# A multi-frequency spaceborne radar perspective of deep convection

###### Abstract

Global numerical weather models are starting to resolve atmospheric moist
convection which comes with a critical need for observational constraints. One
avenue for such constraints is spaceborne radar which tend to operate at three
wavelengths, Ku-, Ka- and W-band. Many studies of deep convection in the past
have primarily leveraged Ku-band because it is less affected by attenuation
and multiple scattering. However, future spaceborne radar missions might not
contain a Ku-band radar and thus considering the view of convection from Ka-
band or W-band compared to the Ku-band would be useful. This study examines a
coincident dataset between the Global Precipitation Measurement (GPM) Mission
and CloudSat as well as the entire GPM record to compare convective
characteristics across various wavelengths within deep convection. We find
that W-band reflectivity (Z) tends to maximize near the Ku-band defined echo-
top while Ka-band often maximizes 4-5 km below. The height of the maximum Z
above the melting level for W-band and Ka-band do not linearly relate to the
Ku-band maximum. However, using the full GPM record the Ka-band 30 dBZ echo-
tops can be linearly related to the Ku-band 40 dBZ echo-top with an $R^{2}$ of
0.62 and a root mean squared error of about 1 km. The spatial distribution of
echo-tops from Ka-band corresponds well to the Ku-band echo-tops, highlighting
regions of relatively large ice water path. This paper suggests that Ka-band
only missions, like NASA’s Investigation for Convective Updrafts, should be
able to characterize global convection in a similar manner to a Ku-band
system.

There has been a long history of studying global storms using Ku-band [2 cm,
13 GHz] spaceborne radar, most likely because of the least number of
challenges (e.g., loss of signal) at Ku-band compared to Ka- [8 mm, 35 GHz]
and W-band [3 mm, 89 GHz]. However, each radar system offers different
perspectives on hydrometeor profiles observed in deep convection that have
remained largely unexplored, perspectives that provide insights into
convective storm systems. Therefore, it is useful to know how storms measured
at Ka-band and W-band compare to storms measured at Ku-band. We find that many
of Ka-band convective properties can be linearly related to Ku-band and thus
Ka-band only mission designs should be suitable for studying convective
storms.

##  1 Introduction

For many places around the world, direct observations of storm characteristics
are difficult to obtain. Regions over oceans, complex terrain, and other
remote areas without access to high temporal and spatial resolution ground-
based remote sensing or in-situ observations are common across the world.
Evaluating the representation of storms in global numerical weather
predictions is therefore a major challenge. This is now becoming particularly
problematic since global numerical weather prediction models have grid-
spacings that are approaching convective allowing scales (e.g., 4 km: DYAMOND;
Stevens et al., 2019). One solution to help observe storms globally is to use
spaceborne cloud and precipitation radars (see Battaglia et al., 2020, for a
review)

The Tropical Rainfall Measurement Mission (TRMM; Kummerow et al., 1998) flew
the first spaceborne precipitation radar that was launched in 1997 and
operated at 13.5 GHz (i.e., Ku-band; 2 cm wavelength). Its focus was on
estimating near-surface rainfall around the tropics. The first spaceborne
cloud radar was launched in 2006, as part of the CloudSat mission. The
CloudSat Cloud Profiling Radar (CPR; CloudSat Stephens et al., 2002) was a
highly sensitive (-30 dBZ) 94 GHz (W-band; 3 mm wavelength) cloud radar with a
focus on studying cloud systems. Following CPR and TRMM was the Global
Precipitation Measurement (GPM) mission (Hou et al., 2014) that was launched
in 2014 and included the Dual-frequency Precipitation Radar (DPR), operating
at 13 GHz (KuPR) and 35 GHz (KaPR) on the GPM core satellite. GPM aimed to
continue the efforts of TRMM. Following GPM, NASA launched a Radar in a
Cubesat (RainCube; Peral et al., 2018) technology demonstration of a Ka-band
precipitation radar housed on a small spacecraft (Cubesat), which provided
evidence that scientific radar data could be collected by smaller-scale
missions at lower costs than its predecessors (e.g., TRMM, GPM). This point
was further underscored in 2023 by the private company tomorrow.io who
launched two pathfinder Ka-band radars built based on RainCube heritage with
plans of launching a fleet of Ka-band scanning radars and microwave
radiometers in the next few years (Roy et al., 2023). After RainCube, a
spaceborne radar was launched by China in 2023, named the FY-3G, carrying a
nearly identical radar to GPM (Zhang et al., 2023). The most recent spaceborne
radar, ESA’s EarthCARE mission, was launched in May 2024, carrying a near-copy
of the CloudSat CPR (Illingworth et al., 2015).

Apart from EarthCARE, none of the previous spaceborne radars have Doppler
capabilities, and except for CPR, are generally focused on measurement of
precipitation size hydrometeors near the surface. To date, the current
spaceborne radar record does not have any direct dynamic information to
characterize the dynamical processes defining the intensity of storms which
would be valuable for assessing the representation of atmospheric moist
convection in Earth system models. Additionally, the potential value of
Doppler radar data from space (e.g., EarthCARE) for this purpose remains an
unresolved topic of research. As an alternative, convective proxies derived
from radar reflectivity profiles, like a storm’s height at a given
reflectivity threshold, have been derived. The general idea for reflectivity-
only convective metrics is that the higher the echo-top height altitude of a
specific reflectivity value, the more intense the convection. The reasoning is
that a stronger updraft can loft more massive hydrometeors to higher
altitudes, thus producing larger reflectivities at higher altitudes. The exact
reflectivity value adopted for the echo-top calculation varies because of the
different saturation values for each wavelength and the radars’ minimum
sensitivity thus offering different insights about the lofting of hydrometeors
on convection. Reflectivity values for convective proxies range from 0 and 10
dBZ for CPR (e.g., Stephens and Wood, 2007; Luo et al., 2008; Takahashi and
Luo, 2014) and 30 to 40 dBZ for TRMM (e.g., Zipser et al., 2006; Houze Jr. et
al., 2015) and GPM’s KuPR (e.g., Skofronick-Jackson et al., 2018). The broad
result of the echo-top convective proxies between missions paints a consistent
picture of stronger convection being generally located over land, with more
frequent locations of intense convection over hotspots like Central Africa,
North-Central Argentina and the central United States (Zipser et al., 2006;
Houze Jr. et al., 2015; Takahashi and Luo, 2014). The differences in echo-top
heights of the different radar systems, not yet researched in detail, also
offers potential insights into processes associated with detraining ice in
upper levels of storms.

