# Bridging time-delayed microwave radiometric observations and deep convection characteristics: a machine learning approach for the C²OMODO mission

Thomas Lefebvre, Hélène Brogniez, Ilhem Gharbi, Laura Hermozo, Dominique

Bouniol, Florent Dralet, Rémy Roca

► To cite this version:

Thomas Lefebvre, Hélène Brogniez, Ilhem Gharbi, Laura Hermozo, Dominique Bouniol, et al. Bridg-
ing time-delayed microwave radiometric observations and deep convection characteristics: a machine
learning approach for the C$^2$OMODO mission. IEEE Transactions on Geoscience and Remote Sensing,
2025, 63, pp.5303117. 10.1109/TGRS.2025.3583571. hal-05136936

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Distributed under a Creative Commons Attribution 4.0 International License
Bridging time-delayed microwave radiometric
observations and deep convection characteristics: a
machine learning approach for the C²OMODO
mission

Thomas Lefebvre, Hélène Brogniez, Ilhem Gharbi, Laura Hermozo, Dominique Bouniol, Florent Dralet, and Rémy Roca

**Abstract**—Deep convective cloud systems are central to the global water and energy cycle, and yet their representation in climate models remains challenging. This study explores the potential of machine learning to classify and characterize cloud structures inside cloud systems using radiometric measurements from the planned C²OMODO (Convective Core Observation through MicrOwave Derivative in the trOpics) mission. The relationships between cloud structure (anvil, stratiform, convective, and deep convective) and geophysical variables such as ice water path as well as integrated vertical ice momentum are investigated using a gradient boosting algorithm both for classification and regression purposes. The gradient boosting classification method achieves an overall accuracy (True Positive) above 70%. Retrievals of the geophysical variables yield R² ranging from 0.60 to 0.99. Furthermore, it is shown that applying a prior classification of the scenes improves the performances of the retrieval. This study highlights the potential of the forthcoming C²OMODO mission in advancing our understanding of convective systems and paves the way for in-depth studies on alternative or refined classification schemes and inputs, which could deliver even better results.

***Index Terms***—Classification and regression models, Cloud detection, Convective systems, Deep convection, Gradient Boosting Decision Tree (GBDT), Microwave radiometers, Time-derivative measurements.

# I. INTRODUCTION

DEEP convection transports mass, water and momentum
from the lower troposphere to the tropopause, generating

This work was supported by Centre national d'étude spatial (CNES) and Airbus Defense and Space (ADS) under the AOS/C²OMODO program. (Corresponding author: Thomas Lefebvre.)

Thomas Lefebvre is with LATMOS, Université Paris-Saclay/UVSQ/CNRS/IPSL, Guyancourt, France. (email: thomas.lefebvre@latmos.ipsl.fr)

Hélène Brogniez is with LATMOS, Université Paris-Saclay/UVSQ/CNRS/IPSL, Guyancourt, France and LSCE, Université Paris-Saclay/UVSQ/CEA/CNRS/IPSL, Gif-sur-Yvette, France.

Ilhem Gharbi is with GIPSA-Lab, Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, 38000 Grenoble, France

Laura Hermozo is with CNES, Toulouse, France

Dominique Bouniol is with CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France

Florent Dralet is with Université Paris-Saclay, ENS Paris-Saclay, DER de Physique, 91190, Gif-sur-Yvette, France

Rémy Roca is with Université de Toulouse, Laboratoire d'Etudes en Géophysique et Océanographie Spatiales (CNRS/CNES/IRD/UPS), Toulouse, France

cumulonimbus clouds that are at the heart of the water and energy cycle [1]. These small clouds can be further organized in a much larger deep-cloud system (DCS). DCSs extend for hundreds of kilometers horizontally and persist for several hours, producing more than 50% of precipitation in the tropics [2]–[6]. The largest and longest-lived of these systems are also strongly related to extreme precipitation events [7]. Their importance is not only restricted to the water cycle, as their extended ice cloud decks strongly interact with the Earth radiation budget [8].

These organized convective systems are not well repre
sented in climate models, where convective parametrization
traditionally fails to incorporate such scales. Emerging km-
scale models, used both for climate and meteorology purposes,
while successfully able to resolve such mesoscale features, still
suffer from strong biases in terms of morphology and duration
[9]–[11]. This could be linked to some known biases in the
representation of deep convection for which strong convective
updrafts intensity is generally underestimated [12]–[16].

To better constrain these models, relevant observations at both the scale of the overall system and the finer scale of deep convective features are needed. Furthermore, the wide diversity of DCS encountered across the globe [17] requires a global perspective. Dedicated satellite observations have demonstrated their ability to support cloud and precipitation research [18]. More specifically space borne radars and passive microwave radiometers in combination with geostationary observations have been extensively used to explore the physics of DCS [19]–[23]. Yet the dynamic features of deep convection remain difficult to access from space.

The recent advent of nadir looking Doppler radar mea
surements from the EarthCARE mission [24], provide a first
exploration into convective dynamics that could be completed
in the future by a more systematic measure of in-cloud winds.
Convoy of radars are also being considered as a way to access
the short-term deep convection dynamics as anticipated by the
INCUS (Investigation of Convective Updrafts) mission [25],
[26]. As for the C²OMODO mission, the primary objective
of INCUS is to measure vertical motions within convective
storms. To achieve this, the mission concept consists of a train
of three RainCube satellites, operating with three time-delays
(30 s, 90 s and 120 s) and carrying Ka-band (37.5 GHz) radars (no swath), supplemented by a passive radiometer measuring at 87 GHz and 183 GHz (TEMPEST-D type radiometer) over a 1000 km swath to provide the meso-scale context of the storms. Because of the expected signal attenuation, INCUS focuses mostly weak to moderate convection and on the upper part of intense convection.

In the same philosophy, the C²OMODO (Convective Core Observation through MicrOwave Derivative in the trOpics) mission aims to investigate dynamic properties of deep convection over a larger swath than INCUS, for delta-t studies, providing complementary observations on intense convective cores and the horizontal extension of convective systems [27]. Proposed by CNES as a contribution to the NASA AOS program scheduled for 2029, the C²OMODO mission focuses on the vertical updraft of deep convective cells. It involves the use of two identical passive microwave radiometers positioned less than 3 minutes apart to observe the temporal evolution of cloud systems over a short period of time.

A study by Auguste and Chaboureau (2022) [28] demonstrates the informational content of C²OMODO measurements. The objective of the present study is to highlight the capacity of the C²OMODO tandem to detect, attribute, and differentiate various parts of convective systems. Classifications based on data from a single radiometer are performed, as well as classifications that consider time-derivative measurements provided by the tandem. Moreover, integrating the characterization of different cloud components into the retrieval processes of geophysical variables (GVs) allows the regression models to be better adapted to these cloud classes. Indeed, cloud properties, particularly vertical motions within updrafts, vary significantly within a deep convective system [29], [30]. It is expected that the relationships between microphysical properties (ice content, production and dissipation) and dynamic properties (ice mass flux) will vary based on the cloud component.

This work is organized as follows. The first part deals with the data used, describing the characteristics of C²OMODO radiometers, the classification criteria for different parts of convective systems, the GVs, and the numerical simulations using the radiative transfer model and the cloud-resolving model. The second part presents the machine learning methods used for the classification and the regression of a subset of GVs targeted. It is not intended here to perform an exhaustive overview of the GVs that are under development for C²OMODO, but rather to use some of them as tools to highlight the added value of the short-time delayed measurements for the detection and classification of convection classification. The third part of the paper is devoted to results and discussion, including an analysis of the performance of both classification and retrieval models. The paper concludes with a summary of the results obtained and the foreseen works on this topic.

## II. DATA

### A. Characteristics of the C²OMODO tandem

The C²OMODO mission uses a temporal differentiation method with twin passive microwave radiometers, separated by a short time delay (dt) of approximately 1-3 minutes. The

underlying idea behind C²OMODO is to interpret short-term brightness temperature (Tb) variations (hereafter dTb/dt) from the radiometers as changes in geophysical variables (GVs) tied to dynamic information.

The temporal derivative of Tb reflects the evolving ice content profile, influenced by horizontal advection, vertical convection, and microphysical processes. The contribution of advection depends on both the horizontal wind speed and the time delay dt. Thus, the delay dt aims at minimizing the contribution from horizontal advection between observations [27] in the case of deep convection, a short dt minimizes the influence of horizontal transport on Tb variations so that they capture mostly vertical motions. This assumption holds well for the HEC simulation, but is not valid for all convective systems.

