The Radio Occultation and Heavy Precipitation (ROHP) experiment on board the PAZ satellite was switched on on 10 May 2018, after a successful launch on 22 February 2018. For the first time, radio occultations (ROs) are acquired at two linear polarizations with the aim to detect heavy precipitation. The technique, called polarimetric RO (PRO), consists of measuring the phase difference between the horizontal (H) and vertical (V) components of the electromagnetic field coming from the global positioning system (GPS) satellites in occulting geometry . This is an augmentation of the capabilities of the well-known RO technique e.g.,. The first preliminary results obtained during the first 5 months of data confirm that the measurement is sensitive to precipitation .

H and V components are measured independently, yet synchronously, with a dual linearly polarized antenna pointing towards the limb of the Earth in the anti-velocity direction of the satellite. The rays, curved and delayed as they penetrate into deeper layers of the atmosphere (with higher density), reach the receiver in occultation geometry. The delay of the rays can be precisely tracked, and information about the thermodynamic state of the atmosphere can be retrieved (e.g., vertical profiles of temperature, pressure, and water vapor pressure) as in standard RO. The fact that in the PAZ satellite the incoming electromagnetic field is acquired at two linear and orthogonal polarizations allows us to retrieve information about media that introduce a differential phase shift between the horizontal and vertical components of the propagating electromagnetic waves. The media introducing this effect are mainly hydrometeors that flatten due to air drag as they fall. The scattering of electromagnetic waves by these asymmetric hydrometeors introduces a differential change in phase between the H and V components that is proportional to the amount and size of the hydrometeors. Therefore, this experiment represents the first technique able to retrieve vertical information about precipitation and the thermodynamic state of the surrounding area within the same measurement, from space.

The first analysis was focused only on the ability of the technique to detect hydrometeors, and a thorough calibration of the receiving system is required before more quantitative results can be obtained. The calibration of the receiving system is critical in assessing the uncertainty level of the measurement and therefore to associate geophysical quantities like rain intensity to each phase measurement . This would enable a wide range of studies and concepts taking full advantage of PRO capabilities, such as those proposed in , , and .

The purpose of the calibration of the receiving system is to remove the systematic effects unrelated to hydrometeors . These include the ionospheric effect on the polarimetric signal, the impurity of the transmitted signal, the ambiguity introduced by the receiver tracking two independent signals, and any other instrumental effects. In addition, the environment around the receiving antenna needs to be characterized. Before launch, a metallic structure had to be added to the satellite in order to adapt it to the a new launch vehicle (see Fig. a). This structure sits 30 mm above the antenna and covers part of the field of view. It introduces a systematic effect that depends on the angle of arrival of the signal at the antenna and changes the antenna patterns from those measured in an anechoic chamber before installation . It is also very likely that the metallic structure has worsened the cross-polarization isolation of the antenna.

In order to calibrate the signal, all the available data from 10 May 2018 to 10 October 2019 are accumulated and grouped based on the corresponding precipitation information: the data are classified into clear skies and cloudy–rainy scenes. This classification is performed using information from the National Centers for Environmental Prediction Climate Prediction Center (NCEP CPC) infrared brightness temperature and Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (GPM) mission (IMERG) rain rates. This allows us to determine the uncertainty in the measurement when no hydrometeors are present so that there is nothing expected to introduce changes in the differential phase between H and V. Then, the effect of the ionosphere (through Faraday rotation) is assessed using colocations between the simulated RO ray paths and the International Geomagnetic Reference Field (IGRF) Earth's magnetic field model and the International Reference Ionosphere (IRI) climatology for the electron density . Finally, the uncertainty and biases introduced by the antenna are characterized so that they can be corrected in each measurement.

Once the receiving system has been calibrated and the data accordingly corrected, these new observables are validated using the GPM products mentioned above. The results of the validation are compared with what was obtained in and also with the predicted performance from the simulations in .

The data collected by the PAZ satellite are downlinked by Hisdesat. The Institut de Ciències de l'Espai (ICE), Consejo Superior de Investigaciones Científicas, Institut d'Estudis Espacials de Catalunya (CSIC, IEEC) collects and owns the data and provides access to the servers at the Jet Propulsion Laboratory (JPL). At the JPL, the raw data are processed and converted to level 1 RO products, which are finally analyzed.

