The concept of measurements by the MTP as a passive total-power radiometer (Denning et al., 1989; Ulaby et al., 1981) is straightforward. The MTP records thermal radiation mainly emitted by oxygen molecules in the atmosphere. Like many radiometers measuring atmospheric temperature, the MTP uses absorption lines of the 60 GHz oxygen complex (“V band”), which are caused by magnetic dipole transitions (Liebe et al., 1992). Passive radiometers pick up the energy transported by the photons emitted in these transitions. In this part of the spectrum, the Rayleigh–Jeans relation (e.g., Ulaby et al., 1981) can be used to describe the source function of the radiance picked up by the MTP: 1Bν,T=2hν3c2⋅1exp⁡hνkBT-1≅2ν2c2⋅kBT, in which the measured radiance is equal to the brightness B of a black body described by Planck's law. This equation implies a linear relationship between the measured radiance and the temperature T of the black body source at a certain frequency ν using the Planck constant, h, velocity of light, c, and the Boltzmann constant kB. This temperature, T, is referred to as brightness temperature (TB), which is the temperature of on an ideal black body emitting the equivalent radiance. The recorded TBs have to be converted to absolute temperature profiles by using a retrieval algorithm that utilizes forward radiative transfer calculations, in which, ideally, all possible impacts on the measured radiance (e.g., water vapor, nitrous oxide, or hydrometeors) have to be considered. For correct interpretation of the fluctuations found in the retrieved temperature fields, it is necessary to have precise knowledge of the instrument characteristics, such as the instrument response function, antenna diagram (see Sect. 3), and the precision and accuracy of the brightness temperature measurements that are input to the retrieval algorithm (see Sect. 4).

In the MTP instrument, a horn antenna guides the incoming atmospheric radiation and, together with the hyperbolic shape of the rotating mirror, determines the spatial response function. The measurements are based on the heterodyne principle, which means that through mixing with a defined frequency, the local oscillator frequency (LO), the incoming signal is converted to an interim frequency (IF) near base band. Both difference frequencies below and above the LO frequency are down-converted to the IF in the double-side-band receiver. Low-pass filtering suppresses any incoming radiation outside the IF bandwidth of 200 MHz such that the symmetric spectrum around the current LO frequency is measured with only a minor gap of approximately 20 MHz at the LO frequency. The IF signal is converted to a voltage, which is proportional to the squared input amplitude, representing the power. This voltage is finally translated to a digital count number, stored in the MTP data file, and later converted into a brightness temperature through calibration (see Sect. 4). The physical temperatures of the important radiometric parts of the radiometer, such as the mixer, synthesizer, amplifiers, and the electronics, are stabilized to minimize the influence of the changing conditions during a research flight on the instrument state and to protect the electronic parts from malfunction due to condensation (see Mahoney and Denning, 2009, for further details).

Using a rotating mirror in front of the instrument's feed antenna (number 3 in Fig. 1b), the direction from which the radiation is collected can be changed. Moving through a single set of elevation angles, as well as the set of frequency channels at each of those elevation angles, is referred to in the following as a measurement “cycle”. This procedure enhances the vertical resolution of measurements in comparison to non-scanning measurements, which derive altitude information solely from exploiting frequency-dependent differences in the optical depth of the atmosphere. The MTP combines both principles. In its standard deployment settings, as programmed in the original JPL instrument software, 10 viewing angles are used during one measurement cycle: five above the horizon, four below, and one pointing exactly towards the horizon. At each angle, measurements at three frequency channels, corresponding to the frequencies of three strong oxygen absorption lines, are subsequently performed (see Table 1) before moving to the next elevation.

Furthermore, a calibration target is built into the instrument (number 2 in Fig. 1b), to which the mirror points after each cycle of atmospheric measurements. The target itself consists of carbon–ferrite on an aluminum plate, which is heated to a constant temperature (approximately 45 ∘C) using two conventional power resistors. The calibration target is surrounded by a 1 in. thick Styrofoam insulation, which is transparent for microwave radiation. The signals recorded while pointing towards the heated target are combined with a noise diode (ND) signal and used for calibration (see Sect. 4) to convert the measured signal to a TB, which is usually not equal to the outside air temperature, since the measured signal is influenced by multiple layers of the atmosphere. To derive absolute temperature from the radiation measurement, radiative transfer calculations have to be carried out and compared to the measured radiances by applying a retrieval algorithm in post-processing. The instrument characteristics presented in the following sections of this work all correspond to the raw measurements or the brightness temperatures, which are input to such a retrieval algorithm. However, a discussion of retrieval algorithms and related uncertainties is beyond the scope of this paper.