The choice of C²OMODO dt shall be a trade-off between several factors: the sensitivity of observations to the target variable, scene evolution due to non-targeted processes (e.g., turbulence, advection), size of the cloud with respect to the size of the observation pixel, radiometric sensitivity and system constraints (interference, collision). This trade-off isn't the scope of this study. Different dt values have been tested, ranging from 60 s to 180 s, but as said above the convective cells of the HEC simulation undergo a globally very weak advection and thus has a negligible impact on the results. Here, the results with a dt=180 s are presented. The impact of horizontal advection shall be evaluated on several less stationary convective systems. This will be assessed in following studies.

Each radiometer of the C²OMODO tandem, which are strictly identical, inherits from the SAPHIR humidity sounder on-board the Megha-Tropiques mission [31]. They benefit from enhancements to improve radiometric performance and adapt the spectral range of observations. This upgraded instrument will sample water vapor absorption lines at 183.31 GHz and 325.15 GHz. A window channel centered around 89 GHz, that benefits from the ESA AWS (Arctic Weather Satellite) EPS (EUMETSAT Polar System) Sterna radiometer, and the ESA/EUMETSAT MetOp-SG MWS (MicroWave Sounder), is also present to better constrain the information on precipitation [3], [32]–[34].

TABLE I summarizes the spectral configuration of the microwave radiometer (hereafter MWR) used in the present study. This configuration closely approximates the final design of the microwave radiometer, which had not yet been finalized at the time of the study. This configuration is based on SAPHIR, with six double sideband channels at 183 GHz and similar sampling at 325 GHz. Gaussian noises have been added to each channel based on the radiometric sensitivity values provided in TABLE I defined by preliminary studies by CNES and ADS on the instrument.

The 183 GHz and 325 GHz measurements are sensitive to the ice hydrometeors present in clouds primarily through scattering processes [35]–[38]. Sensitivity to various ice crystal sizes is achieved with both bands: 183 GHz responds to larger icy hydrometeors while 325 GHz is more sensitive to smaller crystals. Hence, measurements at 183 GHz are commonly employed to detect deep convection as well as associated
<table><caption>TABLE I
DESCRIPTION OF SPECTRAL CONFIGURATION OF THE MICROWAVE RADIOMETER (MWR) USED IN THIS STUDY.
NEDT: NOISE EQUIVALENT DELTA TEMPERATURE;
IFOV: INSTANTANEOUS FIELD OF VIEW.</caption><thead><tr><th>Central frequency (GHz)</th><th>Channel (GHz)</th><th>Bandwidth (MHz)</th><th>NEDT (K)</th><th>Targeted IFOV (km)</th></tr></thead><tbody><tr><td rowspan="3">183</td><td>±0.2</td><td>200</td><td>2.73 | 5.9</td><td>≤ 10</td></tr><tr><td>±1.1</td><td>350</td><td>2.06 | 4.4</td><td>5 at nadir</td></tr><tr><td>±2.8</td><td>500</td><td>1.73 | 3.9</td><td></td></tr><tr><td rowspan="3">325</td><td>±4.2</td><td>700</td><td>1.46 | 3.2</td><td>≤ 6</td></tr><tr><td>±6.8</td><td>1200</td><td>1.11 | 2.5</td><td>3 at nadir</td></tr><tr><td>±11.0</td><td>2000</td><td>0.86 | 1.9</td><td></td></tr><tr><td>89</td><td>89</td><td>4000</td><td>0.5</td><td>≤ 20<br>10 at nadir</td></tr></tbody></table>

overshooting phenomena [39], [40]. Moreover, these frequencies capture radiation from different altitudes, and multiple observation channels per band provides information on the vertical distribution of hydrometeors [41]–[43].

## B. Cloud resolving simulations

Cloud resolving numerical simulations of DCSs are performed using the MESO-NH model [44]. This numerical model is extensively used to investigate cloud and precipitation characteristics leveraging satellite observations [39], [45], [46].

The MESO-NH configuration used here is the same as in Auguste and Chaboureau (2022) [28] and Brogniez et al (2022) [27], representing the deep convective cloud called “Hector” (hereafter HEC) that develops over the Tiwi Islands, north of Darwin, Australia [47]. The simulation spans six hours with a 30-second timestep, covering an area of 256 × 200 km² at 1 km horizontal resolution. The simulation has 146 vertical levels of varying widths, from 60 m near the surface to 500 m at 30 km. The portion where convection occurs (~4 km to 20 km) has 200 m-width layers.

The initial conditions for this simulation (called hereafter S) are derived from Darwin radiosonde data at 00:00 UTC on November 30, 2005, as in Dauhut et al. (2015) [47]. To expand the dataset, four additional simulations were generated by increasing humidity by +10% (named S10% hereafter) and +20% (named S20% hereafter). S10% and S20% have been generated without other perturbations. The other two simulations are similar to S10% and S20% but were generated without any horizontal wind in the initial conditions, and are named S10%-noHW and S20%-noHW, respectively. Such modifications enable to intensify convection, particularly due to increased humidity, while the simulations initialized without horizontal wind allow for a different evolution of the convective system, ensuring a more diverse dataset for the training and evaluation of the retrieval method.

## C. Radiative transfer model for synthetic measurements

The COMODO-R measurements, expressed in Tb, are computed for each time step of the MESO-NH HEC simulations

using the radiative transfer model RTTOV (Radiative Transfer for the Television and Infrared Observation Satellite - TIROS Operational Vertical Sounder), version 13 [48]. The size and shape distribution of hydrometeors are set as default as described in Geer et al (2021) [49], which could be questionable, but sensitivity studies on assumptions on the particle size distribution and shape of the hydrometeors are off the scope of the present study.

In the present experiments, the Tb are idealized and do not account for observation geometry (pixel resolution of each frequency, number of observations per scan, viewing angle, pixel distortion according to these angles, and parallax effects). They are considered at nadir at the top of the atmosphere for each column of the MESO-NH simulation, with the same resolution as the cloud simulations. A future sensitivity study will address the impact of observation geometry and instrumental effects on inversion methods.

## D. Classification of the structure of convective systems

Following Feng et al (2011) [50] and Marinescu et al (2016) [29], the atmospheric columns of MESO-NH simulations are categorized into classes using a physical threshold partitioning whose criteria are given in TABLE II: undefined (UND), anvil (ANVL), stratiform (STRAT), convective (CONV), and deep convective (DC). Note that the UND class includes mostly clear-sky situations, but also some cloudy cases that do not satisfy any of the classification criteria. The partitioning method considers: the precipitation rates (PR), the vertical velocity of air ($W_{air}$), and the cloud top altitude ($Z_{top}$) defined as the highest altitude where the mixing ratio of ice ($r_{ice}$) exceeds 0.1 g.kg⁻¹. An IR window channel, here simulated at 11.5 µm based on the MVIRI sensor from METEOSAT-7, is used to detect ANVL regions. Data from the geostationary satellites on operation at the time of the C²OMODO mission will provide such information. For CONV and DC classes, criteria 2 and 3 in TABLE II require that $W_{air}$ exceed thresholds at any altitude above freezing (criterion 2) or below freezing (criterion 3).

The C²OMODO radiometric measurements are used as inputs to the machine learning models, while outputs correspond to cloud structure (classification) and geophysical variables (regression). This is illustrated in the flow chart Fig. 4. The variables used to define either the cloud structures (TABLE II), the retrieved GV's (Section II.E), or to compute C²OMODO measurements via RTTOV, originate from MESO-NH simulations. However, these variables are not directly used in the machine learning model, neither as inputs nor as outputs.

