a. Data processing.

The methodology that has been followed to process and assess the Spire observations has been as similar as possible to what has been done for the ROHP-PAZ observations (e.g., Padullés et al. 2020). However, there are differences between the acquisition of PRO observables by Spire and ROHP-PAZ that have important implications. First of all, Spire receivers have synchronized channels that allow tracking of the H and V components simultaneously, whereas that was not the case for PAZ. This implies that interpolation into common time stamps was needed for the ROHP-PAZ processing, and it is not necessary when processing Spire PRO observables, which simplifies the process. Another important difference is the tracking mode of the PRO: Spire uses OL tracking during the whole event, while PAZ starts the tracking using closed loop (CL) and changes to OL at an approximate height of 7–8 km above Earth’s surface. Collecting the whole profiles using the same tracking mode avoids a transition between modes, which avoids phase tracking issues that happen during such a transition (Padullés et al. 2020).

Furthermore, Spire receivers are able to track all major GNSS constellations in both setting and rising configurations, whereas the PAZ receiver only tracks setting GPS satellites. As a reminder, a setting (rising) RO is obtained when the transmitting satellite sets below (rises above) the horizon. This results in a substantial increase in the number of collected observations per satellite and in the first rising PRO profiles ever recorded. It must be pointed out that Spire satellites only have one PRO antenna; therefore, the collection of rising and setting is not simultaneous but depends on the satellite attitude (i.e., whether the PRO antenna is pointing toward the velocity or anti-velocity direction).

The processing of the Spire data at ICE-CSIC, IEEC starts from the level-1 data files prepared by Spire (Talpe et al. 2025), which are in the standard format established by the University Corporation for Atmospheric Research (UCAR) RO processing team. The main observables that are contained in these files are the excess phase and the SNR. In brief, the basics of the processing are explained in the following paragraphs.

The PRO observable ΔΦ(t) is obtained by differencing the excess phase measurements obtained in the H and V channels, respectively. Once differenced, remaining issues with the tracking of the phase may arise: The most common tracking issues are known as cycle slips and can occur during drops of the SNR. These are corrected in the low-level processing before generating level 1 profiles, but since their detection may be masked by the phase noise, sometimes their effect is further emphasized in ΔΦ observable. When this happens, they are identified and further corrected. Each time step is assigned to a height using the geometric optics approach with the RO processing package (ROPP) software (Culverwell et al. 2015).

A height-dependent quality control for ΔΦ was introduced in Padullés et al. (2024) and is being implemented here. Basically, this parameter identifies whether ΔΦ(h) suffers any anomaly (e.g., tracking issue impossible to be corrected, loss of track, etc.) and at which height it happens, and it is called the height_flag parameter. Profile heights below this flag are considered of poor quality.

The profiles are set to have a common reference at a given high altitude; that is, ΔΦ is set to have a value of 0 mm at a height of 30 km above the surface. Henceforth, the remaining of the profiles are always relative to that height, where it is assumed there is no precipitation nor clouds that could substantially affect PRO observables. Furthermore, a linear trend correction based on the upper part of the profile (i.e., between 20 and 60 km) is applied to subtract potential residual effects from the ionosphere (e.g., Padullés et al. 2020). And finally, a 1-s smoothing is applied to the profiles.

Further details on the processing can be found in Padullés et al. (2020, 2024). The resulting ΔΦ(h) is the observable that will be used in this manuscript. Please note that the units are given in millimeters of polarimetric delay (i.e., not precipitation rate related). This delay relates to the electromagnetic phase as mm/λ_EM.

The excess phase obtained at both H and V ports can be combined and used to derive the bending angle profile. Such a combination has been tested with the PAZ observables, and the resulting profiles have equivalent quality to those obtained from standard RO missions with comparable hardware (Padullés et al. 2024). From the bending angle, it is straightforward to derive the atmospheric refractivity profiles (e.g., Hajj et al. 2002). Once refractivity is obtained, the so-called thermodynamic or wet retrievals (i.e., water vapor pressure and temperature profiles) can be obtained using 1DVAR techniques (e.g., Wee et al. 2022). The wet retrievals are routinely generated by processing centers like UCAR, NOAA Center for Satellite Applications and Research (STAR), NASA-JPL, and the RO Meteorology Satellite Application Facility (ROM SAF) for all RO missions with available data, and those from Spire have been evaluated for their standard satellites (e.g., Jing et al. 2023; Ho et al. 2023). The quality of the bending angles obtained from the PRO satellites being used in this study (e.g., FM166, FM167, and FM170) is evaluated in Talpe et al. (2025), where they show that the quality is not degraded with respect to their standard RO satellites.