Differences to older instrument designs are presented in Lim et al. (2013) and Haggerty et al. (2014). The most important upgrade is that the LO is now defined as a frequency near (or ideally at) an oxygen absorption line center so that the two flanks that are measured belong to the same line, which lowers the brightness temperature error, as discussed in Mahoney and Denning (2009) and Lim et al. (2013). The instrument is pointing forward, measuring the temperatures of air masses in front of the aircraft. The filter bandwidth of the HALO MTP is fixed to ±200 MHz around the LO, with a gap of approximately 20 MHz at the line center (see Fig. 2a). The synthesizer used to generate the LO for down-conversion of the signal can be tuned between 12 and 16 GHz. The synthesizer output is doubled twice, potentially allowing for a frequency range of 48 to 64 GHz for atmospheric measurements. The preset (“standard”) set of LO frequencies used was chosen based on the considerations presented in Mahoney and Denning (2009) and Lim et al. (2013). This set of frequencies is used for this study.

Two significant modifications to the original instrument were made by DLR: an embedded computer and an inertial measurement system including a Global Positioning System (GPS) antenna. In the original setup a Visual Basic software package was provided by NASA–JPL to run the instrument during research flights. With the onboard computer and integration of the inertial sensor, this software was translated to a LabView code, which was adjusted to use the additional data provided by the inertial sensor. With those modifications, the HALO MTP can be operated autonomously, i.e., independent from a connection to a cabin computer, which is still provided and can be used, e.g., to adjust settings during research flights using the HALO LAN network.

The HALO MTP was first deployed during the Midlatitude Cirrus Experiment (ML CIRRUS) in 2014 (Voigt et al., 2017). The focus of this mission was to probe natural cirrus clouds and contrail cirrus throughout various stages of their life cycles. The MTP was part of the wing-probe instrumentation and recorded data during all mission flights. In total, the HALO MTP produced almost 63 h of data during 13 mission flights, recording 17 476 individual measurement cycles. Data from this campaign will be used to derive the HALO MTP noise characteristics and in the investigation of calibration methods in the following sections.

The measurements of the instrument transmission functions, as well as of the antenna diagram, were made in a chamber completely covered in microwave absorbers. The MTP was installed on a rotatable platform. A tuneable signal source with a horn antenna was placed at 5 m of distance to the MTP instrument. The signal was then measured by the MTP and by a power meter for reference. The power of the source signal was chosen such that the MTP signal was well above its inherent noise level. For the measurement of the filter function, the source frequency was tuned between LO - 300 MHz and LO + 300 MHz in steps of 1 MHz. The measured signal is normalized and then corrected for frequency dependency based on the Friis transmission equation (e.g., Balanis, 1997): 2countscorr=countsnormf2/min⁡f2. Finally, the signal power of the source, Pcorr(f), is taken into account in a final normalized signal representing the relative forward transmission, countsfinal: 3countsfinal=countscorrPcorr(f). The resulting instrument transmission functions for the three standard frequency channels are shown in Fig. 2a. It shows symmetrical shapes for all frequency channel functions (i.e., radiances are recorded symmetrically from both flanks of the probed oxygen line), confirming a transmission of the signal at ±200 MHz around the LO (the width of the plateau). The gap in the center is created by the receiver architecture using a double-side-band receiver as explained in Sect. 2. A certain “waviness” with an amplitude of about 0.5 dB is visible next to this gap. To exclude reflections from the chamber as a source, the measurements were repeated multiple times with slightly different positioning of the source antenna and the instrument. Since the results were similar in all measurements, the source of this waviness is attributed to some internal source within the instrument due to electromagnetic wave propagation through the instrument parts.