Fig. 1 illustrates the application of the classification criteria on a longitudinal transect of an HEC cloud simulation, (as described in Section II.B). This figure presents the ice mixing ratio (Fig. 1(a)), vertical air velocities (Fig. 1(b)), and both the precipitation rate and infrared Tb at 11.5 µm Fig. 1(c)). These variables are used to apply the classification criteria (see TABLE II). This figure also displays the Tb and dTb/dt of C²OMODO along the transect, in addition to the three GV's presented in Section II.E. This example demonstrates the relationship between C²OMODO radiometric measurements (Fig. 1(d)) and cloud structure (Fig. 1(a), (b) and (c)).
<table><caption>TABLE II
CLASSIFICATION CRITERION [29] FOR INDIVIDUAL ATMOSPHERIC COLUMN. PR: TOTAL PRECIPITATION RATE; W<sub>air</sub> (Z): VERTICAL VELOCITY OF AIR; T: AIR TEMPERATURE; Tb<sub>11.5 µm</sub>: Tb IN THE 11 µm WINDOW; Z<sub>top</sub>: ALTITUDE OF CLOUD TOPS.</caption><thead><tr><th>Classes</th><th>Criteria</th></tr></thead><tbody><tr><td>CONV &amp; DC</td><td><ul><li>At least one of the following:<ol><li>PR &gt; 25 mm.h<sup>-1</sup></li><li>|W<sub>air</sub>(z)| (T &gt; 0°C) &gt; 3 m.s<sup>-1</sup></li><li>|W<sub>air</sub>(z)| (T ≤ 0°C) &gt; 5 m.s<sup>-1</sup></li></ol></li><li>CONV: Z<sub>top</sub> &gt; 6 km</li><li>DC: Z<sub>top</sub> &gt; 12 km</li></ul></td></tr><tr><td>STRAT</td><td><ul><li>PR &gt; 0.1 mm.h<sup>-1</sup></li><li>Z<sub>top</sub> &gt; 6 km</li></ul></td></tr><tr><td>ANVL</td><td><ul><li>T<sub>b,11.5 µm</sub> &lt; 270 K</li><li>Z<sub>top</sub> &gt; 6 km</li></ul></td></tr><tr><td>UND</td><td>None of the previous criteria are met</td></tr></tbody></table>

As seen on the map of Fig. 1, the east-west transect crosses cloud systems within a portion of the HEC simulation, over the Tiwi Islands. Several convective cells are identified along the transect, which later aggregate at a more advanced simulation time (not shown) to form a deep convective system (DCS) known as Hector. One of these developed convective clouds, located around 130.5°E, exhibits high ice content and weak vertical velocities (generally < 3 m.s⁻¹), indicating a partially stationary state, with slow downdrafts caused by the terminal velocities of hydrometeors. This region includes ANVL, STRAT, and some DC zones, where vertical velocities are slightly stronger. Additionally, several growing convective regions (classified as CONV) are identified at 130.6°E, 130.8°E, and near 131.5°E.

The cloudy regions show a strong depression in Tb, especially in the convective classes (CONV and DC), due to the attenuation of radiation from ice scattering. Tb do not vary in the same manner depending on the observation channel. Comparing Tb at 183 GHz and 325 GHz in clear-sky and cloudy conditions, we see that Tb decrease slightly near the center of the absorption line (± 0.2 GHz), whereas Tb decrease significantly in the presence of ice particles at the wing of the line (± 11.0 GHz). This is due to the wings of the 183/325 GHz channels being associated with lower atmospheric opacity related to water vapor, making these channels more sensitive than those at the line centers. The 325 GHz tend to shown an even greater Tb decrease than 183 GHz, which is particularly apparent in the section of ANVL at 130.9°E. Fig. 1 demonstrates the good agreement of the present classification with this former study.

Fig. 2 shows, for the entire set of HEC, the mean profiles and standard deviations of condensed water phases (liquid and ice) and the vertical component of atmospheric velocity for the different identified classes. ANVL contains a small amount of

condensed water, almost entirely in solid form, with vertical velocities close to zero. This is consistent with high-altitude clouds maintained aloft by minimal vertical motion, which explains their buoyancy [30].

The STRAT class shows a higher amount of ice, a small precipitation rate, and small vertical velocities. In contrast, CONV and DC classes exhibit much stronger vertical velocities and intense precipitation. The CONV class water content extends to lower altitudes (below 12 km) compared to the DC class, probably corresponding to convective cells in the growth phase or convective cells with lower tops. On the other hand, the DC class ice content shows a much greater vertical extension, indicative of more fully developed convective regions. Both classes show near cloud top higher amount of graupel with respect to other species.

These profiles agree well with the common definitions found in the literature [29], [30], [51]–[56]: the anvil is characterized by air detained from the upper part of the convective regions, which remains at high altitude due to its neutral buoyancy. Stratiform regions are defined as cloudy regions containing both liquid and frozen water, with low precipitation rates and slow cloud rise. Convective regions of an individual thunderstorm contain precipitation and vertical velocities, positively or negatively, much stronger than those in the surrounding regions such as the anvil and stratiform regions [29], [30].

### E. Geophysical variables related to the production of ice

Ice Water Path (IWP, in kg.m⁻²) is defined as:

$$ \text{IWP} = \int_{z} \rho(z) r_{\text{ice}}(z) dz \quad (1) $$

with ρ being the density of dry air (kg.m⁻³), r<sub>ice</sub> the mixing ratio of total ice water (kg.kg⁻¹), and z the altitude (m).

The short time delay between successive measurements of C²OMODO can be used to infer the rate of change of IWP over time, dIWP/dt (in kg.m⁻².s⁻¹), expressed as:

$$ \frac{d\text{IWP}}{dt} = \frac{\text{IWP}_{t_f} - \text{IWP}_{t_i}}{t_f - t_i} \quad (2) $$

where t<sub>i</sub> is the time of measurement of the leading radiometer and t<sub>f</sub> the time of the trailing radiometer.

Moreover, the in-cloud vertical velocity of ice is estimated following Auguste and Chaboureau (2022) [28], who proposed an integrated variable w̅<sub>ice</sub> that can be related to the temporal variability of Tb, and defined as:

$$ \overline{w}_{\text{ice}} = \frac{\int_{z} W_{\text{air}}(z) \rho(z) r_{\text{ice}}(z) dz}{\int_{z} \rho(z) r_{\text{ice}}(z) dz} \quad (3) $$

where W<sub>air</sub>(z) is the vertical wind velocity (m.s⁻¹). Thus, w̅<sub>ice</sub> represents the averaged vertical velocity of ice particles within the cloudy atmospheric columns.

These three variables serve as benchmark to assess the performance of inversion methods for specific scene properties. Fig. 1(d), (e) and (f) illustrate the relationship between Tb and IWP on one hand, and the consistency between dTb/dt, dIWP/dt, and w̅<sub>ice</sub> on the other hand. As previously mentioned, Tb are lowest when IWP is high and increase as
<figure><img src="image_2.png" /><figcaption>Fig. 1. Application of classification criteria (color bar on the right-hand side) on a longitudinal transect of the HEC cloud simulation, for a single snapshot, illustrated in (b) with IWP field and located North of Australia as shown on map (a); (c): Mixing ratio of ice, $r_{ice}$; (d) Vertical wind velocity, $W_{air}$; (e): Infrared Tb at 11.5 µm in red and Precipitation Rate, PR, in green; (f) Tb of 5 C²OMODO channels; (g): dTb/dt of the same 5 channels; (h): IWP in blue, $\bar{w}_{ice}$ in red, dIWP/dt in cyan (GVs defined in Section II.E).</figcaption></figure>

IWP decreases. Peaks in dIWP/dt correspond to opposite-sign peaks in dTb/dt, showing strong relationship between these variables. High values of $\bar{w}_{ice}$ appear to coincide with low Tb and non-zero dTb/dt regions. Comparing Fig. 1(a) and Fig. 1(b) with Fig. 1(e), it is shown that high $\bar{w}_{ice}$ values

correspond to regions where both the IWP and the vertical wind velocities are both significant.

While Fig. 1 shows the variation of GVs accordingly to Tb and dTb/dt along a transect of one HEC simulation, Fig. 3 generalizes these relationships for an entire HEC simulations
<figure><img src="image_3.png" /><figcaption>Fig. 2. Mean vertical profiles and standard deviations of mixing ratios of water species and vertical wind velocities for each cloudy class in the entire set of HEC simulations.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Relationships between Tb and IWP (a)-(d), dTb/dt and dIWP/dt (b)-(e), dTb/dt and $\bar{w}_{\text{ice}}$ (c)-(f) for channels at the center (a,b,c) and wings (d)-(e)-(f) of the 183 GHz line for each of the cloud classes.</figcaption></figure>

(spanning 6 hours with a 30 second temporal resolution over a 256 × 200 km² domain). Fig. 3(a) shows the relationships between Tb, at the center and wings of the 183 GHz line and IWP across cloud classes. Tb decrease almost linearly as IWP increases, with a stabilization beyond 45 kg.m⁻² for both channels due to a saturation effect. All classes exhibit a similar relationship, except CONV at the center of the 183 GHz line, which shows a less pronounced decrease in Tb at the center of the 183 GHz line but not at the 183 GHz wing.

The distinct Tb-IWP behavior observed in the CONV class can be attributed to the channel's sensitivity to higher altitudes due to the water vapor absorption band. The central channel of the 183 GHz line is opaque to lower altitudes, as radiation

is absorbed by water vapor. As shown in Fig. 2, the CONV class includes areas of intense precipitation and significant ice content below 12 km, resulting in a higher ice concentration at lower cloud tops, even for thicker ice layers. A more in-depth analysis (not shown) shows that the CONV class corresponds to lower cloud top altitudes, even for the highest IWP values. Consequently, a large part of the ice layer is positioned at altitudes to which the channel is less sensitive, resulting in reduced radiation attenuation by ice scattering and thus higher Tb values, even at relatively high IWP, compared to other cloud classes.