Currently, at the ICE-CSIC, we do not have the capability to generate the wet retrievals, and therefore, the results and shown examples in this study will focus on ΔΦ profiles. However, potential applications using both ΔΦ and the corresponding thermodynamic profiles are going to be discussed, since the capability of obtaining both simultaneously is one of the main advantages of the PRO technique.

b. Data filtering.

The elevation and azimuth of the incoming signals as seen from the antenna are computed, similarly as done in Padullés et al. (2020). Although an on-orbit antenna pattern for further calibration of the profiles is not necessary for Spire data (i.e., it was necessary for PAZ due to the partially blocked FoV), these variables are used to detect maneuvers during the occultation events. Data are then filtered to discard the following:

• those profiles where a maneuver is detected (i.e., defined as having a standard deviation in the azimuth variable larger than 5.5°);

• profiles with average ΔΦ(h) between 0 and 10 km lower than −20 mm;

• profiles with ΔΦ(h) RMS between 20 and 40 km larger than 0.75 mm.

Furthermore, the profiles are truncated at the vertical level indicated by the height_flag parameter (i.e., the part of the profile below the flag is discarded). Since there is not yet an agreed quality control (QC) criterion for PRO, these filters remove data with anomalous measurements. Table 2 shows the number of valid profiles applying the filtering mentioned above, at two different heights.

Table 2.

Number of valid profiles before and after filtering, separated by FM, provided at 10- and 5-km altitude and with an indication of the % of the total.

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Spire data used in this study comprise the periods between April and October 2023 for FM166 and FM167 and between May and August 2023 for FM170. The global sampling distribution of these data for the months of June, July, and August is shown in Fig. 1 (top row) for binned grids of 10° × 10°. There is a drop in the daily counts of observations for FM170 after 13 August 2023, which is negatively impacting the sampling as can be seen in Fig. 1c. The global distribution of the observations follows the typical pattern of RO collected from high-inclination LEO orbiters (e.g., Biondi et al. 2011); that is, it maximizes around ±30° and ±60° latitude. In this case, the pattern is slightly modified due to the nanosatellites’ duty cycle.

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Binned averaged maps for (top) Spire PRO observation sampling counts, (middle) mean ΔΦ between the surface and 10 km, and (bottom) IMERG surface precipitation for (left) June, (center) July, and (right) August. The size of the bins is 10° × 10°.

Citation: Bulletin of the American Meteorological Society 106, 4; 10.1175/BAMS-D-23-0322.1

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c. PRO observable ΔΦ spatial resolution.

The rays traveling from the GNSS satellite to the receiving LEO cross a large part of the atmosphere as the occultation advances. Contributions to ΔΦ could come, in theory, from anywhere along these ray paths. However, in practice, ΔΦ is affected only within the portion of the atmosphere where large and anisotropic hydrometeors are present. Therefore, the horizontal resolution of ΔΦ measurements along the ray-path direction is dependent on height, with very short distances where hydrometeors can contribute near the top of the clouds, increasing toward the surface. Assuming, for example, a sensed area where the maximum cloud-top heights are assumed to be at 14 km, the maximum expected horizontal resolution of the ray whose tangent point is at 5-km height is of around 700 km (e.g., Padullés et al. 2024). This indicates that such a ray travels this distance below 14 km on its way from the GNSS satellite to the LEO. This resolution improves with increasing ray’s tangent height and can be further constrained using ancillary imagery from, for example, LEO or geostationary satellites as described in Padullés et al. (2024).