The main result of measuring the antenna diagram is the field of view (FOV) of the instrument, defined by the full-width half-maximum (FWHM; red dashed lines in Fig. 2b and c) of the antenna diagrams. It is actually mainly defined by the hyperbolic shape of the rotating mirror at the front of the instrument. The measurement was made using the same laboratory setup as for the measurement of the transmission function. Both the horizontal and the vertical plane were measured in steps of 1∘ rotation. The symmetric shape of the diagram implies that radiance is picked up equally strong from all directions. Note that the maxima of the side lobes in the antenna diagrams have a maximum at -30 dB, meaning the signals from these spatial directions are 1000 times weaker than the signal picked up from the main viewing direction. The FOV is about 7.0–7.5∘ in the horizontal and about 6.5–7.0∘ in the vertical at all frequencies.

A spillover measurement of the horn antenna (as investigated, for example, in McGrath and Hewison, 2001) and a test of the stability of the LO frequency generator were not possible, as this would have required disassembling parts of the instrument, which was not an option at that time due to aircraft certification issues.

To investigate the temperature dependence of instrument performance, a series of measurements inside a cold chamber was performed (see Fig. 3). During this measurement series, the temperature of the cold chamber was successively lowered from 21 to -15 ∘C in steps of 5 ∘C. This temperature range resembles the temperatures the MTP experienced during its deployment in the ML CIRRUS campaign in 2014, as shown in Fig. 4b. The pod air temperature sensor monitors the temperature inside the MTP's housing during the flight (see Fig. 1b). In the cold chamber, the housing was not installed to prevent overheating of the instrument at higher temperatures. As a result, the readings of this sensor show the air temperature inside the cold chamber. The scanning unit temperature sensor keeps track of the temperature of the MTP instrument within close proximity to the crucial parts of the radiometer, such as the amplifiers and the mixer. The readings of this sensor give an impression of the state of the instrument and its thermal stability. It can be seen that the response to lowering the cold-chamber temperature is different between the two sensors. This is caused by the placement of the sensors, with one being closer to some heated parts of the instrument, indicating that changes in the environment of the instrument do not equally influence all parts of the instrument. Moreover, from the readings of the scanning unit temperature sensor (black line in Fig. 4a) it can be seen that the MTP instrument takes some time to stabilize under the new temperature conditions. This time required for stabilization depends a lot on the operating environment, such as the size of the laboratory space, ventilation, and ambient temperature. In this setting, it takes up to 15 min after the initial temperature change. Only those parts of the measurement series are used in which the scanning unit temperature is stable (the difference between two readings being smaller than an empirical threshold value of 0.04 K) to exclude effects from the instrument adjusting to new environmental conditions.

Along with the MTP instrument two microwave absorbers (Telemeter Electronic GmbH EPP51 broadband pyramidal absorber) at ambient temperature (hereafter referred to as “ambient targets”) and a similar microwave absorber submerged in liquid nitrogen (hereafter referred to as the “cold target”) were placed in the chamber in order to perform calibration measurements throughout the complete measurement series. The third type of calibration target used in this measurement series is the built-in calibration target of the MTP instrument (see Sect. 2), hereafter referred to as the “hot target”.

The instrument's noise was characterized using the signal measured when pointing towards the hot target. It is assumed that due to the temperature stabilization of the target, the mean measurement signal should not change over time. Hence, the deviation from the mean represents the noise added by the instrument. An example of the measured signal while looking at the hot target during one measurement segment at constant cold-chamber temperature is shown as the grey line in Fig. 6. Obviously, absolute stability can hardly be reached in a cold environment, while parts of the sensor unit are heated to approximately 40 ∘C, which is taken into account by applying a linear fit to the measured data of one segment (black line in Fig. 6) instead of simply subtracting the mean (blue line in Fig. 6). Using all segments of the cold-chamber measurements, the resulting HALO MTP noise characteristics, as shown in Fig. 7 (top), can be described by a Gaussian distribution with a standard deviation of approximately 6 counts (approximately 0.25 K) and a mean of 0 counts.