As depicted in Fig. 3(b), (c), (e), and (f), the relationship between GVs (dTWP/dt and $\bar{w}_{\text{ice}}$) and dTb/dt varies across
cloud classes and channels of the 183 GHz absorption line. Firstly, the ANVL and STRAT classes exhibit strongly negative dTb/dt values for low dIWP/dt, likely due to significant horizontal detrainment, while they generally show low $\overline{w}_{ice}$ with dTb/dt close to zero. In contrast, CONV and DC classes show higher $\overline{w}_{ice}$ values associated with significantly negative dTb/dt, reflecting dynamic processes or cloud top elevation.

The relationships between GVs and dTb/dt also differ between the central and wing channels of the 183 GHz line. At ±0.2 GHz, CONV and DC show similar behavior, with $\overline{w}_{ice}$ corresponding to decreasing dTb/dt. However, at ±11.0 GHz, while CONV maintains this pattern, DC shows very high $\overline{w}_{ice}$ with near-zero dTb/dt. This can be explained by a lower increase in hydrometeor concentration despite the presence of very high vertical velocities in the DC class for mature, quasi-stationary cases. It could also be due to a saturation effect when the ice water content becomes particularly high.

Since lifecycle stage is not explicitly considered in this analysis, these results likely reflect a sensitivity to convective evolution. For instance, Prasanth et al. (2023) [57] have shown that changes in cloud top altitude, acting as a proxy for convective development, can influence retrievals of both the maximum vertical wind and its altitude. The CONV class may include early-stage cells with rapid growth, whereas DC includes more mature systems. A full quantification of lifecycle impacts, such as through an uncertainty budget, will be necessary in future studies.

These varied relationships suggest that a tandem like C²OMODO will be efficient in providing the required measurements to retrieve the targeted variables, with a potential improvement if an initial step of cloud structure detection (UND, ANVL, STRAT, CONV, DC) is performed.

### III. CLASSIFICATION AND RETRIEVAL METHODS

In this study, the Gradient Boosting Decision Tree (GBDT) [58], [59] is used for both the cloud classification and the GV retrieval. The model inputs and outputs are outlined in Fig. 4. This method belongs to the family of supervised learning methods. The general concept of supervised learning is briefly introduced, followed by a description of the GBDT method. The metrics used to assess the performance of the statistical models are outlined and presented in more detail in Appendix B and C.

#### A. *Supervised learning*

Supervised machine learning algorithms build predictive statistical models from labeled datasets by learning from input-output pairs, where inputs are features and outputs are target values. Through iterative adjustments of model parameters to minimize prediction errors, the algorithm refines its accuracy based on a predefined loss [60]. Supervised learning encompasses classification, where input data is assigned to predefined categories by identifying patterns that enable discrete class predictions, and regression, which predicts continuous values by modeling relationships between input features and target variables, as seen in linear or polynomial regression models.

#### B. *The Gradient Boosting Decision Tree algorithm*

The GBDT algorithm, an iterative learning technique based on decision trees, is widely used for its strong generalization abilities, making it popular across diverse machine learning applications [58], [59], [61], [62]. It builds a sequence of decision trees, each correcting the errors of the previous one, gradually improving accuracy by predicting residuals. Although more computationally intensive, deep learning techniques like Convolutional Neural Networks (CNNs) have also proven effective for classification tasks. Liu et al. (2018) [63] uses CNNs for cloud classification, while Liu et al. (2020) [64] develops a Multi-Evidence and Multi-Modal Fusion Network. Similarly, Zhang et al. (2020) [65] combines CNNs with Recurrent Neural Networks (RNNs) to enhance classification performance. While gradient boosting is simpler and less resource-intensive than CNNs but does not achieve the same level of performance, it remains effective and is ideal for preliminary studies like this one.

This study employs Light Gradient Boosting Machine (LGBM) for robust classification and regression, leveraging its optimized implementation of GBDT [62]. LGBM efficiency with large-scale datasets and its robustness in dealing with non-linear relationships makes it ideal for cloud class prediction (Section II.D) and GV retrieval (Section II.E). A key feature of GBDT-based classifiers is their probabilistic output, which provides valuable insights into prediction confidence across classes.

GBDT, and by extension LGBM, relies on several critical hyperparameters to control statistical model training, balancing complexity, preventing overfitting, and enhancing accuracy. This study emphasizes potential C²OMODO observation applications with basic tests rather than full parameter optimization. The adjusted hyperparameters, defined using performance metrics are provided in Appendix A.

The classification algorithm's performance is evaluated using Precision (P), Recall (R) also known as Hit Rate, and F1-score, calculated based on True and False predictions (see Appendix B). F1-score serves as the primary metric for comparing classification model performance, while Precision and Recall aid in fine-tuning LGBM hyperparameters, especially class weight (Appendix A). For regression analysis, key evaluation metrics, Coefficient of Determination (R²), Root Mean Square Error (RMSE), and Mean Bias Error (MBE), provide essential insights and are detailed in Appendix C.

### IV. RESULTS AND DISCUSSION

#### A. *Setting of the statistical models*

Various spectral configurations of the C²OMODO microwave radiometers (from TABLE I) are tested as inputs to the statistical models to evaluate their impact in both the classification and the GVs retrieval. To avoid any misunderstandings in the following of the study, the tandem concept is named C²OMODO while the spectral configurations are named below for the remainder of the study:

* MWR-183: 183 GHz channels (6 channels)

* MWR-325: 325 GHz channels (6 channels)

* MWR-HF: 183 & 325 GHz channels (12 channels)
<figure><img src="image_5.png" /><figcaption>Fig. 4. Schematic representation of machine learning models (classification and regression).</figcaption></figure>

* MWR-LF: 183 & 89 GHz channels (7 channels)

* MWR-All: 183 & 325 & 89 GHz channels (13 channels)

Different delays (dt) between the head and tail radiometers have been tested, but not shown here, because there is a small impact of dt on the results. In this study, results are presented for dt=180 s, except for instantaneous variables (classification and IWP) where dt=0 s.

As outlined in Section II.B, five independent HEC simulations are used. The training dataset is derived from S10% and S10%-noHW simulations, with 10% of these points set aside for validation. The test dataset is created from S20% and S20%-noHW simulations, while the fifth simulation provided data for the map and dispersion diagrams. Alternative combinations for training and testing were tested and showed no significant impact on performance, supporting the robustness of the methodology. The use of multiple simulations ensures a sufficiently diverse representation of each cloud class in the dataset.

Classification models are trained based on criteria applied to HEC simulations, serving as the reference, while regression models aimed to estimate GVs from Tb and dTb/dt. Both global and specific regression models (Section IV.D) are trained to evaluate the impact of classification on retrievals: global models aggregate data across all cloud classes, whereas specific models are trained per cloud class and combined in a second step.

The regression models take Tb and dTb/dt as inputs, with dTb/dt restricted to dt=180 s. Fig. 5 (left panel) displays the number of points per class in the test dataset at dt=0 s, showing similar distributions of each class in the training dataset, except for the CONV class which is underrepresented. Class weights (see Appendix A) are applied in Section IV.B.a to overcome these disparities. Fig. 4 (right panel) illustrates the class-specific reduction of the number of points when dt > 0 s. Only points where initial and final classes ($t_i$ and $t_f$) match are included in the analysis, avoiding rapid class transitions and potentially contributing to performance differences at various

dt values in Section IV.D.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Distribution and reduction of training data Points. Left: Number of points in the training dataset for each class; Right: Reduction in the number of points for each class based on dt=180s.</figcaption></figure>

## B. Cloud classification using a single radiometer

1) *Selection of class weight configuration:* This section focuses on the selection of the appropriate class weight configuration. As explained in Section III.B, LGBM assigns different weights to classes to handle imbalanced datasets. As the dataset used is highly imbalanced (Fig. 5), three tests were conducted to assess how different weight configurations impact classification performance.

TABLE III presents scores for classification models trained with different class weights (see Appendix A). While F1-scores are similar, Precision and Recall vary with respect to class weights. The unweighted model has higher Precision but lower Recall, leading to poor identification of the underrepresented class. The balanced model achieves higher Recall but lower Precision, while the compromise weight configuration strikes a balance between False Positive (FP) and True Positive (TP) (see Appendix B).