In addition to EarthCARE, there are also several planned missions with radar
concepts that aim to produce measurements of vertical velocity or surrogates
of this vertical motion. NASA’s INvestigation of Convective UpdraftS (INCUS),
applies a novel sampling strategy using three Ka-band non-Doppler radars in a
train to measure the change in reflectivity at short time scales (30, 90 and
120 seconds) to derive the vertical motion and convective mass flux
information about storms (Prasanth et al., 2023; Dolan et al., 2023). INCUS is
currently slated to launch in late 2026 and will be followed with two Doppler
radars as part of NASA’s Atmospheric Observing System (AOS). One radar will
operate at Ku-band in an inclined orbit and with a performance similar to the
GPM KuPR and a second will operate at higher frequencies (Ka- and W- or both)
in a polar orbit. At the time of writing this the second radar is still in its
formulation phase.

Past papers have compared the profiles of reflectivity measured by CloudSat,
TRMM and GPM. Some papers compared sensors to one another (TRMM to CloudSat;
Sindhu and Bhat, 2013), and others compared the profiles with ground-based
radars (Fall et al., 2013), showing the strengths of each radar. CloudSat was
designed to observe clouds, the formation of precipitation and as well as
precipitation that goes undetected by GPM (e.g., Berg et al., 2010; Behrangi
et al., 2016), whereas TRMM and GPM were designed to detect larger
hydrometeors and more intense liquid precipitation rates. Beyond the measured
reflectivity profiles, retrieved precipitation rates, both rain and snow, have
been compared between the satellites and ground-based estimates. Initial snow
estimates from GPM were substantially lower than those of CloudSat (Casella et
al., 2017; Skofronick-Jackson et al., 2019; Mroz et al., 2021), but could be
improved by adjustments to assumptions in the solid phase retrievals shown by
Chase et al. (2020, 2021, 2022b). For liquid precipitation, Hayden and Liu
(2018) suggested the use of CloudSat precipitation retrievals for the lower
precipitation rates (approximately 1 $\mathrm{mm\ hr^{-1}}$) and GPM for the
larger precipitation rates to help create a more complete picture of the
global precipitation. Liang et al. (2024) also suggested a combined dataset
between CloudSat and GPM’s KaPR to better capture the full profile of
hydrometeors.

Interpretation of radar echoes suffers from complicating factors, including
effects of attenuation (e.g., Meneghini and Kozu, 1990; Lhermitte, 1990),
multiple scattering (e.g., Battaglia and Panegrossi, 2020) and non-Rayleigh
scattering that get exacerbated as the operating frequency of the radar
increases. These challenges are more prevalent in convection, where vertical
motions support the formation of larger hydrometeors. Although these
difficulties are understood, there has been a dearth of both qualitative and
quantitative comparisons of Ku-, Ka- and W-band reflectivity to assess these
effects.

The research reported in this study compares Ku-, Ka- and W-band radar
profiles measured within deep convection. Given Ku-band is the least affected
by attenuation, multiple scattering and non-Rayleigh scattering, the primary
objective is to compare the Ka-band measured profiles to the Ku-band radar
profiles and quantify how much of the Ku-band information content is captured.
Ka-band is the primary evaluation because this paper intends to evaluate how
the emerging Ka-band only platforms such as INCUS, and tomorrow.io will
perform in deep convection. This study further compares the Ku- and Ka-band
profiles to those obtained by the W-band CPR of CloudSat. The intent of this
comparison is not to highlight the benefits of combining the information
provided by these different frequencies, as this will be a topic of a future
study, but rather to provide some insight, both qualitative and quantitative,
on the attenuation, non-Rayleigh scattering, and multiple scattering
experienced by the millimeter wavelength radars (W-, and Ka- band) within deep
convection in contrast to the Ku-band reflectivity. The aims of the study are
achieved both by analysis of coincident GPM and CloudSat observations complied
in the Turk et al. (2021) database and by analysis of the entire Ku- and Ka-
band reflectivity GPM record. The primary focus of the analyses is limited to
echoes above the melting level and near the tops of intense deep storms where
convective updrafts are often maximized (e.g., Varble et al., 2014).

##  2 Data and Methods

###  2.1 Radar descriptions

The two radars used in this study are the CloudSat Cloud Profiling Radar (CPR;
Stephens et al., 2002) and the Global Precipitation Measurement mission’s
Dual-frequency Precipitation Radar (DPR; Hou et al., 2014). The CPR is a
W-band (94 GHz; 3 mm) non-scanning radar (i.e., single beam) with a vertical
resolution of 500 m, a horizontal resolution of about 1.4 km and a minimum
sensitivity of about -30 dBZ early in the life of the radar to approximately
-25 dBZ toward the end of the mission life. The CPR was launched in 2006 into
a polar orbit with an inclination of 98.2 degrees as part of NASA’s A-train
(Stephens et al., 2008). While the radar was initially planned to operate for
24 months, it succeeded in operating for 17 years and the mission formally
ended in December 2023. In 2011, a spacecraft battery anomaly occurred which
prevented CPR from collecting observations during night (i.e., no sunlight on
the solar array). CPR collected data regularly in the daylight only mode until
the end of the mission, with interruptions to the record occurring because of
reaction wheel failures and the introduction of a solution designed to sustain
the measurement record (e.g., Hallowell et al., 2022).