The same method as for the cold-chamber measurements is used for HALO MTP data recorded during the ML CIRRUS campaign in 2014. Here, the criterion used to determine flight segments with nearly stable instrument states is a difference in the scanning unit temperature of less than 0.04 K between two measurement cycles. Additionally, it was ensured that no altitude changes were made (Δz≤25 m) and no curves were flown during these segments. From all ML CIRRUS mission and test flights, 61 segments could be identified that satisfied the criteria and were at least 5 min long to ensure significance of statistical results from the length of one segment: with the length of one measurement cycle (including a calibration measurement at the end) at 13 s each segment includes at least 22 recordings of the hot target measurement signal. Figure 7b shows the noise characteristics at 56.363 GHz. The results from the flight data evaluation are in excellent agreement with the values found in the laboratory environment, showing even smaller standard deviations of 5.2–5.7 counts, depending on the frequency channel. This is strong evidence that the HALO MTP noise characteristics do not change between flights, and laboratory assessment can be used to determine overall instrument health and comparability of measurements between campaigns, also serving as information for the retrieval development.

For the spectral analysis of the MTP measurement noise the 61 ML CIRRUS mission flight segments are used again. Due to the varying lengths of the individual flight legs, the data are concatenated to a single timeline for spectral analysis. The power spectrum of the noise signal of the HALO MTP at 56.363 GHz, as shown in Fig. 7 (bottom), reveals that the measurement noise can best be described as red noise, which is characterized by the autocorrelation α between a data point of the time series and its precursors. According to Torrence and Compo (1998), the corresponding theoretical noise power spectrum for a range of wave numbers k, Pk, is given by 5Pk=1-α21+α2-2αcos⁡(2πk/N). For the three standard frequency channels, the lag-1 autocorrelation of MTP measurements during the ML CIRRUS campaign is α≅0.7. Fit parameters characterizing the noise characteristics at the three standard frequency channels are summarized in Table 2.

With the above findings, characterizing the HALO MTP measurement noise as Gaussian-shaped, with a mean of 0 counts and a standard deviation of 6 counts, as well as with the knowledge of the inherent periodic structure of the noise signal, it is now possible to determine whether periodic structures in an MTP temperature measurement time series are significant (high probability that they result from atmospheric temperature fluctuations) or noise-induced. Additionally, the standard deviation of the Gaussian distribution of noise values can be used to determine the variance of TBs derived from the raw signals once the calibration parameters are known. While it would be interesting to investigate the integration time needed to significantly reduce the measurement noise (e.g., by applying the Allen variance), any increase in integration time will decrease the horizontal resolution of measurements taken on a jet-engine aircraft. The current settings present a well-chosen compromise between the measurement noise and the horizontal resolution of the MTP data (MJ Mahoney and Richard Denning, private communication, 2013). As the calibration measurement is already made at the end of each measurement cycle, the instrument is calibrated as frequently as possible, and the calibration performance cannot be further improved by adding more calibration measurements during mission flights.

When performing cold target measurements, the interference with a standing wave present between the instrument's receiver hardware and the surface of the slowly evaporating liquid nitrogen (see also Sect. 4.1.1 in Küchler et al., 2016) was taken into account. As the HALO MTP is a total-power radiometer (Denning et al., 1989), the output voltage of the detector is proportional to the square of the incoming intensity (Ulaby et al., 1981; Woodhouse, 2005). Thus, the times with the least interference of the original signal and the standing waves are defined by minima in the measured signal time series. To find those minima in the cold-chamber measurement time series, several steps were taken: (i) a running average (N=25) is used to minimize the noise in the data; (ii) a spline fit is used to find a smooth curve, representing the measurements; (iii) the fit is used to interpolate to a higher time resolution; and (iv) the minima of this interpolated curve are used to identify those individual measurement cycles closest to the minima in the time series on which the calibration will be based. Due to noise, the calibration becomes more reliable if a mean of more than one measurement close to a minimum in the time series is used; hence, the five measurements closest to the time of a minimum in the smooth curve are always included in the analysis.

The resulting calibration parameters are plotted over the corresponding scanning unit temperatures at the time the minimum in the cold target measurements occurred. Figure 8 clearly shows that the parameters change with the scanning unit temperature. That corroborates the assumption that HALO MTP flight data cannot simply be calibrated by using fixed calibration parameters from laboratory measurements at single arbitrary room temperatures, since such measurements are only representative of specific instrument states. Still, it is possible to apply a linear fit to the data by providing a relationship between the MTP scanning unit temperature and the calibration parameters to be used at these temperatures. The same is true when using the hot target measurement signal as a reference, which might better represent the current state of the instrument than the scanning unit temperature. The linear fit parameters are summarized in Table 3.