The antenna pattern characterizes the response of the antenna depending on the direction from which radio waves from GPS satellites arrive at the LEO. By having a good characterization, we can set the zero level of the measurements, i.e., the measurement obtained without anything affecting the signal. For this reason, we establish the on-orbit antenna pattern using only data that we know for sure have not crossed precipitation and were obtained under low ionospheric activity. In fact, this is not an actual antenna pattern, but it also contains some features arising from the transmitted/propagated signal effects. Therefore, it represents an “effective” antenna pattern.

The direction of arrival is given by the azimuth and elevation defined on a particular reference frame. To define such reference frames we need to know, very precisely, the position of the GPS that emits the radio wave and the position and relative orientation of the PAZ antenna with respect to the emitter. To account for the relative orientation, we use the information about the satellite attitude provided along with the orbit data.

Faraday rotation (Ω) in the ionosphere can introduce a differential phase shift between the H and V components . It depends on the electron density (ne), the magnetic field (B), and the relative orientation of the propagation direction (r) and the magnetic field vector as follows: 8Ω=-2.36×104f2∫ne(r)B⋅rdr, where the constant is in international units, and the Faraday rotation is in radians. The Faraday rotation induces a rotation of the polarization axis of the ellipse described with a linear basis. If the electromagnetic wave is perfectly circularly polarized, this rotation does not induce a differential phase shift. However, if the wave is not circularly polarized, the rotation induces a ΔΦ between the H and V components. There are two instances that can lead to a non-circularly polarized wave in a situation like the one we are analyzing here, which are as follows:

The first is imperfect emission. Ideally, GPS satellites emit RHCP radio waves. However, it is not guaranteed that this emission is perfect, and some impurities are to be expected. Therefore, if the emission is not perfect, radio waves travel through the ionosphere, experiencing a ΔΦ that is proportional to the Faraday rotation : 9ΔΦ=-2msin⁡(2Ω+Δ), where m and Δ characterize the difference in the emitted wave from the perfect circular polarization, i.e., E=(1,meiΔ){eR,eL}.

We have gone through the different, necessary steps before performing the calibration of the observables, from the acquisition of the signal to the antenna pattern characterization, and taken into account all the possible effects that can induce a differential phase shift, besides precipitation. The steps followed to calibrate the ΔΦ are identified and described in Fig.  and summarized below.

First is the acquisition of the signal. The incoming electromagnetic signal is collected at two independent linearly polarized antennae, orthogonal to each other, oriented to get the horizontal and the vertical components of the radio wave, simultaneously. The difference between the excess phase of both ports (H and V) gives us the observable (step 1 in Fig. ), which is further corrected for remaining cycle slips (step 3) and set to 0 in the regions above where any precipitation is possible (step 4). The observations are obtained as a function of time, but having precise information about the location and relative orientation of both the GPS and the PAZ satellites we can link time to azimuth and elevation from the receiving antenna point of view so that we can obtain the measured differential phase shift as a function of such variables: ΔΦm(φA,θA). After the processing, time can also be linked to height, so we can have ΔΦm(h) as well (step 2).

Data linked to no rain and low ionospheric activity are used to build the antenna pattern ΔΦpattern(φ,θ) (step 7). And this antenna pattern is used to correct the whole dataset of observations (step 8) as follows: 11ΔΦci(φ,θ)=ΔΦmi(φ,θ)-ΔΦpattern(φ,θ), where the subscript “c” stands for corrected.

The possible Faraday rotation effect, although expected to be small in general (e.g., see Sect. ), is not fully corrected by this process. The antenna pattern characterization captures these ionosphere-induced trends and possible errors induced by the performance of the antenna. It is intentionally constructed with low ionospheric activity data so that it does not capture the stronger trends induced by the active ionosphere, since they can be different and have nothing to do with the relative angle at which they arrive at the antenna. Therefore, every ΔΦci(φ,θ) is corrected for remaining possible linear trends present above 20 km (step 9) as follows: 12ΔΦi(h)=ΔΦci(h)-trend(ΔΦci(h>20km)), where the linear trend is evaluated above 20 km and extrapolated to all heights. With this last step we obtain the calibrated ΔΦi(h). After the whole calibration, we expect that ΔΦi(h) is as similar to ΔΦprecipi(h) as possible, where ΔΦprecipi(h) is the differential phase shift induced only by precipitating hydrometeors. Note that the preliminary calibration in did not include steps 5 to 8.

