# The Microwave Temperature and Humidity Profiler: Description and Preliminary Results
## 3 Calibration Strategy  
As with other radiometers, MTHP measurements require frequent calibration to compensate for \(T_{receiver}\) variations and gain fluctuations. To calibrate MTHP measurements, a three-point calibration method is used for the 60 GHz channel, and a two-point calibration method is performed for the 183 GHz channel. The two-point calibration method uses the two internal calibration loads (ambient and hot), and the three-point calibration method uses the two loads and the static air temperature (SAT) read by the airplane's temperature sensor. At cruise altitude, the cross-section of air in front of the instrument is maximum, hence the measured brightness temperature at 60 GHz matches the SAT since the oxygen at the exact absorption band behaves as a blackbody ([22], Chapter 8). Note that the ambient temperature load at high altitudes (altitude > 10 km) is never as cold as the SAT since it is affected by the heat generated by the instrument. This calibration scheme would enhance the estimation of the system noise temperature and gain on the 60 GHz channel. The first step to calibrate the data is to collocate all measurements with respect to the rotor position. This is performed in post-processing once all data collected by the instrument are retrieved. The rotor position readings are synchronized with the spectral measurement at both 60 GHz and 183 GHz channels to ensure independent data. The rotor data synchronism is achieved by measuring two ABZ optical encoders mounted on the rotor assembly, one for each backend the 60 GHz and the 183 GHz channel. Bins of \(5^{\circ}\) are generated between \(0^{\circ}\) and \(360^{\circ}\) resulting in a total of 72 angular bins. A drop-in-the-bucket strategy is followed, and each measurement is assigned to its closest angular measure. To obtain a 60 GHz \"full spectrum\" (i.e., 8 GHz, from 51 to 59 GHz) measurement, four consecutive rotations (6.48 s or 4 rotations) are grouped together and averaged as follows:  
* Two consecutive measurements of the lower-side band (51-55 GHz) are averaged together and concatenated to two consecutive measurements of the upper-side band (55-59 GHz), which are also averaged together. * Four rotations of the 183 GHz channel are averaged together. Note that since the atmosphere does not drastically change within 6.5 s (assuming travel of approximately 2 km at maximum Airplane speed), averaging 4 full rotations and considering it to be a single sample is acceptable for our case. Therefore, we obtain a multi-incidence angle (\(5^{\circ}\) resolution) acquisition sample from 51 to 59 GHz and the 183 GHz channels together every 6.48 s.  
The 72 angular points for each of the 60-GHz 2048 frequency samples and the 4 183-GHz frequency samples are treated as a single atmospheric measurement. Additionally, to reduce the receivers' noise at the 60 GHz channels, 8 consecutive frequency bins are averaged, producing a total of 256 channels covering 8 GHz of the spectrum (\(B_{N_{\mathrm{6}}y}=34.6\) MHz/channel). This strategy allows us to reduce the NETD of the 60 GHz spectrometer by a factor of 2.48, i.e., from 3.63 K down to 1.46 K.  
The calibration continues by taking the 72 angular points for the 60 GHz moderate-resolution spectrogram (31.25 MHz bandwidth, 256 channels) and 72 angular points for 4 measurements (250 MHz bandwidth) at 183 GHz across the entire rotor range of motion every 6.48 s. To calibrate the measurements using the external targets at 60 GHz, points at a rotor angle of \(\theta=[300^{\circ},340^{\circ},~{}90^{\circ}]\) are retrieved. Those points are facing two internal targets and forward, respectively. For the 60 GHz channel, the airplane SAT and the thermistor measurements of the thermally controlled and ambient targets are compared. The three-point calibration method uses a linear regression to estimate the model: \(T_{est}=a+b\cdot m\), with \(m\) being the raw measurement counts in the spectrogram, and a and b the estimated receiver noise and system gain, respectively.