The DPR was launched in early 2014 into a 65-degree inclination operating at
Ku- (KuPR; 13 GHz; 2 cm) and Ka-band (KaPR; 35 GHz; 8 mm). The KuPR and KaPR
are scanning radars with 49 cross-track beams creating a 250 km swath. The
KuPR has a vertical resolution of 250 m, a horizontal resolution of about 5
km, and a minimum sensitivity of near 15 dBZ (Masaki et al., 2022). The KaPR
has two scan modes, one that was originally matched to the inner swath of the
KuPR, which has a vertical resolution of 250 m and a minimum sensitivity of 19
dBZ. The second scan mode was originally located interlaced in the inner swath
of the KuPR, but these scans were moved in May 2018 to match the outerswath of
the KuPR enabling full swath coincident dual-frequency measurements (Furukawa
et al., 2018). The vertical resolution of the second scan mode is 500 m and
has a minimum sensitivity near 14 dBZ. The only notable complications of the
GPM bus are that the satellite is down to three reaction wheels and there was
an orbit raise in November 2023. Data collected after November 2023 are
currently under quality control with the GPM team.

###  2.2 GPM-CloudSat Coincidence

The coincidence dataset between GPM and CloudSat (2B.CSATGPM; Turk et al.,
2021) is quantitatively used to compare profiles available from the three
wavelengths of the two radars operating in space. The dataset is made by
finding all points within the GPM swath that intersect the CloudSat ground
track within 15 mins of one another from 2014 through 2019. The data are
collocated by taking the closest footprint of GPM to each footprint of
CloudSat. See Turk et al. (2021) for more specific details of the matching
procedure. From all coincidences, we sub-sample the dataset to only
convectively labeled profiles from the GPM algorithm (i.e., Awaka et al.,
2021) and profiles that extend at least 5 km above the surface elevation,
where the top was determined from the GPM storm top algorithm
(heightStormTop). These criteria were used to isolate deep convection. The
result is approximately 5,000 profiles of coincident measurements globally and
a map of their locations can be found in the appendix (Fig. S1).

###  2.3 GPM-DPR dataset

To extend the multi-wavelength comparison of storms to a larger sample size,
the entire GPM-DPR dataset, ranging from March 2014 to November 2023, is also
analyzed. Both the 2A.DPR files and the 2B.CMB files are acquired to enable
the use of both the raw radar measurements (2A.DPR) and the combined radar-
radiometer retrievals of precipitation rate and water content (Grecu et al.,
2016; Olson, 2022). Data are sub-sampled in the same way as the coincident
dataset. After all subsampling, more than 39 million profiles are available
for the analysis described in Section 3.2.

###  2.4 Convective Proxies

Figure 1: Example profile from GPM-DPR over the Arabian Peninsula on 11 June
2018. Several convective proxies are shown including the 20 dBZ (square red
marker) and 30 dBZ (circle red marker) echo-top for the KaPR, the maximum of
KaPR above the melting level (red star), 30 dBZ (square blue marker) and 40
dBZ (circle blue marker) and the maximum of KuPR above the melting level (blue
star). The horizontal black lines are the melting level (dashed) and the
surface (solid). The text on the bottom of the figure is the combined
retrieval of ice water path (IWP), rainwater path (RWP) near surface
precipitation rate (R), two-way path integrated attenuation at Ku and Ka
(PIAKu and PIAKa respectively).

A wide variety of convective proxies are used to compare the results here with
those in the literature to understand how these proxies differ according to
the operating frequency of the radar measurements they are derived for. Echo-
tops of 0 dBZ and 10 dBZ are extracted from the CPR profiles, 20 dBZ and 30
dBZ are extracted from the KaPR, and 30 dBZ and 40 dBZ are extracted for the
KuPR. We also leverage the heightStormTop product which is the top of the DPR
data determined by a coherent precipitation echo in the KuPR data (Kubota and
Takahashi, 2021). Beyond the echo-tops we also extract a variety of retrieved
quantities from the 2B.CMB retrieval (Version 7; Olson, 2022; Grecu et al.,
2016). Specifically, we use the water content split into ice water path (IWP)
and rain water path (RWP), the near surface instantaneous precipitation rate
(R), and the path integrated attenuation (PIA) at Ku- and Ka-band. Lastly, the
height of the maximum reflectivity above the melting level (MAML) is
extracted. A larger MAML value indicates a stronger convective updraft capable
of lofting large hydrometeors to higher altitudes. We use the melting level
instead of the surface as the reference point partly to avoid the influence of
the radar bright band, which can have large reflectivity values, but also
because convective updrafts tend to be strongest above the melting layer
(Varble et al., 2014). The melting level is determined from the 2A.DPR
algorithm (Kubota and Takahashi, 2021), which uses the bright band location if
one is detected, or the 0°C isotherm from a numerical weather prediction model
if not. An example of convective profiles with annotated convective proxies
can be found in Fig. 1. For this case, collected on the west coast of the
Arabian Peninsula, the maximum reflectivity from KaPR is found at 18 km ASL
and 35 dBZ, while the less attenuated KuPR is lower in the atmosphere,
maximizing at about 9 km ASL and almost 50 dBZ. For the global maps of
convective proxies (Section 3.c.2) we use the standard anomaly which is
defined as

$z=\frac{(x-\mu)}{\sigma}$ (1)

where $x$ is the KuPR or KaPR data observation, $\mu$ is the mean value of $x$
across all KuPR or KaPR observations and $\sigma$ is standard deviation of $x$
across all GPM observations. The standard anomaly is used to evaluate in a
relative sense where stronger convection is located globally across multiple
metrics.