Conversely, the resolution in the across direction of the rays, that is, perpendicular to the ray trajectory, as well as the vertical resolution, is only limited by the Fresnel cone and is of approximately 1 km (e.g., Kuo et al. 2000; Anthes 2011). This means that two spatial dimensions are relatively well constrained, whereas the other one is not. This implies that for this kind of observations, it is important to know the orientation of each measurement and not to simply represent each event as a representative latitude–longitude point.

a. Comparison with two-dimensional GPM products.

To assess the statistics of the Spire PRO observations under a diversity of acquisition scenarios, the occultations are grouped by receiving nanosatellites (e.g., FM166, FM167, and FM170), by tracked constellation (e.g., GPS, GLONASS, Galileo, and Beidou), and by different precipitation thresholds. Precipitation data are obtained from the GPM mission (Hou et al. 2014), in particular, from NASA’s IMERG (Huffman et al. 2023). A caveat may be noted: IMERG provides valuable global data for comparison to the PRO observations, but with several limitations. First of all, it is a two-dimensional product, which implies that some characteristics of the precipitation structure are missed, and conclusions inferred about the vertical structure of ΔΦ(h) are indirect. In addition, precipitation estimates are generated mostly from infrared, which is less reliable than the microwave (e.g., Tan et al. 2016). Finally, IMERG is provided every 30 min, and the PRO events happen within a few minutes. All these being noted, IMERG still provides the best possible means of comparison for evaluating the performance of ΔΦ measurements on a global scale. To mitigate some of the IMERG limitations and to account for ΔΦ horizontal resolution, the mean surface rain rate averaged in an area of 2° × 2° around the occultation point is used as the precipitation value linked to each PRO event.

The first comparison between PRO observations and IMERG is in terms of the geographical patterns. The monthly binned means of ΔΦ(h) averaged between Earth’s surface and 10 km is shown in Fig. 1 (middle row), and the corresponding means for IMERG surface precipitation are shown in Fig. 1 (bottom row). The size of the bins is 10° × 10°. The patterns of both quantities resemble very well, with good qualitative agreement especially along the ITCZ.

The assessment of the statistics of the vertical profiles of ΔΦ grouped by different precipitation scenarios is shown in Fig. 2. Figures 2b, 2d, and 2f contain the average of ΔΦ as a function of height for each of the groups based on IMERG precipitation, separated by receiving satellite, respectively. For this first analysis, all tracked constellations are considered altogether. The black line corresponds to the nonprecipitating cases. Figures 2a, 2c, and 2e show the standard deviation SD_ΔΦ(h) of the group corresponding to nonprecipitating cases, for the three receiving satellites, respectively. This can be considered as the measurement noise level at each altitude level. The different lines in SD_ΔΦ(h) panels correspond to each of the tracked constellations. The corresponding result for the whole ROHP-PAZ experiment is included for comparison, in Figs. 2a, 2c, and 2f as dashed line and in Figs. 2g and 2h for the same quantities as for the Spire data. The statistics of the ROHP-PAZ experiment used here are computed in Padullés et al. (2024) using the same approach described above.

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Statistics for the vertical profiles of ΔΦ(h) depending on the rain situation under which they are collected. (a),(c),(e) The vertical profile of SD_ΔΦ(h) corresponding to those Spire PRO collected under no-rain conditions, according to IMERG; (g) PAZ data. Different colors represent different transmitting constellations [G: GPS (blue); E: Galileo (orange); R: GLONASS (green); C: Beidou (red)] and the results for the ROHP-PAZ mission (black dashed lines) for comparison purposes. The four different panels correspond to FM166, FM167, FM170, and PAZ, respectively. (b),(d),(f),(h) The mean ΔΦ(h) for each group of PRO observations obtained under the rain conditions (regardless of transmitter) as specified in the colorbar, for FM166, FM167, FM170, and PAZ, respectively. Large ambiguity in the time–height relationship is expected below 2-km height (dashed horizontal line). The vertical dashed line indicates the 1.5-mm SD_ΔΦ(h).