The choice of class weighting depends on the objective. If identifying the CONV class whenever it occurs is prioritized, the balanced model is preferred. Conversely, if ensuring accuracy when the CONV class is detected is the objective, especially as it is underrepresented, an unweighted model is more suitable. For this study, which aims to assess the
<table><caption>TABLE III
PRECISION (P), RECALL (R), F1-SCORE (F1) FOR EACH CLASS
PREDICTION OVER 3 CLASS-WEIGHT HYPERPARAMETER
CONFIGURATIONS USING MWR-ALL. RESULTS ARE EXPRESSED AS
PERCENTAGE.</caption><thead><tr><th rowspan="2">Class-weight options</th><th colspan="3">Unweighted</th><th colspan="3">Balanced</th><th colspan="3">Compromise</th></tr><tr><th>P</th><th>R</th><th>F1</th><th>P</th><th>R</th><th>F1</th><th>P</th><th>R</th><th>F1</th></tr></thead><tbody><tr><td>Score</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>UND</td><td>92</td><td>97</td><td>94</td><td>94</td><td>94</td><td>94</td><td>92</td><td>97</td><td>95</td></tr><tr><td>ANVL</td><td>91</td><td>87</td><td>89</td><td>94</td><td>79</td><td>86</td><td>94</td><td>84</td><td>89</td></tr><tr><td>STRAT</td><td>53</td><td>54</td><td>53</td><td>41</td><td>69</td><td>51</td><td>48</td><td>64</td><td>55</td></tr><tr><td>CONV</td><td>49</td><td>52</td><td>50</td><td>16</td><td>91</td><td>27</td><td>36</td><td>70</td><td>48</td></tr><tr><td>DC</td><td>72</td><td>69</td><td>70</td><td>66</td><td>71</td><td>69</td><td>70</td><td>70</td><td>70</td></tr></tbody></table>

feasibility and information content of C²OMODO tandem, the compromise model is selected.

2) *Results of the compromise classification model:* TA-BLE IV shows the Precision (P), Recall (R) and F1-Score of the classification for each class across different spectral configurations when applying the compromise class weighting. Performance for MWR-All varies according to the class: UND and ANVL are consistently predicted with F1-score of 95% and 89%, respectively. The DC class is moderately well-predicted with a 70% F1-score, while STRAT and CONV classes show a slightly higher prediction uncertainty, with F1-scores of 55% and 48%, respectively. These trends remain for all spectral configurations, with slight variations in F1-score.

Examining Precision and Recall separately reveals a clear disparity, with Precision generally lower than Recall across scores. For instance, Precision for the CONV class in the MWR-All is 36% compared to Recall of 70%, indicating a high rate of FP. While the DC class predictions are relatively accurate with few FP, the CONV class, though frequently predicted, suffers from more FP.

Spectral configurations impact performance with the MWR-183 outperforming the MWR-325 for STRAT, CONV, and DC classes, whereas MWR-325 performs better for UND and ANVL. Combining the 183 and 325 GHz channels (MWR-HF) slightly improves predictions while combining 183 and 89 GHz (MWR-LF) provides limited improvements, except for STRAT. Optimal results are achieved by adding the 89 GHz channel, particularly enhancing predictions for STRAT, CONV, and DC. Each band (183, 325 and 89) contributes valuable information to the classification model. In the remainder of this section, we will take a closer look at the classification model of the spectral configuration using all the channels (MWR-All).

The confusion matrix in Fig. 6 details the classification model performance for MWR-All, comparing true and predicted class labels, where each row represents the true class and each column the predicted class. UND and ANVL classes are generally well predicted (over 80% accuracy), whereas STRAT is often misclassified as ANVL (15%) or DC (17%). CONV is sometimes misclassified as ANVL (9%) or STRAT (13%), while DC is frequently misclassified as STRAT (22%). Misclassifications may arise from several sources. First, the dataset itself is imbalanced, skewing class weights during

training. Second, radiometric measurements can be similar for classes with similar microphysical properties (see Fig. 2 and Fig. 3), complicating classification. In contrast, distinct classes like UND and ANVL exhibit fewer errors due to their clearly differentiated measurements.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Confusion matrix of compromise classification model using MWR-All, expressed as percent. Diagonal are the correct prediction (TP), off-diagonal are the misclassifications.</figcaption></figure>

Fig. 7 shows a classification map comparing true (left panel) and predicted classes (right panel) for MWR-All at a specific simulation moment when the cloud system is well developed, with $Z_{top}$ between 6 km and 18 km, a maximum IWP of 50 kg.m⁻², and a horizontal extent exceeding 100 km. The map shows that the overall structure of the HEC cloud system, including ANVL, STRAT, and DC classes, is well captured, with isolated CONV cells also accurately predicted. However, distinguishing precisely between STRAT, CONV, and DC classes remains challenging.

The partitioning method, partially based on dynamic information (see TABLE II), results in classes with distinct vertical structures and dynamic properties (see Section II.D). Their temporal evolution depends on these characteristics. C²OMODO tandem measurements are expected to help retrieve both the classes evolution and their associated dynamics.

3) *Analysis of class prediction probabilities:* To investigate retrieval errors and uncertainties, it is important to examine prediction probabilities for each class, as shown in Fig. 8. The classification model assigns probabilities to each grid point in the HEC simulation, selecting the class with the highest probability. Grid points with probabilities of 50% or higher are necessarily assigned to that class, although this does not always indicate high confidence in the classification.

Fig. 8 displays a probability map for each class, highlighting variability, particularly for the STRAT class, where probabilities often fall below 80%, indicating uncertainty. In contrast, ANVL is predicted with high confidence, except near boundaries with other classes (see Fig. 6 and Fig. 7). Some grid points display probabilities above 25% for multiple classes, indicating the similar microphysical and radiometric characteristics mentioned in the previous section.

To better understand the classification model’s errors, confusion matrices were computed across specific probability ranges, treating each cloud class separately. This approach enables to identify points that appear in multiple classes within the same probability range. Fig. 9 illustrates this, where rows represent true classes and columns represent predicted classes, displaying the percentage of points within each probability
<table><caption>TABLE IV
PRECISION (P), RECALL (R), F1-SCORE (F1) FOR EACH CLASS PREDICTION OVER 5 SPECTRAL CONFIGURATIONS. RESULTS ARE EXPRESSED AS PERCENTAGES.</caption><thead><tr><th rowspan="2">Configuration</th><th colspan="3">MWR-183</th><th colspan="3">MWR-325</th><th colspan="3">MWR-HF</th><th colspan="3">MWR-LF</th><th colspan="3">MWR-All</th></tr><tr><th>P</th><th>R</th><th>F1</th><th>P</th><th>R</th><th>F1</th><th>P</th><th>R</th><th>F1</th><th>P</th><th>R</th><th>F1</th><th>P</th><th>R</th><th>F1</th></tr></thead><tbody><tr><td>Score</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>UND</td><td>88</td><td>91</td><td>90</td><td>92</td><td>96</td><td>94</td><td>92</td><td>97</td><td>95</td><td>88</td><td>92</td><td>90</td><td>92</td><td>97</td><td>95</td></tr><tr><td>ANVL</td><td>86</td><td>80</td><td>83</td><td>88</td><td>82</td><td>85</td><td>91</td><td>84</td><td>87</td><td>90</td><td>80</td><td>85</td><td>94</td><td>84</td><td>89</td></tr><tr><td>STRAT</td><td>43</td><td>45</td><td>44</td><td>39</td><td>38</td><td>38</td><td>44</td><td>48</td><td>46</td><td>47</td><td>63</td><td>54</td><td>48</td><td>64</td><td>55</td></tr><tr><td>CONV</td><td>30</td><td>62</td><td>40</td><td>25</td><td>68</td><td>37</td><td>32</td><td>69</td><td>44</td><td>34</td><td>61</td><td>43</td><td>36</td><td>70</td><td>48</td></tr><tr><td>DC</td><td>66</td><td>69</td><td>68</td><td>63</td><td>66</td><td>65</td><td>68</td><td>70</td><td>69</td><td>69</td><td>69</td><td>69</td><td>70</td><td>70</td><td>70</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Classification map comparison between reference and predicted class for MWR-All.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Map of classification prediction probability for the cloud scene and model presented in Fig. 7, with: (a) ANVL, (b) STRAT, (c) CONV, (d) DC.</figcaption></figure>

range that belong to the true class. For example, 83% of the points predicted as CONV with a probability between 0.9 and 1 are correctly classified. The right panel shows the distribution of points for each class across probability ranges

within the entire HEC simulation.