##  3 Results and Discussion

###  3.1 Case Studies: Coincident Dataset

Before presenting broad statistical comparisons between CloudSat, KaPR and
KuPR, a few examples of coincidences in strong convection are analyzed. Strong
convection is chosen to highlight a few cases where attenuation and multiple
scattering would most likely occur (i.e., worst case scenario).

####  3.1.1 12 June 2018

Figure 2: A convective coincidence within the GPM-CloudSat dataset
exemplifying the view of convection from the three spaceborne wavelengths. For
this case, a nocturnal MCS is observed by NEXRAD, GPM and CloudSat at about
0831 UTC on 12 June 2018. (a) plan view of the composite reflectivity from the
KSGF radar, located with the square marker. The dashed lines are the GPM
swath; the transparent line across the swath is the CloudSat ground-track. The
two filled circle markers are the start and end of the cross-section in b-e.
(b) Along track calibrated brightness temperatures from GPM-GMI. (c) KuPR
along the CPR track. (d) KaPR along the CPR track. (e) CPR reflectivity. All
color scales are the same. Horizontal white lines are the location of the mean
profile in Fig 3.

On 12 June 2018 at about 0830 UTC a mesoscale convective system producing
surface winds greater than 65 mph and numerous reports of downed trees (SPC
storm reports, not shown) was sampled by the ground-based S-band (KSGF), GPM
and CloudSat all within 5 minutes of each other near Springfield, Missouri,
USA. The plan view of the scene is shown in Fig. 2a, where the ground-based
radar composite reflectivity exemplifies a prototypical nocturnal MCS with a
leading line of convection and trailing stratiform region. GPM’s microwave
radiometer (GMI) onboard the same spacecraft as DPR provides additional
context to the ongoing convection, showing depressions in the brightness
temperatures from 19 GHz and higher frequencies. The polarization corrected
minimum brightness temperature of 260 K for 19 GHz is right at the cutoff
between storms containing hail and not containing hail according to Mroz et
al. (2017) (261 K) and is estimated at a 15$\%$ chance of containing hail from
Bang and Cecil (2019).

The cross-sections of all frequencies (Fig. 2c-e) show the convective echoes
associated with the leading line of convection (700 - 750 km on x-axis). All
radar frequencies indicate a characteristic bright-band in the trailing
stratiform portion of the storm (550 - 700 km). The magnitude in radar
reflectivity detected depends on the radar wavelength. The KuPR peaks near 50
dBZ, while KaPR peaks near 35 dBZ and CPR around 20 dBZ. Lastly, a clear
attenuation signal is evident in both CPR and KaPR, with reduced surface
echoes (700 - 750 km). Even the KuPR has a relatively reduced surface echo
near 730 km (Fig. 2c) compared to adjacent scans which suggests some degree of
attenuation, although less that at the other two frequencies.

Figure 3: Mean reflectivity profiles from along the convective line in Fig 2
b-e showing the different wavelengths of radar for the same location and time.
KuPR is in blue, KaPR is in red and CPR is in yellow. Square and circle
markers show common echo-top height locations from the literature and the star
is the maximum value above the melting level. The dashed black line is the
melting level, the dotted line is the surface.

Fig. 3 presents the mean profile across the leading line of convection (white
line in Fig. 2b-e). For this case, CPR 0 and 10 dBZ echo-tops are 2 - 4 km
taller than the echo-top heights from the KaPR and KuPR. In fact, CPR observes
echo up to 15 km, while the KuPR and KaPR only have echo up to 13 and 11 km
respectively, primarily because of the lack of sensitivity of GPM’s radars
(compared to CPR). The maximum reflectivity for each wavelength happens at
different parts of the profile as well. CPR peaks at 17 dBZ at about 10 km,
while KaPR maximizes at 31 dBZ at 6 km, KuPR at 41 dBZ at 5.6 km.

####  3.1.2 08 May 2019

Figure 4: A contrasting convective example from the GPM-CloudSat dataset with
a more isolated storm morphology. This case is from Paraguay on the afternoon
of 08 May 2019 and panel (a) has the GOES-16 visible image instead of the
NEXRAD image.

On 08 May 2019 a storm located over Paraguay was observed by GPM and CloudSat.
The GOES visible image from 18:10 UTC shows an overshooting top and above
anvil cirrus plume likely indicative of severe weather (Fig. 4a; Bedka et al.,
2018). Note that the visible image is from 1810 UTC while the CloudSat
overpass is from near 1802 UTC and the GPM data are from about 1812 UTC.
Despite the about a 10 min difference between GPM and CloudSat a similar
structure to the storm is seen with echoes from all wavelengths extending to
15 km, about 5 km taller than the storm sampled in Fig. 2 (Fig. 4c-e). GMI
detects polarization corrected brightness temperature depressions from 19 GHz
and higher frequencies (Fig. 4b). The minimum brightness temperature of 235 K
at 19 GHz is indicative of hail (e.g., Mroz et al., 2017) and using the Bang
and Cecil (2019) regression with the 19 and 35 GHz polarization corrected
temperatures suggests a $72\%$ likelihood that the column contains hail.

Figure 5: As in Fig. 3, but derived from the tallest echoes in Fig. 4 (the
Paraguay case)

The mean reflectivity profiles for the core of the storm (tallest echoes) are
shown in Fig. 5 (white line in Fig. 4c-e). For this case, all the echo-tops
correspond better to one another. CPR’s 0 and 10 dBZ echo-tops are at about 17
and 16 km while KaPR’s 20 and 30 dBZ echo-tops are at 15.75 and 13.5 and
KuPR’s 30 and 40 dBZ echo-tops are at 15 and 12.5 km. The maximum in
reflectivity location for each wavelength shows the effects of attenuating
radars. CPR and KaPR peak in the upper portion of the column with CPR
maximizing at about 20 dBZ around 14 km ASL and KaPR maximizing at 33 dBZ
around 12.3 km ASL. As in the previous case study, the maximum of KuPR is
found at a lower altitude than for the other frequencies with 47 dBZ at 6km.

