error prior to calibration: 18.39 degrees Average absolute error after calibration: 4.39 degrees
The performance of the FC compass seemed to change around 4/18. So the calibration was run in two parts. This is confirmed by looking at the scatter plots. However, the scatter about the large-amplitude error curves was fairly small, leading to the good absolute error results shown below. First group; FCa: Cases prior to 4/18/95. Number of samples: 3,892 Average absolute error prior to calibration: 82.36 degrees Average absolute error after calibration: 3.35 degrees First group; FCb: Cases after 4/18/95. Number of samples: 18,196 Average absolute error prior to calibration: 16.72 degrees Average absolute error after calibration: 4.29 degrees
CAM1 had consistent errors through the whole season. Number of samples: 11,933 Average absolute error prior to calibration: 5.31 degrees Average absolute error after calibration: X.XX degrees
Veh A B C D E ave abs error P1 5.2103 -3.0160 -2.8220 -0.2519 0.1059 2.91 P2 7.4855 -3.0830 -1.9402 -0.4022 -0.3234 2.61 P3 4.0520 -2.6925 -3.6788 -0.6090 -0.5131 3.02 P4 0.539 -0.7660 -4.4933 -0.2732 -0.2292 3.28 P5 7.7902 -0.9188 -3.9160 0.0324 -0.4591 2.72 P6 10.248 -0.6967 0.0610 -0.5260 -0.5933 2.90 P7a -41.678 -4.1116 -0.0619 -0.7489 -0.3579 2.11 P7b 3.8138 -1.7244 -3.2351 -0.1186 -1.0482 2.63 P8 7.5597 -2.3033 -2.9932 -0.3886 -0.3699 2.77 P9 5.5201 -4.7514 -5.4312 -0.9971 -1.0899 2.56 T1 6.6508 -3.1098 3.5417 -0.5266 -0.0637 2.67 T2 7.7146 0.5168 -3.7172 -0.4984 0.5528 2.75 N1 11.8505 -8.8821 -3.2433 -0.166 -0.2618 3.54 N2 8.6005 6.5244 4.6025 -0.5648 1.2422 4.59 N4a 83.2274 18.1516 18.0258 1.8348 1.1860 4.58 N4b -6.3063 17.6484 -17.007 -0.8563 -0.5729 4.39 FCa -82.126 -9.8598 -22.914 -1.1593 -0.5630 3.35 FCb 7.5719 23.4466 -7.616 1.7824 -0.1171 4.29 C1 3.4844 -0.7399 -1.8489 -1.2279 -0.3748 3.18