Confusion is notable in the 0.50-0.75 range, especially between UND and ANVL, and among STRAT, CONV, and DC classes. STRAT often overlaps with CONV and DC,
<figure><img src="image_10.png" /><figcaption>Fig. 9. Confusion matrix for prediction probability bins (Three left panels). Percent of points of each true class within a probability bin (Right panel).</figcaption></figure>

and DC is similarly mistaken for STRAT and CONV. Errors
decrease significantly in the 0.75-0.90 range. At the highest
confidence level (0.90-1.00), errors are minimal, though 11%
of points predicted as CONV actually belong to DC. UND
and ANVL are confidently predicted, with over 60% of
their points in the 0.90-1.00 range, while DC has 24% and
CONV only 9% at this confidence level. STRAT is rarely
predicted with high confidence, having almost no points in
the 0.90-1.00 range and only 7% in the 0.75-0.90 range,
indicating limited confidence in STRAT predictions. This is
likely due to its transitional nature, as STRAT shares both
physical and radiometric characteristics with multiple other
classes. Despite the limitation of the STRAT class, the overall
classification performance remains high for the other classes,
with an accuracy exceeding 0.83 when a class prediction
probability is above 0.90. These promising results indicate that
the MWR-All spectral configuration contains the necessary
information to infer the physical processes defining each
class. Furthermore, the dTb/dt provided by C²OMODO tandem
enables short-term temporal cloud evolution analysis, which
could improve the classification, especially near boundaries
between different classes.

C. Ice variation phase classification using C²OMODO tandem

After evaluating the potential of cloud classification using
single-radiometer data, C²OMODO tandem measurements,
using MWR-All spectral configuration and dt=180 s, are
introduced and assessed for their classification capabilities.
This approach, among other possible methods, extends clas-
sification to include both cloud classes and phases of ice
variation. The model now categorizes 13 classes: UND, and
ANVL, STRA, CONV, DC, each of the cloud classes sub-
divided into three ice variation phases: neutral (dIWP/dt =
0 kg.m⁻².s⁻¹), production (dIWP/dt > 0 kg.m⁻².s⁻¹), or
dissipation (dIWP/dt < 0 kg.m⁻².s⁻¹). TABLE V presents
F1-scores for MWR-All for dt=180 s, with the first row is for
each cloud class and phase, and the second row is for all ice
variation phases, and across all cloud classes.

TABLE V shows that both ice variation phases and cloud
classes are generally well predicted. F1-scores are high for
neutral phases in UND and ANVL, which predominantly

exhibit this phase. The STRAT class, with lower dIWP /dt
values, achieves higher scores than CONV and DC, despite
having fewer points in the neutral phase. Scenes identified
in the production phase align closely with single-radiometer
classifications, showing slightly lower scores for ANVL (76%)
but higher scores for convective classes, particularly DC
(76%). Finally, scenes belonging to dissipation phase are also
well predicted, with a large improvement of performance
for the STRAT class (67%), although the identification of
CONV cases slightly declines, as this class often corresponds
to growing convective cells, hence better detection during
production phases.

When focusing on ice variation phases alone (fourth line
TABLE V), the classification model achieves high F1-scores:
98% for neutral, 89% for dissipation, and 90% for produc-
tion phases. This indicates that the C²OMODO tandem can
effectively detect ice production phases, though some cloud
class identification errors persist. Lower F1-scores for specific
classes and phases result from combined errors in cloud class
and ice phase classification.

Assessing the model's ability to detect cloud classes inde-
pendently of ice production phases, Fig. 10 shows significant
improvements over single-radiometer classification (Section
IV.B). TP increase for ANVL (from 84% to 89%), STRAT
(from 64% to 71%), and DC (from 70% to 81%), with a
notable reduction in FP and improved Precision. Specifically,
STRAT is less frequently confused with DC (from 17% to
11%) and vice versa (from 22% to 13%).

D. Evaluation of regression model

Retrieval performances of three GVs: IWP, dIWP/dt and
*\bar{w}*<sub>ice</sub> are assessed across the spectral configurations described
in Section IV.A. Dynamic variables dIWP/dt and *\bar{w}*<sub>ice</sub> are
evaluated at dt=180 s, while IWP, as an instantaneous variable,
is assessed at dt=0 s.

TABLE VI presents retrieval scores for each GV across
different spectral configurations. With MWR-183, IWP shows
a high R² of 0.95, indicating that the regression model is able
to explain a large part of the IWP variability, alongside a low
RMSE and negligible MBE, reflecting low error dispersion
and minimal systematic error. The MWR-325 performs worse,
<table><caption>TABLE V
F1-SCORES OF THE TANDEM CLASSIFICATION MODEL, FOR NEUTRAL, PRODUCTION AND DISSIPATION PHASES FOR EACH CLOUD CLASS. THE SCORES SHOW BOTH INDIVIDUAL CLASS PERFORMANCE AND OVERALL PHASE SCORES.</caption><thead><tr><th rowspan="2">Phase</th><th colspan="5">Neutral</th><th colspan="4">Production</th><th colspan="4">Dissipation</th></tr><tr><th>UND</th><th>ANVL</th><th>STRAT</th><th>CONV</th><th>DC</th><th>ANVL</th><th>STRAT</th><th>CONV</th><th>DC</th><th>ANVL</th><th>STRAT</th><th>CONV</th><th>DC</th></tr></thead><tbody><tr><td>Class</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>F1 per class</td><td>97</td><td>92</td><td>45</td><td>19</td><td>23</td><td>76</td><td>37</td><td>65</td><td>76</td><td>71</td><td>67</td><td>41</td><td>73</td></tr><tr><td>F1 per phase</td><td></td><td></td><td>98</td><td></td><td></td><td></td><td>89</td><td></td><td></td><td></td><td>90</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_11.png" /><figcaption>Fig. 10. Confusion matrix of classification model of ice variation phase using MWR-All and focusing only on cloud class detection, express as percent. Diagonal are the correct prediction (TP), off-diagonal are the misclassifications. For a given class, FP are the misclassifications on its column.</figcaption></figure>

with a R² of 0.85. The MWR-HF shows similar performance to MWR-183, indicating that the 325 GHz channel does not improve retrievals. In contrast, the MWR-LF and MWR-All achieve the best performance, with R² of 0.99 and reduced RMSE, highlighting the importance of the 89 GHz channel.

For MWR-183, the dIWP/dt regression model has R² of 0.70, significantly lower than that of IWP, with an RMSE of 2.60e-3 kg.m⁻².s⁻¹, indicating small errors, and a negligible MBE, showing no bias. MWR-325 shows lower performance with R² of 0.43, and MWR-HF does not improve results of MWR-183. However, MWR-LF and MWR-All achieve a much higher R² of 0.90 and 0.91 respectively.

The retrieval of $\bar{w}_{ice}$ also depends on the spectral configuration but with lower R², between 0.28 and 0.55, and an RMSE around 1 m.s⁻¹, suggesting higher errors, while the low MBE indicates no bias. MWR-All significantly improves the retrieval performances. Overall, 183 GHz shows better performance as it saturates less quickly with increasing ice content compared to 325 GHz. MWR-HF provides a slight improvement in performance compared to MWR-183, with an R² of 0.44 instead of 0.40 and a reduced RMSE. Including the 89 GHz, MWR-LF and MWR-All, channel further enhances retrieval with R² of 0.53 and 0.55 respectively, as its sensitivity to precipitation helps identify regions with stronger positive (updrafts) and negative (downdrafts) vertical wind velocities.

Testing different time steps (not shown) reveals that performance slightly improves as dt increases, possibly due to the averaging effect, as extreme, short-lived events are less captured at larger dt. To explore whether classification can improve dIWP/dt and $\bar{w}_{ice}$ predictions, retrievals were performed with and without classification. Real classes were used to avoid propagation errors, which are not discussed here.

TABLE VII compares retrieval scores for three GVs across

two regression models: specific models trained on points from specific classes, and global model that ignores class distinctions. Specific models show that dIWP/dt predictions are relatively consistent across classes, though slightly lower for the DC class, likely due to a saturation effect in Tb at high ice content [27]. For $\bar{w}_{ice}$, there is a notable improvement in the CONV and DC classes, with R² of 0.67 and 0.80, compared to 0.17 and 0.21 in the ANVL and STRAT classes, confirming that retrievals of this dynamic variable are more accurate in convective zones with strong vertical wind velocities (updrafts or downdrafts).

Another key aspect is the comparison between specific and global models. TABLE VII highlights improved performance with specific models, particularly for $\bar{w}_{ice}$, with R² increases of 0.12, 0.15, 0.13, and 0.04 for the ANVL, STRAT, CONV, and DC classes, respectively. Given that GBDT is a non-linear inversion model based on decision trees, it could be assumed that the global model might capture the relationships between Tb and GVs across classes. However, specific models perform better, likely because each class has partially different Tb-GVs relationships, reducing retrieval uncertainty when points are class-separated.