####  3.1.3 Case Study Discussion

For both cases, the general structure of the core convection of the storms
aloft ($>$ 5km ASL) is captured no matter the wavelength, radar resolution
(i.e., along-track spacing) or sensitivity. The differences arise from the
echo-top height locations, the anvil characteristics and the depth at which
the shorter wavelengths become affected by attenuation and multiple
scattering. Contextualizing these two cases of very strong convection in the
broader convective proxy literature, both cases would be used in CPR studies
of deep convective clouds with 10 dBZ echo-tops exceeding 10 km (e.g.,
Takahashi et al., 2023).Meanwhile from the KuPR perspective, the MCS on 12 Jun
2018 would be within the top $0.33\%$ of storms and the more isolated storm
from 08 May 2019 would be within the top $0.03\%$ within the Zipser et al.
(2006) framework (see Fig. 6 in Skofronick-Jackson et al., 2018). In the
University of Washington classifications both storms are considered the Deep
and Wide classification (Houze Jr. et al., 2007), but note the part sampled by
the three radars for the MCS case was likely not the most intense part of the
storm (stronger GMI brightness temperature deficits were found outside the DPR
swath; not shown).

These two cases provide insight on how to interpret single frequency missions
when examining the strongest convective storms. It is known that shorter
wavelength radars suffer from more attenuation (e.g., Table 4.7 in Meneghini
and Kozu, 1990) and multiple scattering effects (e.g., Battaglia et al.,
2010), which suggests missions that only have Ka- or W- band radar are likely
to have complications with retrieving information within deep convection. Both
examples discussed were intense convection and contained hydrometeors
responsible for strong attenuation and multiple scattering. The combined
radar-radiometer retrieval from GPM shows large amounts of ice mass and
estimated the amount of two-way path integrated attenuation at 42 and 59 dB
for Ka-band for the two cases respectively. These are likely extreme cases in
anticipating the potential signal of the shorter wavelengths in deep
convection. Despite the strong nature of these convective profiles, the Ka-
band information matches well with the Ku-band for about 5 km of depth (i.e.,
echo-top to 6 km in the first case). This is encouraging for Ka-band only
missions, like INCUS and tomorrow.io, because there is clear signal from the
Ka-band in the upper portions of the storms where convective motions, and thus
convective mass flux, are the greatest (e.g., Varble et al., 2014). The W-band
has a similar signal but, as expected, the depth of profile where it mimics
the Ku-band is limited to about the first 2 km (starting from the KuPR echo-
top). In the next section, we use the entire coincident dataset to draw some
statistical relationships between echo-top heights between sensors as well as
the general profile characteristics.

###  3.2 Coincident Dataset Statistics

Figure 6: The potential relationship between the height of the maximum
reflectivity above the melting level (MAML) between (a) KaPR and KuPR and (b)
CPR and KuPR.

Using the full coincident dataset (approximately 5000 points) we first compare
the height of the maximum of reflectivity above the melting level (MAML)
between the shorter wavelengths (Ka- and W- band) and Ku-band (Fig. 6). It is
not expected that the MAML for the shorter wavelengths should be identical to
Ku-band because of the nuances of attenuation and non-Rayleigh scattering but
the magnitude of the correlation could show that the shorter wavelengths have
a similar signal in convective intensity. For the entire database considered,
the MAML derived from both the Ka- and W- band show relatively weak
correspondence to the Ku-band based heights (Fig. 6), with small coefficients
of determination ($R^{2}$). Thus, the convective proxy of MAML for for KaPR
and CPR are not reproduced in the same manner in KuPR data.

The correspondences between the radar profiles are measurably closer when
expressed in terms of echo top heights (Fig. 7). $R^{2}$ values follow
expectation with generally decreasing $R^{2}$ with larger differences in
reflectivity thresholds. The largest $R^{2}$ values are between the 30 dBZ
KaPR height and the 30 dBZ KuPR height, with a value of almost 0.9 (blue line
Fig. 7), while the smallest $R^{2}$ is between CPR’s 0 dBZ echo-top height and
KuPR’s 40 dBZ echo-top height with a value less than 0.2. Considering the top
of the KuPR echo (heightStromTop), the CPR 10 dBZ echo-top corresponds
reasonably well with an $R^{2}$ of 0.74. All linear fits between different
echo-tops are shown in Table 1, along with the root mean squared error if the
linear fit was used to translate KaPR or CPR echo-top height to a KuPR echo-
top height. For example, if the KaPR 20 dBZ echo-top was translated to a KuPR
20dBZ echo-top, the root mean squared error is 0.62 km. Note that the linear
regression coefficients in Table 1 for the KaPR to KuPR echo-tops are near 1
for both the 20 dBZ and 30 dBZ echtops, implying you can use the KaPR echo-top
interchangeably with the KuPR echo-top.

Figure 7: The strength of a linear relationship (coefficient of determination)
between radars for different echo top height thresholds in the combined GPM-
CloudSat dataset.

Contoured frequency by altitude diagrams (CFADS) oriented from the
heightStormTop (i.e., KuPR top; approximately 12 dBZ) characterize the broad
shape of the profiles between the three frequencies for the entire database.
For KaPR, the median (line Fig. 8a) of the CFAD increases at 3 dB/km toward
about 4 km where the slope changes to 1 dB/km. Meanwhile KaPR (Fig. 8b)
increases at a rate of 2 dB/km to 3 km from GPM echo-top and stays constant at
about 25 dBZ toward lower altitudes. Lastly, CPR shows echoes deep above the
GPM echo-top, sometimes more than 5 km taller (Fig. 8c). The slope in the
W-band remains constant from about 2.5 km above the GPM echo-top to about 1 km
below the GPM echo-top at 5.7 dB/km and decreases at a constant rate of 1.7
dB/km towards lower altitudes.