Citation: Bulletin of the American Meteorological Society 106, 4; 10.1175/BAMS-D-23-0322.1

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It can be noted that the mean ΔΦ(h) for the nonprecipitating group follows the 0-mm line with no appreciable biases, for the three of the Spire satellites and for PAZ. The SD_ΔΦ(h) of the nonprecipitating group behave as expected: increasing with decreasing height, with values lower than 0.5 mm above ∼20 km, with a slight increase within the troposphere, and reaching values around 2 mm at a height of 2 km. Small differences can be observed among constellations and the receiving Spire nanosatellites, although all values are well within the theoretically predicted levels before the PAZ launch, and inside the limits for detectability of precipitation (e.g., Cardellach et al. 2014). In comparison with the actual ROHP-PAZ results [black dashed line in Figs. 2a, 2c, and 2e; and whole (Figs. 2g,f)], it can be seen how in general the Spire SD_ΔΦ(h) is slightly larger for the most part of the vertical profile, with two exceptions. The first one is around ∼7 km, where especially FM167 performs slightly better than PAZ. This is due to the increase in the PAZ SD_ΔΦ(h) around this height, attributed to the region where the CL to OL transition happens. Spire receivers track the occultations in OL mode for the whole time, and therefore, no artifacts linked to such a transition are observed. The second exception is in the lowermost part of the troposphere (e.g., below 2 km), where Spire SD_ΔΦ(h) is substantially lower than that of PAZ. This could be linked to a better phase tracking from Spire receivers at these altitudes, but given the ambiguity in height at these portions of the atmosphere (due to the atmospheric multipath and the use of the geometric optics method to map time with height), this is impossible to assess. As for the tracked constellation, GPS is the one that exhibits lower SD_ΔΦ(h) consistently thorough the three receiving Spire nanosatellites.

The mean ΔΦ(h) for the precipitating groups show the expected behavior for the three Spire satellites, consistent with already observed features in ROHP-PAZ data. Although differences can be observed in the magnitude of ΔΦ(h) for PAZ data, this can be linked to the fact that PAZ has sensed more precipitation types and characteristics during the 6 years of the mission. Furthermore, the different orbits mean that precipitation is sensed at different local times, which can also induce statistical differences.

The more relevant features observed in Fig. 2 are the sensitivity to precipitation, as clearly observed with positive ΔΦ(h) for the cases with precipitation; the sensitivity to precipitation intensity, observed as increasing mean ΔΦ(h) for increasing mean precipitation rain rates within the groups; and the shape of ΔΦ(h). Such shape indicates that ΔΦ(h) generally maximizes above the melting layer (around 4–5 km in the tropics), consistent with the sensitivity of PRO to oriented snow (e.g., Padullés et al. 2022, 2023). Slight differences in the shape of ΔΦ(h) can be observed between the two satellites in the same orbit (FM166 and FM167) with respect to the third satellite (FM170), and these can be explained by the fact that FM170 is collecting less observations in the tropics due to its duty cycle schedule. Therefore, the kind of precipitation being observed by the three satellites may differ in characteristics, for example, FM170 is likely to capture less deep convective events which are more probable in the tropics.

The shape of ΔΦ(h) is a consequence of two factors: the first one is that ΔΦ is sensitive to horizontally oriented hydrometeors, such as large ice or snow particles that can be lifted to high altitudes. Such sensitivity, not anticipated when the PRO technique was proposed (e.g., Cardellach et al. 2014, 2017), has been demonstrated with the ROHP-PAZ data (e.g., Padullés et al. 2022, 2023). The second factor is geometrical: the distance that the rays travel within areas where ice and snow are found increases toward the top of the freezing level and then decreases toward the surface. The decrease responds to rays traveling below the frozen area for longer portions as the occultation advances (e.g., see Fig. 1 in Padullés et al. 2023). Heavy precipitation also contributes to ΔΦ, and that is why ΔΦ does not decrease to 0 mm below the freezing level, but it is statistically less probable to hit, as it is generally distributed in scattered heavy rainfall cells underneath big and more homogeneous clouds.

It is also worth mentioning that most of the occultations collected by FM166 and FM167 were in setting mode, while most of those collected by FM170 were in rising mode [see Talpe et al. (2025), for a more detailed description of the satellite orbits and configurations]. Therefore, statistics for FM170 are mainly for rising occultations. This is relevant because no rising occultations are collected with ROHP-PAZ, and these results show how the quality is equivalent to those obtained in setting mode.

b. Comparison with PAZ.