For MWR-All, R² for the global model is around 0.55 (see TABLE VI). TABLE VII shows that both global and specific models explain $\bar{w}_{ice}$ variability better in the CONV class, with R² of 0.67 (global) and 0.80 (specific). The DC class has R² of 0.60, while ANVL and STRAT classes fall to 0.21 or lower, suggesting challenges in retrieving accurate values for these classes, whose values are close to zero (see Fig. 2), resulting in small retrieval errors that significantly affect performance.

Fig. 11 displays scatter plots of retrieved as a function of reference (true) GVs for global and specific models. Both models accurately reproduce IWP (Fig. 11(a) and (d)) and dIWP/dt (Fig. 11(b) and (e)), though the global model misses higher IWP values (>40 kg.m⁻²), primarily in the DC class, which the specific model reproduces well without the observed saturation effect. This saturation in the global model likely stems from data imbalance, as fewer data points with high IWP values limit the regression model's ability to fully express this range of IWP. Additionally, specific models help differentiate points with similar Tb-GVs relationships, reducing retrieval uncertainties. Points with lower IWP values (<40 kg.m⁻²) are more abundant, giving them more weight in training, which leads to better retrieval of lower values at the expense of higher ones. The prior classification enables the models to specialize for specific value ranges, enhancing their performance in distinct regimes.

Fig. 11(c) and (f) show that the scatter plot points are well
<table><caption>TABLE VI
R², RMSE, AND MBE OF RETRIEVED GVS ACROSS 5 SPECTRAL CONFIGURATIONS FOR DT=180S.</caption><thead><tr><th rowspan="2">Variable</th><th colspan="3">IWP</th><th colspan="3">dIWP/dt</th><th colspan="3">w&#773;<sub>ice</sub></th></tr><tr><th colspan="3">(kg.m<sup>-2</sup>)</th><th colspan="3">(kg.m<sup>-2</sup>.s<sup>-1</sup>)</th><th colspan="3">(m.s<sup>-1</sup>)</th></tr><tr><th>Metric</th><th>R<sup>2</sup></th><th>RMSE</th><th>MBE</th><th>R<sup>2</sup></th><th>RMSE</th><th>MBE</th><th>R<sup>2</sup></th><th>RMSE</th><th>MBE</th></tr></thead><tbody><tr><td>MWR-183</td><td>0.95</td><td>0.84</td><td>7.30e-03</td><td>0.70</td><td>2.60e-3</td><td>6.96e-6</td><td>0.40</td><td>1.12</td><td>3.56e-4</td></tr><tr><td>MWR-325</td><td>0.85</td><td>1.43</td><td>4.50e-03</td><td>0.64</td><td>3.66e-3</td><td>1.70e-5</td><td>0.28</td><td>1.22</td><td>7.99e-4</td></tr><tr><td>MWR-HF</td><td>0.95</td><td>0.81</td><td>8.20e-03</td><td>0.71</td><td>2.57e-3</td><td>4.81e-6</td><td>0.44</td><td>1.08</td><td>5.38e-5</td></tr><tr><td>MWR-LF</td><td>0.99</td><td>0.44</td><td>4.93e-03</td><td>0.90</td><td>1.41e-3</td><td>2.76e-6</td><td>0.53</td><td>0.94</td><td>-9.30e-4</td></tr><tr><td>MWR-All</td><td>0.99</td><td>0.39</td><td>1.70e-03</td><td>0.91</td><td>1.46e-3</td><td>3.79e-6</td><td>0.55</td><td>0.97</td><td>-2.58e-3</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>Fig. 11. Scatter plots of retrieved IWP (a)-(d), dIWP/dt (b)-(e) and $\overline{w}_{ice}$ (c)-(f) as a function of true values for global (a)-(b)-(c) and specific (d)-(e)-(f) regression models. Predictions are obtained for MWR-All using the $S_{ref}$ simulation data.</figcaption></figure>

<table><caption>TABLE VII
R² METRICS OF REGRESSION MODELS FOR 3 VARIABLES (IWP, dIWP/dt, $\overline{w}_{ice}$) ACROSS 4 CLOUDY CLASSES FOR GLOBAL MODEL (TRAINED FOR ALL POINT) OR SPECIFIC MODEL (TRAINED FOR EACH CLASS) USING MWR-ALL.</caption><thead><tr><th rowspan="2">Variable</th><th colspan="2">IWP</th><th colspan="2">dIWP/dt</th><th colspan="2">w&#773;<sub>ice</sub></th></tr><tr><th colspan="2">(kg.m<sup>-2</sup>)</th><th colspan="2">(kg.m<sup>-2</sup>.s<sup>-1</sup>)</th><th colspan="2">(m.s<sup>-1</sup>)</th></tr><tr><th>Model</th><th>Global</th><th>Specific</th><th>Global</th><th>Specific</th><th>Global</th><th>Specific</th></tr></thead><tbody><tr><td>ANVL</td><td>0.99</td><td>0.99</td><td>0.92</td><td>0.93</td><td>0.05</td><td>0.17</td></tr><tr><td>STRAT</td><td>0.99</td><td>0.99</td><td>0.93</td><td>0.94</td><td>0.06</td><td>0.21</td></tr><tr><td>CONV</td><td>0.97</td><td>0.98</td><td>0.92</td><td>0.94</td><td>0.67</td><td>0.80</td></tr><tr><td>DC</td><td>0.97</td><td>0.98</td><td>0.89</td><td>0.90</td><td>0.56</td><td>0.60</td></tr></tbody></table>

centered around the diagonal line where Prediction equals Reference. However, there is noticeable dispersion, with a denser cluster of points around values close to zero. Additionally, while the difference between global and specific models is subtle, it becomes apparent when comparing the R² values of 0.61 and 0.65, showing a slight improvement in accuracy for the specific model. Overall, the regression models provide a good agreement in reproducing $\overline{w}_{ice}$.

V. CONCLUSION AND PERSPECTIVE

Deep convection, which generates clouds central to the water and energy cycles, has a significant impact on Earth's meteorological systems but remains poorly understood due to limited observations. This lack of understanding affects its representation in weather and climate models. The C²OMODO
mission, a CNES contribution to the AOS mission, aims to
address this observational gap by studying storm dynam-
ics through innovative radiometric observations. This paper
evaluates the potential and information content of the future
C²OMODO observations.

We propose a cloud classification method and a geophysical
variable regression method based on a gradient boosting algo-
rithm. These methods use five distinct spectral configurations,
incorporating radiometric channels at 183 GHz, 325 GHz,
183+325 GHz, 183+89 GHz and 183+325+89 GHz. The final
configuration, 183+325+89 GHz, closely approximates the
finalized spectral configuration fixed for C²OMODO mission.
Reality-like cloud simulations were performed using MESO-
NH, and synthetic radiometric measurements were generated
with RTTOV. The classification method efficiently categorizes
convective system structure into four categories: ANVIL,
STRAT, CONV and DC; using brightness temperature data
from a single radiometer. The model achieves, for each class,
an accuracy of 89%, 71%, 73%, and 81%, respectively, for
each class. Misclassifications can be explained by the simi-
larities in microphysical and radiometric properties between
stratiform, convective and deep convective classes.

The use of time-derivative brightness temperatures allows
for highly effective detection ice variation phases with high
performances. This approach significantly improves the classi-
fication of the four cloud system structure classes compared to
classification using a single radiometer. The regression method
demonstrates excellent performance, with 99% recovery for
IWP, up to 94% for dIWP/dt and up to 80% for wice; providing
vertically integrated insights on ice water content and vertical
velocities within convective systems. Prior cloud classification
enhances retrieval accuracy by better constraining relationships
between Tb and different geophysical variable ranges. For
extreme IWP values, particularly in deep convective clouds,
retrieval performance improves by overcoming saturation ef-
fects. Additionally, dIWP/dt retrievals are refined near-zero
values across all classes, while wice retrievals improve most
notably for convective and deep convective classes, which
exhibit strong vertical dynamics.

Overall, the MWR-All spectral configuration using 183,
325, and 89 GHz channels shows higher performance. The 183
GHz channels alone outperform the 325 GHz channel. Com-
bining 183 and 325 GHz provides slight gains for the classifi-
cation method, but not for GVs regression. In contrast, adding
the 89 GHz channel (MWR-LF and MWR-All), offers slight
improvement for the classification method but substantial
improvements for GVs regression. The limited improvement
from the 325 GHz channel can be attributed to the retrieval of
integrated variables, which does not fully exploit its capability
to provide vertically resolved information, completing the 183
GHz, using atmospheric sounding principle. Combining these
channels could be valuable for retrieving vertical profiles of ice
water content and vertical wind velocities, which may require
alternative methods such as a variational approach (1D-VAR).
This will be explored in future work, with preliminary results
already showing potential.