The smoothed calibrated measurements 〈ΔΦ〉1s are to be validated against IMERG. For comparison and standardization purposes, we interpolate the 〈ΔΦ〉1s for a 100 m grid, spacing profiles from 0 to 30 km: ΔΦ(h100m). For these profiles we can perform the mean and the standard deviation at each altitude. First of all, we group them by their linked precipitation and brightness temperature: (1) no precipitation (R=0 mm h-1 and Tb>250 K), (2) precipitation (R>0.1 mm h-1), and (3) heavy precipitation (R>1 mm h-1). For these three groups we compute the mean and standard deviation as a function of height. In Fig.  we show the results. We can see how for the no-precipitation group the ΔΦ(h100m) averages to 0 for the whole vertical profile (by design), and the standard deviation, σΔΦ(h), increases with decreasing altitudes. In the right panel of Fig.  we show a more detailed profile of the σΔΦ(h).

The first remark is that σΔΦ(h)=1.2mm at 2 km of height. This is better than the study performed in , which is expected since here we calibrated the signal using the antenna pattern and we have performed the weighted average smoothing. It is also very close to the theoretically predicted sensitivity in . The second noticeable feature is the peak in σΔΦ(h) around 7 km. This feature is due to instrumental effects in some occultations near the CL to OL transition and is an open issue under investigation. Finally, a small negative bias is observed within the lower 1 km. As we have explained in Sect. , the results below 2 km have to be treated with caution, since many uncertainties (tangent height determination, atmospheric multipath, etc.) come into play.

Still in Fig. , the precipitation and heavy precipitation groups (blue and red, respectively) exhibit large positive values below 10 km, although positive values start to be noticeable below 15 km. The positive peaks are well above the standard deviation of the no-precipitation group, indicating sensitivity to precipitation and consistent with .

As it was done in , we can characterize each PRO observation by a single value derived from the ΔΦ(h100m). This is done by averaging ΔΦ(h100m) between two different heights. In this case, we use 0 to 10 km, obtaining 〈ΔΦ〉0–10 km. To associate one single measurement is useful to validate the observations against the precipitation products. In Fig.  we show 〈ΔΦ〉0–10 km as a function of the associated rain rate. The binned mean (solid line) shows how 〈ΔΦ〉0–10 km values tend to increase as R increases, exhibiting sensitivity to the intensity of precipitation.

It is also interesting to assess the percentage of cases that exceed a certain threshold of 〈ΔΦ〉0–10 km given a precipitation value. This sets a detectability metric of 〈ΔΦ〉0–10 km based on the colocations, and we can assess the quantity of false positives. We show the results in the Fig. a. In this plot we see how for no precipitation, there are 6 % of cases that exceed 〈ΔΦ〉0–10 km=0.5mm, while there are almost no cases exceeding 1 mm (or higher). This tells us that the rate of false positives is very low, and depending on the threshold we choose, is almost nonexistent. The same plot shows the percentage of cases exceeding different thresholds of 〈ΔΦ〉0–10 km (represented by different colors; see legend inset). For example, as we can see in Table , 85 % of the cases exceed 〈ΔΦ〉0–10 km=1mm when precipitation is heavier than 1 mm h-1, and more than 93 % of the cases exceed 〈ΔΦ〉0–10 km=2mm when precipitation exceeds 5 mm h-1.

In the same way, we can assess which percentage of cases exceeds certain precipitation given a 〈ΔΦ〉0–10 km. This is shown in Fig. b. In this way we can assess the false negatives and see how likely it is to detect precipitation given a 〈ΔΦ〉0–10 km. The leftmost region of the plot shows the fraction of cases exceeding certain precipitation when the observed 〈ΔΦ〉0–10 km is small (i.e., smaller than 0.1 mm). For a precipitation threshold of 0.01 mm h-1, this fraction is around 19 %, while for precipitation heavier than 1 mm h-1 (and higher) it is almost 0 (see Table ). We can also see how, for example, when the measured 〈ΔΦ〉0–10 km is larger than 1 mm, there is an 81 % chance of measuring precipitation with 0.1 mm h-1 or higher.