Direct comparison with PAZ observations is not possible due to the difference in orbits: All satellites are in polar orbits, but these have different equatorial crossing times, meaning that the observations are mostly obtained at different local times (i.e., PAZ crosses the equator at 0630/1830 UTC, while FM166 and FM167 cross the equator at approximately 0930/2130 UTC and FM177 at 2230/1030 UTC). Such a difference leads to the absence of observations from PAZ and Spire that are sufficiently close in location and in time. However, the observations can be compared statistically. For example, Fig. 3 contains the mean ΔΦ averaged between 0 and 10 km, for each global bin of 10° × 10°. For this comparison, only PAZ data collected between May and August (all years within the 2018–23 period) are included, so that a more fair comparison is conducted between PAZ and Spire. Although differences can be observed between the two datasets (linked to the fact that PAZ has been sounding different years and different local times than the Spire nanosatellites), the general patterns are in agreement.

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General pattern of ΔΦ for PAZ and Spire for ΔΦ averaged between 0 and 10 km at each 10° × 10° bin. (left) PAZ data collected between May and August (for all years between 2018 and 2023). (right) The Spire data being evaluated in this study (using data between May and August 2023).

Citation: Bulletin of the American Meteorological Society 106, 4; 10.1175/BAMS-D-23-0322.1

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The patterns of ΔΦ for both PAZ and Spire observations reproduce recognizable precipitation patterns, such as those described in Liu and Zipser (2015), that were build using the GPM dual-frequency precipitation radar (DPR). In particular, the pattern of the highest values of ΔΦ matches best the DPR pattern for the highest maximum 20-dBZ echo-top height, which is an indicator of the presence of precipitation-sized particles at high altitudes (e.g., Liu and Zipser 2015, Fig. 1). This is consistent with PRO being very sensitive to horizontally oriented snow particles.

a. Dense observations of weather phenomena.

This study focuses on the PRO observations obtained around TC Mawar, one of the strongest TCs of 2023. Mawar formed on 19 May and lasted until 3 June. PRO observations within 500 km of the TC best track have been identified using IBTrACS (Knapp et al. 2010, 2018). A total of 33 PRO have been found. For comparison, during the same period, only two ROHP-PAZ observations were found fulfilling the same criteria.

Figure 4 shows the Spire PRO observations (black dots) near the Mawar TC track (dashed line), with the background images showing the geostationary infrared (IR) 10.8-μm brightness temperature T_b from Janowiak et al. (2017), at two different moments (1204 UTC 23 May 2023 and 1115 UTC 26 May 2023). In the right panels, the observations corresponding to within 15 min to the times of the background images are shown.

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Example of PRO observations along the Mawar TC track. (left) The locations of PRO observations (black dots) with a line crossing it that indicates the direction of the occultation. The dashed black line indicates the track of the TC, obtained from IBTrACS. The background images correspond to the IR 10.8-μm T_b at two different moments, separated using dashed lines, colored borders. Each border color in (left) is linked to the right panels’ legends [e.g., red dashed border in (left) corresponds to (b), whereas the green dashed one corresponds to (c)]. The colored circles highlight the occultations showed in the two right panels, with the same color.

Citation: Bulletin of the American Meteorological Society 106, 4; 10.1175/BAMS-D-23-0322.1

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It can be seen in Fig. 4 how, depending on the distance to the deep convective regions of the TC (bluer color indicating more vertically developed clouds), the shape of ΔΦ(h) changes. For instance, the PRO observation involving GPS12 and FM167 on 1115 UTC 26 May 2023 shows a constant increase in ΔΦ(h) with decreasing height because it hits the heavy precipitation far from the tangent point. On the other hand, the PRO observation involving GPS12 and FM166 on 1115 UTC 26 May 2023 shows a large ΔΦ(h) peak of around ∼30 mm right above the melting layer, since it hits the rainy outer band of the TC much closer to the PRO tangent point. Accounting for the geometry of both observations, the shapes and magnitudes are consistent with the presence of high concentrations of nonspherical oriented hydrometeors above the melting layer (e.g., Skofronick-Jackson et al. 2008; Sieron et al. 2018). Further knowledge on the vertical distribution of such nonspherical hydrometeors is potentially relevant for better understanding passive microwave observations and their assimilation (e.g., Kim et al. 2024; Geer 2021).