When applying this (default) calibration method to MTP data, everything builds on the following two assumptions: (i) the ND offset signal is the same each time the calibration measurements are performed, and (ii) the TB measured when pointing towards the heated target corresponds to the measurements of the temperature sensors at the back of the target. Both assumptions are tested in the following using the calibration measurements performed in the cold chamber.

There are eight different ways to perform the calibration calculations with and without applying the corrections discussed in the previous sections, as summarized in Table 6. All methods are compared to find the best practice of deriving TBs from MTP raw counts by applying all eight methods to the same set of mission data. To do so, segments from all ML CIRRUS mission flights are used during which the altitude of the aircraft did not change by more than 50 m during a measurement cycle and no curves were flown (roll smaller than 5∘). Note that this definition of usable segments is not based on any parameters connected to the instrument state of the HALO MTP (e.g., scanning unit temperature), leading to the inclusion of measurement cycles with possibly unstable measurement conditions, e.g., shortly after altitude changes. The only exception is that only those segments are used, during which the ND did not show failures, to ensure comparability of all calibration methods. This way, 38 flight segments with at least a 10 min duration (i.e., including at least 50 measurement cycles) could be identified. The TBs are calculated based on each individual measurement cycle, but using the calibration coefficients (scal and TR) calculated from the average of the relevant data from the seven previous cycles, the seven following cycles, and the cycle itself (N = 15) to account for noise in the calibration measurement signals. As an example, the resulting TBs of the 56.363 GHz measurements at a 0∘ limb-viewing angle during one segment of ML CIRRUS flight MLC10 on 11 April 2014 are shown in Fig. 10 (top panel). The TBs resulting from all calibration methods show the same time-dependent variations and mainly differ in their offset to HALO TS, indicating that differences in the respective calibration coefficients affect the absolute accuracy of the derived TBs more than the precision.

To further investigate the precision of the MTP measurements, a leg-mean value of the HALO TS and the TBs of the 0∘ elevation measurements is used to determine the offset, which is subtracted from the TBs at all elevation angles: 9TBcorrνLO,α=TBνLO,α-TBνLO,0∘‾-TS‾, with TBνLO,αand TBcorrνLO,α denoting the original and the corrected TBs under elevation angle α and at a specific frequency channel (i.e., LO), respectively. TBνLO,0∘‾ denotes the leg mean of the original TBs measured under 0∘ elevation, and TS‾ represents the leg-mean HALO TS. By using leg-mean values to determine the offset, the corrected TBs will still contain individual small-scale structures, which might differ from those in the HALO TS measurements. Furthermore, large-scale trends of the background atmospheric temperature are also conserved in the resulting data. For individual calibration strategies, the subtracted offset can be as small as 0.8 K or as large as 7 K (see Fig. 10, top panel). The good agreement between all eight corrected TBs under the different viewing angles (see Fig. 10, lower part) indicates that removing the offset will not significantly change the shape of the temperature profile calculated in the retrieval. Moreover, the absolute accuracy of brightness temperature measurements now matches that of the HALO TS, which has an overall error of 0.5 K (Ungermann et al., 2015).

After applying the offset correction, the root mean square (rms) difference between the 0∘ TBs and HALO TS, as shown in Fig. 11, gives a good impression of the capabilities of the different calibration strategies. Naturally, the methods that make use of HALO TS show the smallest deviation from HALO TS readings. However, it is the intention to maintain an independence of the MTP measurements from other measurement systems, increasing the value that MTP data add to the package of instruments flown on HALO. Of those calibration methods that do not use the HALO TS, the most reliable results are obtained when applying the method CCH, which uses the calibration values from the hot–cold calibration in the cold-chamber measurements related to the current hot target measurement signal. Whenever reliable ND measurements are available, this calibration method provides equally reliable results. Applying the corrections to TND or Thot does not significantly change the result, but slightly smaller deviations from HALO TS are seen for the TBs derived using only the Thot correction (method TND1b) and both corrections (method TND2). Considering the ND failures during the ML CIRRUS campaign, the favored calibration strategy is method CCH, also applying the offset correction between the leg-mean 0∘ TB and the leg-mean HALO TS. The deviation between the resulting 0∘ elevation TBs and HALO TS is ≤ 0.38 K at all three frequency channels for all ML CIRRUS flight legs with stable instrument conditions. This value is only exceeded when using the calibration method CCS – for all other methods it can be interpreted as the precision of MTP brightness temperature measurements, as will be shown below.