These findings highlight the potential of C²OMODO for
both structural classification and microphysical and dynamic

properties retrievals of DCSs. They enable enhanced charac-
terization of convective updraft intensity at the scale of deep
convective features, with a global perspective along the tropics.
Such results offer promising insights for meteorology and cli-
matology, contributing both to forecast improvements through
data assimilation and to a more profound understanding of
convective processes. However, dataset limitations must be
considered in evaluating model performance. Statistical model
errors and uncertainties may stem from under-representation
of certain cloud classes or high IWP ranges.

In this study, the MESO-NH version used specific physical
parametrizations and a one-moment microphysical scheme.
Hector is an idealize case of strong deep convective thun-
derstorms [47]. The diversity of all convective systems at
global scale is not captured. Further work is needed to evaluate
the method's applicability to other convective systems that
will be targeted by the C²OMODO tandem, within the ±55°
latitude band. Key limitations include the possible influence
of horizontal advection, differences in convective organization,
and transitions between cloud types that may require adapted
classification schemes (e.g., [50]). Additionally, although sur-
face effects were negligible here, the 89 GHz channel may
be sensitive to surface emissivity in thin cloud or early-stage
convective cases, especially under variable surface conditions
[66].

Assumptions in RTTOV, such as particle size and shape
distributions, introduce further uncertainties in the simulated
measurements. The sensitivity of radiative transfer to mi-
crophysical assumptions is an important consideration. The
methodology used in this study relies primarily on correlation
between dTb/dt and the target variables, and not on the
absolute value of dTb/dt. Tests using different microphys-
ical parameterizations [49], [67], applied uniformly across
cloud classes, showed minimal impact on classification and
GVs retrieval performance, supporting the robustness of our
approach. However, if microphysical assumptions varied by
cloud type, this relationship could change, potentially improv-
ing retrievals but requiring prior knowledge of cloud type
and associated microphysics, which would be complex to
implement in an operational context. However, this remains
a hypothesis worth exploring in future studies.

There is still room for improvement. The classification
scheme used here, based on Feng et al (2011) [50] and
Marinescu et al (2016) [29], is adapted to deep and intense
convective storms that have characteristic similar to tropical
storms such as Hector. It tends to miss early stages of
convective development, occasionally misclassified as UND
due to overly restrictive cloud presence criteria. Adjusting
these thresholds could improve the detection of convection
initiation.

Further improvements could be achieved by enriching the
machine learning model with additional inputs. Water vapor
(e.g., from 23 GHz channels) and thermodynamic context
variables (temperature, humidity, convective available potential
energy, wind shear) from reanalyses could strengthen physical
consistency. High-frequency microwave channels (448–600
GHz) enhance sensitivity to cloud microphysics. Radar obser-
vations from dual-frequency or Doppler systems (e.g., GPM
[68], CloudSat [69], EarthCARE [24], INCUS [25], [26]) could better constrain cloud structure and vertical velocities. The JAXA Wide Swath Ku-band nadir-Doppler Radar, flying alongside a C²OMODO radiometer, will provide nadir observations over a 225 km swath that could be propagated across the 750 km swath of C²OMODO-R to improve consistency. Finally, integrating cloud lifecycle context from geostationary satellites using tools such as TOOCAN could help refine the classification based on convective evolution stages.

The aim of this study is to evaluate the feasibility and performance of the retrieval approach rather that to determine the optimal inversion method. Nevertheless, other machine learning methods (Random Forest, Logistic regression, Support vector Machine) have been tested and lead to slightly significative similar results (not shown).

Deep learning techniques, particularly Convolutional Neural Networks (CNNs), could enhance identification and characterization of convective system structure by leveraging the spatial coherence and horizontal structure of convective systems, albeit at the cost of increased computational and temporal resources. Future work could also explore tandem classification approaches, such as tracking cloud structure transitions between times $t_i$ and $t_f$ using dTb/dt to detect these shifts. This would require careful parametrization and consideration of numerous classes. Focusing on realistic phase transitions is crucial; for instance, a direct shift from clear-sky to deep convection in minutes seems improbable unless horizontal advection within the numerical model grid is accounted for. Another, more complex, approach would involve identifying regions of cloud growth, stability, or decay based on a study of ice content evolution, its vertical profile, and vertical wind velocities within convective systems.

Finally, a dedicated study will assess the impact of spatial observation geometry and tandem parameters on classification and regression retrieval performance, using an end-to-end C²OMODO simulator named RadioSpy (Radiometer Simulator in Python) developed by CNES. While the current study uses idealized C²OMODO measurements, the simulator will provide more realistic measurements, enabling a closer examination of the potential and informational content that C²OMODO could offer in an operational context following tandem launch.

## ACKNOWLEDGMENTS

The authors acknowledge the CNES and Airbus Defense and Space for funding support under the AOS/C²OMODO program. Jean-Pierre Chaboureau is acknowledged for providing the MESO-NH assistance. The authors thank also Thomas Fiolleau and Franck Auguste for insightful discussions for cloud structure classification criteria thresholds. The authors thank Friederike Hemmer for her valuable support in testing various machine learning methods for the classification-based inversion approach and for her help in correcting editorial errors. The authors also acknowledge the NWPSAF team, and in particular the helpdesk which provided support for RTTOV. This study benefited from the IPSL mesocenter ESPRI facility for data and computing resources.

# APPENDIX A
## LIGHTGBM MODEL PARAMETERIZATION

For each of the parameters shown below, the configured value is shown in square brackets.

* Learning Rate [0.01]: Controls the step size during boosting. A lower learning rate reduces each tree's impact, requiring more trees but potentially improving accuracy and generalization by making training more gradual and controlled.

* Subsample for Bins [200000]: Determines the sample size for constructing histograms to find optimal splits. Reducing the subsample can save memory and computation time but might lead to less precise binning, potentially affecting model performance.

* Number of Leaves [400]: Sets the maximum number of leaves per tree. More leaves allow the model to capture complex patterns, but an excessive number may lead to overfitting.

* Number of Estimators [500]: Specifies the total number of trees in the model. Increasing the number reduces bias but may increase overfitting and computational cost if not properly regularized.

* Class Weight (classification only): Addresses class imbalance by assigning weights, focusing on minority classes to improve performance. Three configurations are tested in this study:

- Unweighted: Equal treatment of all classes, often underperforming on minority classes.

- Balanced Weighted Class: Weights computed as:

$$weight_i = \frac{N}{n_i}$$

Where N is the total sample count and $n_i$ is the sample count for class i. This approach assigns higher weights to less frequent classes.

- Intermediate Compromise: Empirically defined weights to balance emphasis, giving distinct importance to certain classes without overemphasizing the least represented. Assigned weights: UND=1, ANVL=1, STRAT=2, CONV=4, DC=2.

# APPENDIX B
## METRICS FOR THE EVALUATION OF THE CLASSIFICATIONS

The performance of the classification algorithm relies on the algorithm's True and False predictions. For a given class, True Positives (TP) represent correctly classified instances. False Positives (FP) are instances incorrectly predicted to belong to the class, while False Negatives (FN) are instances from the class that were misclassified. True Negatives (TN) represent instances accurately identified as not belonging to the class.

Then the performance criterion include Precision, Recall, and F1-score. Precision (P) measures the proportion of correct predictions for a specific class among all predictions made for that class, highlighting the rate of false detections. Recall (R), also known as Hit Rate, indicates the ratio of correct predictions for a class relative to all actual instances of that
class. The F1-score (F1) provides a balanced measure by
taking the harmonic mean of Precision and Recall, effectively
addressing both false positives and false negatives. These
metrics are calculated as follows:

$$
\text{Precision (P)} = \frac{\text{TP}}{\text{TP} + \text{FP}}
$$

$$
\text{Recall (R, also called Hit Rate)} = \frac{\text{TP}}{\text{TP} + \text{FN}}
$$

$$
\text{F1-score} = \frac{2 \times P \times R}{P + R}
$$

APPENDIX C

METRICS FOR THE EVALUATION OF THE RETRIEVALS

R² measures the goodness of fit, showing how well it
explains variance in the target variable, with values close
to 1 indicating strong explanatory power. RMSE assesses
prediction accuracy by measuring the average deviation be-
tween predicted and actual values, expressed in the same
units as the target variable. Finally, MBE evaluates prediction
bias, identifying whether the statistical model systematically
overestimates or underestimates predictions. Together, these
metrics allow for a comprehensive evaluation of performances,
and are defined as follows:

$$
R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}
$$

$$
\text{RMSE} = \sqrt{\frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{n}}
$$

$$
\text{MBE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)
$$

Where $y_i$ is the observed value of sample $i$, $\hat{y}_i$ is the
predicted value for this sample, $\bar{y}$ is the mean of observed
values, and $n$ is the total number of observations.

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