The example shown in Fig. 4 emphasizes two important aspects. First, it can be seen how the same TC is observed at different times, locations, and life-time stages, allowing potential studies on the evolution of the vertical structure using PRO, both in time and as a function of the sensed portion of the TC. The vertically resolved ΔΦ(h) profiles inform about the presence of horizontally oriented hydrometeors and could help constrain precipitation processes (e.g., Gong et al. 2020). The sampling achieved with such constellations could enable studying such precipitation processes at different locations of the TC, similarly as has been done with vertical gradients of reflectivity using the GPM radar (e.g., Brauer et al. 2024), but at the larger scales that PRO permits.

The second aspect is that these observations provide additional means of evaluating simulation studies and forecasts. Forward operators that allow to generate synthetic ΔΦ observations based on model outputs are being developed, with a first version already implemented by Hotta et al. (2024). Using such forward operators, experiments of several simulations using different microphysics assumptions could be tested against actual ΔΦ observations to discriminate among them based on the distribution of hydrometeors they yield. These kinds of studies were first proposed by Murphy et al. (2019). Using synthetic data, Murphy et al. (2019) showed that PRO sensitivity is large enough to discriminate among microphysics schemes. This approach has been applied by Chen et al. (2025) in the context of simulation studies for TC forecasts, using PAZ data alone. Spire observations will enhance these kinds of studies with simultaneous observations of the same event.

Furthermore, PRO observations could complement passive radiometry and space-based radars, often used in the evaluation of modeling studies (e.g., Galligani et al. 2017; Hristova-Veleva et al. 2021), with vertically resolved observations providing additional insight informing about the presence and orientation of hydrometeors at various vertical levels.

b. Clustering of observations.

To collect nearly coincident PRO observations in space and time has been suggested as an observational means for scientific studies aiming to better characterize the interaction of the thermodynamics controlling deep convection with its immediate surroundings (e.g., Turk et al. 2019, 2022). PRO observations complement the current observing system by providing both vertical profiles of thermodynamic variables, like temperature and water vapor, and a vertical indication of the presence of liquid and solid precipitation. The emphasis here is to the fact that these observations can be obtained with high vertical resolution, and regardless the presence of thick clouds. Therefore, nearby PRO observations offer capability to infer spatial gradients of moisture at different vertical levels and to assess how these control heavy precipitation, potentially constraining entrainment processes (e.g., Sahany et al. 2012).

The initial idea was to obtain such observations with dedicated CubeSats launched to orbit in a train-like formation (Turk et al. 2019). The aim of this section is to assess whether equivalent observations to the desired ones are possible with the current three Spire nanosatellites, provided that two of them are orbiting very close together.

A cluster of observations is defined here as PRO observations with occultation points within 800 km obtained within 15 min of each other. Similar approach has been followed to assess the precision of RO measurements using the early stages of the COSMIC-1/Formosa Satellite 3 (FORMOSAT-3) and COSMIC-2/FORMOSAT-7 missions, where the satellites of the constellations were orbiting close together before they separated and were placed in their final orbits (e.g., Schreiner et al. 2007, 2020). In this study, however, we allow for extra distance separation and less time difference because the aim is to infer spatial differences in the atmosphere associated with convective events. The clusters are obtained in the following situations, depending on which receiving satellites and tracked GNSS are involved:

1. 1)one single satellite tracking different GNSS transmitters,
2. 2)different receiving satellites tracking the same GNSS transmitter,
3. 3)different receiving satellites tracking different GNSS transmitters.

The first situation occurs when the receiver aboard the receiving satellite can track a large number of sources, simultaneously. This depends on the relative position between the transmitters and the receiver, and also on the receiving antenna azimuth range from which occultations are collected. A larger azimuth range not only implies more occultations but also a larger tangent point drift [i.e., horizontal movement of the tangent point, e.g., Foelsche et al. (2011)]. That may be relevant when scanning small-scale weather events.