In this paper we have described the steps and the procedure followed to calibrate and validate the PRO ΔΦ observable. The calibration of the observable is a critical step in the mission, which has to ensure the quality and robustness of the observables. Being the first time that these kind of measurement are being obtained, the validation of the observables is also very important, since it will establish a reference for future missions.

First of all, the calibration of the signal has been performed by using the existing data to characterize the antenna pattern. Such an exercise is more important than it should be due to the interferences introduced by a metallic adapter that had to be installed above the antenna, to adapt the satellite to a new launcher. In order to not introduce features coming from the kind of signals that we aim to detect (i.e., precipitation-induced ΔΦ), the characterization is performed using only data collected in rain-free scenarios. Furthermore, ionosphere could introduce a small ΔΦ through the Faraday rotation; hence observations that have sensed regions with high ionospheric activity are also discarded for the calibration. Finally, the antenna pattern is then used to correct all the observations, regardless of precipitation or ionospheric activity.

The corrected observations are thoroughly validated. First, we have performed the statistical analysis of both no-precipitation and precipitation groups of observations. The mean and standard deviation of the no-precipitation profiles set the quality of the observations. Without the presence of precipitation, what remain are the uncertainties and the unsought effects, so the standard deviation tells us the noise level of the measurement. Inside the noise level we assume that we can have the thermal noise arising from the phase measurements, residual effect from the calibration, and cross-polarization terms from the non-perfect isolation of the antenna. In spite of that, the vertical profile of the standard deviation (see Fig. ) shows a good noise level (below 1.5 mm above 2 km, below 1 mm above 3 km, and better than 0.5 mm above 8 km), close to what was predicted in the initial sensitivity studies for the experiment . It is also confirmed that the Faraday rotation effect on the final observable is small and that the transmitter polarization impurities are negligible.

In addition, the mean ΔΦ measurements as a function of height for the precipitation groups exhibit a clear and distinguishable positive peak, reaching altitudes above 10 km and exceeding ΔΦ=5mm in the lower layers for the group comprising the precipitation rates larger than 1 mm h-1. This clearly indicates that the measurement is sensitive to precipitation, corroborating the initial findings in . It also indicates that the measurement might be sensitive to higher-altitude phenomena other than precipitation, such as ice or melting particles, usually present above the freezing level and particularly in the heavy tropical precipitation structures.

Further validation is performed using the vertical average of ΔΦ(h100m) between the surface level and 10 km for each individual observation, defined as 〈ΔΦ〉0–10 km. This allows us to use single values rather than vertical profiles associated with each observation for simplicity in the validation process. Using this approach we can assess the variation in 〈ΔΦ〉0–10 km with increasing R (see Fig. ). The fact that 〈ΔΦ〉0–10 km keeps increasing as R increases tells us that ΔΦ measurements are sensitive to not only precipitation but also its intensity. Here we want to remind readers that in this context precipitation intensity means higher mean rain rate integrated for the sensed region (see Sect. ), which could either mean more intense precipitation, a larger precipitation cell, or both.

The same ΔΦ(h100m) measurement is used to evaluate the detectability of precipitation for different thresholds (see Fig. ). For example, we can state that more than 80 % of the cases with R>1 mm h-1 exceed ΔΦ(h100m)=1.5 mm. In a different, yet equivalent, way we can state that 50 % of the cases with ΔΦ(h100m)>2 mm exceed a R=1 mm h-1, but more than 90 % will have R>0.1 mm h-1. Therefore, the detectability will depend on the threshold that one sets. On the other hand, the same study shows low values for false positives and false negatives regardless of the chosen threshold. Setting the thresholds towards the heavier rain range (although heavy rain is not qualitatively defined here) decreases the false positives and negatives dramatically, exhibiting a very good performance of the technique in detecting rain. It is important here to emphasize the fact that we are evaluating the performance in detecting rain rather than quantifying its rate, and the validation in the context of this paper confirms this capability.

These results confirm the potential of the PRO technique to provide joint measurements of precipitation and thermodynamics, becoming a very valuable and unique technique. Further analyses need to be done in order to address the quantification of precipitation, as well as to exploit this and other scientific applications.