The overall uncertainty of the MTP measurements includes both systematic errors (e.g., the bias described above), and random errors (e.g., noise). In the case of the HALO MTP, the former can be related to HALO TS, as shown above, and the latter mainly influences measurement precision and the ability of the instrument to pick up atmospheric temperature fluctuations. In the literature (e.g., Ulaby et al., 1981), the standard formula to derive radiometric sensitivity (corresponding to the measurement precision of an ideal radiometer) is defined as the minimum detectable change in the radiometric antenna temperature of the observed scene: 10ΔTtheo=TsysΔf⋅τ=TR+TatmoΔf⋅τ, in which Δf denotes the filter bandwidth, and τ represents the integration. The HALO MTP has an ideal filter width of Δf=200 MHz (see Fig. 2a) and uses an integration time of 200 ms. Assuming a receiver noise temperature of 493.79 K (see Table 7) and a mean atmospheric temperature of 250 K, this leads to a theoretical value of ΔTtheo=0.117 K. However, these values used to derive the theoretical value do not take into account gain fluctuations or the fact that the effective filter bandwidth is smaller than the ideal value due to small deviations depending on frequency and because of the gap in the center of the transmission function (see Fig. 2), so larger errors are expected for a real measurement system.

In the calibration process, the main uncertainties arise from the use of the different reference temperatures, as summarized in Table 7. It is clear that the individual uncertainties assigned to each of the contributing values are not all independent. For example, the uncertainty of the y intercept (TR) directly follows from the uncertainty of the slope of the line, but it is also directly influenced by the changing instrument state. Hence, a quadratic sum of the individual errors is not suitable and can lead to a large overestimation of the total TB error. Thus, a sensitivity analysis to estimate the overall measurement uncertainty is performed: reference values (see last column in Table 7) for all parameters with uncertainties are used in a reference calculation. With these values, TBs are calculated for a range of counts between 17 500 and 19 725, which corresponds to the measurement signal range for atmospheric temperatures, as seen during the ML CIRRUS campaign (approximately 200–300 K). Two control calculations are made, adding the corresponding individual uncertainties (see column 4 in Table 7) in a way that the slope of the calibration line becomes as steep as possible (scalmax⁡, red lines in Fig. 12) or as flat as possible (scalmin⁡, blue lines in Fig. 12), following 11ascalmax⁡=T1+ΔT1-T2-ΔT2c1-c2-2Δc,11bTRmax⁡=T2-ΔT2-scalmax⁡⋅cs+Δc

12ascalmin⁡=T1-ΔT1-T2+ΔT2c1-c2+2Δc,12bTRmin⁡=T2+ΔT2-scalmin⁡⋅cs-Δc, assuming that T1 (with associated measurement signal c1) is the warmer temperature used in the calibration. Comparing the TBs of the reference calculation to those of the two control calculations reveals the maximum uncertainty in the derived TBs.

Furthermore, in parallel to the offset correction introduced in the previous section, a TB correction for the control calculations is introduced: here, the offset correction is calculated from the difference between the TBs of the control calculation (TBctr) and that of the reference calculation (TBref) at 18 500 counts (∼ 250 K): 13TBcorrc=TBctrc-TBctr18500-TBref18500. Results for all three calibration methods are shown in Fig. 12. Within the typical region of measurements of one set of elevation angles (vertical grey shaded region in Fig. 12), the resulting uncertainty is comparable to or smaller than the expected error from the measurement noise itself (ΔTB=Δc⋅scalref-TSysref), indicated by the horizontal black dashed lines. The three approaches to calibrate MTP measurements produce comparable uncertainties in the derived TBs. However, the calibration method relating to the cold-chamber measurements is the most reliable in the case that the measured signals at certain viewing directions deviate largely from the measurement signal at the horizontal elevation (i.e., if large vertical temperature gradients are present around the current flight level). For all methods, the overall uncertainty is clearly below the already established value of ∼ 0.38 K mainly caused by the measurement noise. This is approximately 3 times larger than the theoretical value, which is expected, as the theory does not consider gain fluctuations (Ulaby et al., 1981). This is not representative of any real radiometric system that is applied outside controlled laboratory conditions, especially the MTP. It also confirms that the uncertainty of derived TBs is dominated by gain fluctuations. Any change in the measurement settings to use larger integration times, and thus reduce this noise, would be at the cost of horizontal resolution.