The second situation listed above assumes receivers that are closely placed in the same orbit with relatively small time separation and the distance at which the resulting observations occur can be controlled by choosing specific orbit parameters. The resulting separation and distribution of occultations depending on orbit parameters were thoroughly assessed in Turk et al. (2019). Therefore, these could be chosen depending on the targeted weather events and/or scientific interest.

The first two situations described above yield occultations with observation directions that are nearly parallel to each other. However, under the third situation, if the receiving satellites are in different orbits adequately separated in equator crossing time, it can result in close by observations with directions perpendicular to each other.

Accounting for all these situations, 60 306 clusters have been found. Examples of the PRO clusters obtained with the Spire nanosatellites are shown in Fig. 5 for 1 day and for 1 week. In the background on the same figures, the daily and weekly precipitation from IMERG is shown to provide an idea of the clusters that can be obtained in precipitating regions. Statistics of these clusters depending on the number of occultations per cluster are summarized in Table 3, and the statistics accounting for the involved transmitters and receivers are summarized in Table 4. In both Tables 3 and 4, the number between parentheses show the statistics corresponding to the clusters where at least one of the observations in the cluster hits precipitation [using as threshold the mean ΔΦ below 10 km, ⟨ΔΦ(h_<10 km)⟩ > 1.5 mm] and at least one of them does not [using ⟨ΔΦ(h_<10 km)⟩ < 1.5 mm]. The fact that observations within the same cluster sense different precipitation regimes despite being close in space allow for characterization of the interaction of the thermodynamics of precipitation with the immediate surroundings and beyond. The distance between observations within the same cluster ranges from several tens of kilometers to a few hundreds (see Table 4).

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Sampling of the clustered observations for (top) 1 day and (bottom) 1 week. Observations corresponding to the same cluster are represented with the same color, so different colors show different clusters. Background image indicates the total accumulated precipitation for the same time period.

Citation: Bulletin of the American Meteorological Society 106, 4; 10.1175/BAMS-D-23-0322.1

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Table 3.

Statistics for the observation clusters based on the number of occultations per cluster. The first column shows the number of occultations defining the cluster; the second column shows the number of such clusters; and the third and fourth columns indicate the mean minimum and maximum distance within the observations in the cluster, respectively. The fifth column contains the mean minimum time difference between two occultations in the cluster. Numbers between parentheses are those corresponding to the clusters where at least one of the observations in the cluster hits precipitation and at least one of them does not (see text).

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Table 4.

Statistics for the observation clusters based on the number of transmitters and receivers involved. Numbers between parentheses are those corresponding to the clusters where at least one of the observations in the cluster hits precipitation and at least one of them does not (see text).

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It is relevant to note the unique capability of Spire nanosatellites to track the four major GNSS constellations, representing currently (beginning of 2024) around 100 active GNSS transmitters in medium Earth orbit (MEO) orbit. With this, already a single receiver with a sufficient number of PRO measurement channels can often collect measurements so closely spaced that they resemble small clusters. This can be seen in the first row in Table 4, where clusters of up to eight occultations can be achieved from a single receiving satellite. Such capability is important when considering studies and missions, since these findings suggest that commercial PRO may be able to achieve the science objectives proposed in Turk et al. (2019, 2022) more easily than previously considered. In fact, clusters involving a single receiving satellite account for more than 50% of the total clusters.

With enough statistics, and with the thermodynamic retrievals of such observations, studies about the differences in the thermodynamics between observations inside and outside deep convection would be possible without the need to account for collocated measurements from other missions and with embedded information about hydrometeor vertical structures.

Finally, another interesting feature from the clusters collected from the Spire nanosatellites is that when such clusters involve FM170 (which is flying in a different orbit than FM166 and FM167), the direction of the observation is different, that is, nearly perpendicular to those obtained from FM166 and FM167. This happens because the coincident observations between FM166/FM167 and FM170 occur when the former two are in the ascending part of the orbit, whereas FM170 is in its descending part. This implies that the same precipitating systems are observed from different view angles, making observations in the clusters rather complementary. Such clusters, with observations crossing over each other in two directions, might be also interesting for assimilation applications, for better chances of capturing spatial gradients of moisture.