Figure 8: Broad statistical profile characteristics from the combined dataset.
These are contour frequency by altitude diagrams for (a) KuPR (b) KaPR and (c)
CPR for the coincident dataset relative to GPM’s heightStormTop. The color
shading is relative frequency normalized to the maximum in each y-axis row.
The white line is the median value for each y-axis row.

The coincident dataset gives both a qualitative and quantitative depiction of
deep convection from the perspective of radar reflectivity at the three
wavelengths currently available from space. In general, the coincident data
results suggest that the maximum in both Ka-band and W-band does not
correspond well to the maximum in the Ku-band. This is expected given the
different sensitivities of each radar and the added challenges of non-Rayleigh
scattering, attenuation, and multiple scattering in interpreting the
reflectivities. That being said, the echo-top height of the Ka-band 30 dBZ
corresponds well to the Ku-band 30 and 40 dBZ echo-top heights. There is then
potential to translate between the previous Ku-band only literature to the new
Ka-band only literature of future missions (i.e., INCUS; Tomorrow.io).

Linear Regression Stats: Coincident Dataset
---
Pairing |  $R^{2}$ |  coefficient |  intercept |  rmse [km]
$\mathrm{KaPR_{MAML}}$ \- $\mathrm{KuPR_{MAML}}$ |  0.28 |  0.82 |  0.52 |  0.96
$\mathrm{KaPR_{20}}$ \- $\mathrm{KuPR_{20}}$ |  0.96 |  0.99 |  0.37 |  0.62
$\mathrm{KaPR_{30}}$ \- $\mathrm{KuPR_{30}}$ |  0.87 |  0.98 |  0.37 |  1.03
$\mathrm{KaPR_{30}}$ \- $\mathrm{KuPR_{40}}$ |  0.71 |  0.69 |  0.25 |  1.30
$\mathrm{CPR_{MAML}}$ \- $\mathrm{KuPR_{MAML}}$ |  0.05 |  0.58 |  2.1 |  1.85
$\mathrm{CPR_{0}}$ \- heightStormTop |  0.59 |  0.66 |  0.95 |  1.80
$\mathrm{CPR_{10}}$ \- heightStormTop |  0.74 |  0.83 |  1.24 |  1.56
Table 1:  Linear statistics between various radars for the coincident dataset.

###  3.3 Full GPM record

####  3.3.1 All profile statistics

The number of samples in the coincident GPM-CloudSat dataset is limited. Here
we also consider the full GPM record where the KuPR and KaPR are coincident.
There are more than 39 million coincident profiles between KuPR and KaPR in
deep convection (see Fig. 11a) for the distribution of samples). The same
analysis presented in Fig. 6 is reproduced for the larger dataset (Fig. 9).

Figure 9: The comparison of the MAML of KuPR and KaPR for the entire GPM
database.

The results of the analysis of the coincident dataset are essentially
reproduced in the analysis of the full GPM dataset which is summarized in
Table 2. The correspondences between the Ku and Ka band height proxies are
closer. For the MAML the $R^{2}$ values of 0.4 suggesting a weak linear
relationship between the KaPR and KuPR MAML. That being said, the root mean
squared error is less than one kilometer for the linear regression fit on KaPR
(0.71 km; Table 2). For brevity, Fig. 7 is not reproduced for the full GPM
dataset but the statistics are included in Table 2. Overall, the various KuPR
and KaPR echo-tops correspond well. The $R^{2}$ values are all greater than
0.6, with the KaPR 30 dBZ echo-top height being able to explain 62$\%$ of the
variation of the KuPR 40 dBZ echo-top height. The best linear correspondence
($R^{2}$ of 0.9) is the 20 dBZ echo-top for both KuPR and KaPR which is
anticipated because 20 dBZ should be close to the Rayleigh scattering regime
for KuPR and KaPR. This bulk analysis shows that KaPR echo-tops linearly
relate to KuPR echo-tops on a global average. This implies an ability to
translate Ka-band echo-tops to Ku-band echo-tops and suggests that Ka-band
only missions can provide a similar measure of convective intensity as a Ku-
band only mission. It is not clear if this global relationship holds for all
locations, for example regions of locally stronger (weaker) convection.

Figure 10: A statistical comparison (CFAD) of the top 1$\%$ tallest storms
(greater than 15 km above the surface) in the entire GPM record. The profiles
are oriented from heightStormTop and normalized to the max count for each
y-axis bin. (a) KuPR profiles (b) KaPR profiles. The total number of profiles
in these CFADs is 372,249.

Beyond looking at the echo-tops, we consider the full reflectivity profiles of
the KuPR and KaPR. In this case, only that portion of the profiles
corresponding to temperatures less than 0degC and profiles where the echo-top
is more than 15 km above the surface were considered. These profiles were
chosen anticipating that they are profiles with the largest likelihood of
attenuation, multiple scattering and non-Rayleigh scattering. Fig. 10 shows
that even in the tallest profiles (top 1$\%$ of profiles), the median KaPR
profile increases alongside the KuPR profile from GPM defined echo-top
(heightStormTop) to 10 km below, maximizing with a value near 30 dBZ. The
primary differences in the CFADs are the slopes of the reflectivity. For the
KuPR, the slope near the GPM echo-top is about 5 dB/km for the first km, but
then reduces to about 2 dB/km until about 10 km below GPM echo-top where the
slope increases again until 12 km. The KaPR CFAD shows a similar 5 dB/km slope
for the first km, but then has a reduced slope of 0.5 dB/km till about 10 km
and the slope then becomes negative. The CFADs of the tallest 1$\%$ of
profiles observed by GPM suggest that despite the added complications of
multiple scattering, attenuation and non-Rayleigh scattering at Ka-band, there
is similar information contained in the Ka-band signal compared to Ku-band.
Thus, Ka-band missions looking to quantify convective intensity, especially
missions looking at the ice phase layer (e.g., INCUS), can expect to have
useable signal.