The position of the HALO MTP instrument underneath the wing of the aircraft makes it sensitive to the altitude and speed of the aircraft. The bending and torsion of the aircraft body parts lead to deviations between the assumed pointing of the instrument and its true viewing direction. Adding to this is the aircraft pitch, which also depends on aircraft altitude and speed, introducing a potential source of a systematic error. During flights, the measurement of the inertial sensor, which is part of the HALO MTP that constantly records the current pitch angle of the instrument, is disturbed by the electromagnetic signal caused by the nearby mounted stepper motor, making the data not reliable enough to allow for a real-time correction of the pointing of the MTP instrument. Thus, the real pointing has to be determined after the flight. Analyzing the few reliable data points available after the two campaign deployments revealed that the relative deviation from the true horizontal plane was less than 1–2∘ during entire mission flights. Compared to this, the MTP's FOV of 7–7.5∘ (see Fig. 2 and Sect. 3.1) is clearly larger. Thus, it is safe to assume that a deviation of the elevation angle of 1–2∘ from the assumed angle does not have a considerable influence on the uncertainty of the retrieval input.

Another error source, which could not be studied in the lab, is a possible shift of the LO frequency. To measure the stability of the LO frequency generated by the synthesizer, it would be necessary to disassemble the instrument, which has serious implications for the certification of flying it on the aircraft. However, because of the placement of the LO frequency in the line center, a small shift will not create serious changes in the recorded TB; however, the measured TB would be caused by a slightly different altitude layer than expected. Because the strongest absorption lines of the absorption band are used, a notable effect would only be seen if the LO frequency shifted so much that one of the flanks of the line moved out of the filter range (in which case the overall health of the instrument should be checked). The effect is also dependent on the aircraft altitude, at which the error occurs due to the effect of line broadening. Furthermore, there is already a smearing effect caused by the FOV of the antenna, which dominates the altitude error, as long as the synthesizer error is small. Further investigation would certainly be useful in the retrieval setup using forward radiative transfer modeling.

There are several settings that can be easily changed when deciding the measurement strategy of the instrument. Both the set of elevation angles and the number and location of frequency channels used in a measurement cycle can be freely chosen. Simple geometric calculations, considering the length of the light path through an altitude layer, lead to a smaller set of elevation angles, which reduces redundancy between measurements due to the field of view of the instrument. Details can be found in the Appendix.

The frequency of the LO can be set between 48 and 64 GHz (see Table 1). Hence, there are quite a few possibilities to choose different frequency channels, including some at weaker absorption lines than in the standard setup. Using those, the instrument is able to view deeper into the atmosphere. As a reference, the MTP flown on the ER-2 research aircraft at ∼ 20 km of altitude only has a measurement range of approximately 2–3 km around flight altitude while using two frequency channels at similarly strong absorption lines to the current instrument (i.e., 57.3 and 58.8 GHz; Gary, 1989). Likewise, the height range of the DC-8 instrument, with LOs at 55.51, 56.66, and 58.79 GHz, has an “applicable range” (within which the weighting function drops to 1/e; see Appendix) of roughly ±2.8 km (Gary, 2006). In their conclusion on NCAR MTP data analysis Davis et al. (2014) mention that “it appears that more than about 3 km below the aircraft, the MTP may have difficulty identifying subtle mesoscale variations of temperature”.

The choice of frequency channels can have consequences on the calibration options but can lead to a clearly enhanced altitude range of sensitivity of the MTP. A pencil-beam calculation of the weighting functions at different frequency channels and viewing angles shows that changing the measurement strategy to include four frequency channels (instead of three) and only eight viewing angles (instead of 10) can significantly increase the vertical range and resolution of MTP measurements while still maintaining the length of one measurement cycle (i.e., not changing the horizontal resolution). However, an in-depth assessment of alternative measurement strategies must include forward radiative transfer modeling, using the information given in Sect. 3, and would go beyond the scope of this study. Details of the pencil-beam radiative transfer calculations and some implications for the calibration strategy are shown in the Appendix.