####  3.3.2 Global Distributions

Figure 11: Global maps of deep convection as observed by GPM retrieved
properties. (a) The count of all deep convective profiles from 2014 – 2023.
(b) The conditional mean standardized anomaly of the combined retrieval near
surface rain rate. (c) as in b but for the retrieved ice water path.

Before we consider the spatial distribution of the radar echo-tops, we first
consider the retrieved quantities out of the 2B.CMB algorithm (Grecu et al.,
2016; Olson, 2022) that provide the best estimate of the hydrometer profiles
(i.e., mass, precipitation rate) using both KuPR and KaPR as well as the GMI
brightness temperatures. Fig. 11 shows the mean standard anomaly in each
latitude-longitude bin. The original unscaled data of Fig. 11 and 12 can be
found in the supplementary material (Fig. S2, S3 respectively).

Using only the instantaneous near surface instantaneous rainfall rate (R) to
characterize the locations of the strongest convection, the data suggest the
primarily oceanic regions with many hotspots located near coastlines around
30∘ N and S (Fig. 11b). Meanwhile, using IWP as a metric of convective
intensity suggests the opposite of rainfall, highlighting mostly continental
locations, with hot spots (greater than 1 standard deviation) being found over
the central US, central Argentina and central Africa (Fig. 11c). Note that
these are conditional statistics on deep convection (i.e., when deep
convection occurs, these are the global hotspots). The seemingly contradicting
results between IWP and R has been shown before, suggesting that the most
intense rainfall rate events are associated with weaker convection (e.g.,
Hamada et al., 2015; Gingrey et al., 2018; Zipser and Liu, 2021; Xu et al.,
2022). These global distributions will serve as a reference for the various
echo-top values examined next.

Linear Regression Stats: Full GPM record
---
Pairing |  $R^{2}$ |  coefficient |  intercept |  rmse [km]
$\mathrm{KaPR_{MAML}}$ \- $\mathrm{KuPR_{MAML}}$ |  0.41 |  0.93 |  0.35 |  0.71
$\mathrm{KaPR_{20}}$ \- $\mathrm{KuPR_{20}}$ |  0.90 |  0.89 |  1.18 |  0.73
$\mathrm{KaPR_{30}}$ \- $\mathrm{KuPR_{30}}$ |  0.84 |  0.95 |  1.19 |  0.83
$\mathrm{KaPR_{30}}$ \- $\mathrm{KuPR_{40}}$ |  0.62 |  0.61 |  0.91 |  0.98
Table 2:  Linear statistics between various radars for the full GPM record.

Qualitatively, all echo-top proxies generally highlight the same areas, which
matches the IWP signal of convective intensity: central Africa, central
Argentina and central United States (Fig. 12 a-f). The differences between the
KaPR maps and KuPR maps are found in Fig. 12 g-i. The MAML shows the largest
difference over central Africa, with KaPR maxima height more than 0.25
standard deviations higher than Ku-band (Fig. 12g). Comparatively, regions of
large IWP over the USA and central Argentina show smaller differences in the
MAML between KuPR and KaPR. This implies a difference in the structure of
convective profiles of KuPR over central Africa, where the MAML is lower in
the atmosphere (i.e., closer to the melting level). We hypothesize this is a
result of a characteristically different convective environments over central
Africa compared to USA or central Argentina, but this is beyond the focus of
this paper. However, this serves to highlight how the differences themselves
offer hints about the vertical structure of the convection, a topic worthy of
future study. As for the differences between the KaPR 20 dBZ and KuPR 30 dBZ
echo-tops (Fig. 12h), in general the high latitude oceans have higher KaPR
anomalies where deep convection is far less frequent (Fig. 11a) and
continental regions show higher KuPR anomalies. Meanwhile the comparison of
the 30 dBZ KaPR to the 40 dBZ KuPR shows that the tropical oceanic regions
have generally higher Ka-band echo-top anomalies (Fig. 12i). Thus, if one were
to use a Ka-band only radar system and the 30 dBZ echo-top, there might be a
systematic bias in characterizing stronger convection over the tropical oceans
compared to Ku-band systems. In summary, the spatial correspondence between
KaPR and KuPR derived convective properties qualitatively match well.

Figure 12: Comparing the spatial distribution of the various measured echo-
tops from KuPR and KaPR. (a) The mean standard anomaly of the height of
maximum of KaPR above the melting level (b) The mean standard anomaly for KaPR
20 dBZ echo-top (c) The mean standard anomaly for KaPR 30 dBZ echo-top (d) The
mean standard anomaly for height of maximum KuPR above the melting level (e)
The mean standard anomaly for KuPR 30dBZ echo-top (f) The mean standard
anomaly for KuPR 40 dBZ echo-top (g) difference between panels a and d (h)
difference between panels b and e (i) difference between panels c and f.

##  4 Summary and Conclusions

There has been a rich history of spaceborne weather radars going back to TRMM
in 1997 and including three main frequencies: W-band (3 mm; CloudSat; CPR),
Ka-band (8 mm; GPM KaPR) and Ku-band (2 cm; TRMM and GPM KuPR). Numerous
studies (e.g., Zipser et al., 2006; Houze Jr. et al., 2015; Takahashi and Luo,
2014) have used the spaceborne measurements to investigate the distribution of
global storm properties, but often use only one frequency in their description
of storms. Thus, those studies are isolated to their specific frequency and
the process of translating the results between frequencies is not trivial.
This paper uses coincidences between GPM and CloudSat (Turk et al., 2021) as
well as the full GPM record to compare the selected convective proxies (i.e.,
various echo-tops) between radars. The results and conclusions are as follows:

  1. 1.

Two cases of strong convection were analyzed using coincident observations
from all three spaceborne radar frequencies: a prototypical nocturnal MCS over
the central USA and a more isolated system over Paraguay. The cases were
chosen to exemplify scenarios of strong attenuation, likely multiple
scattering and non-Rayleigh scattering effects (i.e., worst case scenarios).
Qualitatively, the two cases showed the potential richness of coincident
multi-frequency radar information as well as the complicating effects for
millimeter wave radars deep convection: (Fig. 2 \- Fig. 5).

  2. 2.

The entire coincident dataset corroborated the qualitative trends observed for
the case studies, including the following:

     * •

Cloudsat’s Cloud Profiling Radar (CPR) tended to maximize near the GPM
detected storm top (i.e., heightStormTop; 12 dBZ at Ku-band) and did not
linearly correspond to the height of the Ku-band (KuPR) maximum reflectivity
($R^{2}$ near 0).

     * •

GPM’s Ka-band (KaPR) reflectivity maximized at lower altitudes than the CPR,
often 4-5 km from GPM heightStormTop, but does not linearly correspond well
with the height of the KuPR maximum in reflectivity ($R^{2}$ of 0.28).

     * •

Specific KaPR echo-top values produced reasonable linear fits to specific KuPR
echo-top values (e.g., 30 dBZ from KaPR to 40 dBZ from KuPR; $R^{2}>0.7$).

  3. 3.

Extending the KaPR and KuPR comparisons to the full GPM record (April 2014 -
November 2023; more than 39 million profiles) showed the following:

     * •

The full GPM record had a similar result to the coincident dataset where the
linear relationship between the height of the KaPR maximum reflectivity and
the height of the Ku-band maximum reflectivity was not strong ($R^{2}$ of
0.4).

     * •

The KaPR 30 dBZ echo-top linear relationship was reasonably strong ($R^{2}$ of
0.62) with the KuPR 40 dBZ echo-top and had a root mean squared error less
than one kilometer.

     * •

CFADS in the tallest 1$\%$ of profiles show that the median KaPR profile
follows the KuPR profile with increasing reflectivity till 10 km below GPM
heightStormTop.

     * •

Maps of echo-tops from KaPR highlight similar regions as KuPR and coincide
well with the areas of strong convection delineated by ice water path.

Note that the conclusions from the coincident dataset between GPM and CloudSat
are from a relatively small sample size (5000 samples). Unfortunately, several
issues with the CPR spacecraft reduce the total size of the coincident
dataset, namely the battery failure in 2011 and the loss of most of the
reaction wheels to accurately point the radar in 2020. A similar W-band
Doppler radar on EarthCARE, launched in May 2024, offers an opportunity to
expand such coincidences between GPM and EarthCARE. Furthermore, the EarthCARE
Doppler radar information could be leveraged in new ways. Another caveat of
this work is that the primary vehicle of analysis were linear relationships
(i.e., linear regression) which were used for the sake of simplicity and
brevity. Non-linear methods, like random forests or neural networks, have
shown good performance in the atmospheric sciences (e.g., Chase et al., 2022a,
2023, and references therein) and might provide more accurate translations
from W-band or Ka-band to Ku-band.

Despite these limitations, the statistical similarity of the KaPR to KuPR in
this paper supports the assertion that Ka-band only missions (e.g., INCUS)
will indeed be able to provide an important characterization of the global
distribution of convection including those of the most intense convective
storms. This said, this paper primarily focused on the region of deep
convective profiles above the melting level which is the likely location of
the strongest convective updrafts (e.g., Varble et al., 2014). The use of a
Ka-band only system for rainfall mapping will have the added challenge of
strong attenuation with liquid phase hydrometeors, but these issues could
potentially be mitigated with incorporation of other constraints (e.g.,
L’Ecuyer and Stephens, 2002) such as coincident radiometric measurements from
microwave radiometers or opportunistic passive microwave temperatures from the
radar itself (e.g., Battaglia and Panegrossi, 2020).

In an ideal scenario, future spaceborne radar missions looking to characterize
convective clouds would have all three available wavelengths to properly
measure the wide spectrum of convective processes and associated hydrometeor
properties and provide multiple constraints for retrievals. Furthermore,
ideally at least one of the available wavelengths would have Doppler
capabilities. Unfortunately, such a system is likely not feasible for at least
the next decade, but as the cost of spaceborne radars (both launching and
building) continues to decrease, agencies should continue to explore
multifrequency radar systems.

###### Acknowledgements.

This work was supported by INCUS, a NASA Earth Venture Mission, funded by
NASA’s Science Mission Directorate and managed through the Earth System
Science Pathfinder Program Office under contract number 80LARC22DA011. K.
Rasmussen was also supported by NASA Grant number 80NSSC22K0608. We would like
to thank Sarah Bang, Pavlos Kollias, Zhoucan Xu and Stephen Nesbitt for their
input to this manuscript. The GPM DPR dataset used in this paper can be found
with this doi: 10.5067/GPM/DPR/GPM/2A/07, while the combined retrieval data
can be found with this doi: 10.5067/GPM/DPRGMI/CMB/2B/07. The coincident
dataset doesn’t have a DOI, but can be found on
https://storm.pps.eosdis.nasa.gov/storm/ or within the arthurhou data system
(https://arthurhouhttps.pps.eosdis.nasa.gov/gpmdata/). The processing scripts
used in this paper and the processed datasets will be available on Dryad upon
publication.

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