SML data were provided by HD Rain, a French company specializing in weather monitoring and forecasting services. The deployment of HD Rain terminals in this region is motivated by its exposure to significant environmental and meteorological hazards. The study area is affected by “épisodes cévenols”, that is, intense Mediterranean rainfall events that can trigger severe flash floods. Given the high flood risk, high-resolution precipitation measurements are essential for improving early warning systems and hydrometeorological models. This need is particularly critical in this region, which comprises large densely urbanized areas where pluvial flooding represents a major hazard. Additionally, the region's complex topography results in highly variable rainfall patterns, which limits the representativeness of conventional rain gauge measurements. SML terminals help address this limitation by providing low cost decentralised fine-scale precipitation data, thereby enhancing meteorological observations in mountainous environments. In addition to precipitation monitoring, the integration of temperature and humidity sensors into these devices (Fig. ) enables their use in forest fire risk assessment and management. This capability is particularly relevant in the study region, which is highly susceptible to wildfires.

The SML sensor measures the loss of signal power, i.e. rain attenuation, caused by rainfall along the propagation path of the microwave signal transmitted by a broadcasting satellite (Fig. ). The average rain intensity between the receiving ground station and the rain-snow transition level is directly related to rain attenuation.

Each HD Rain SML consists of a satellite dish (around 75 cm in diameter) equipped with a standard TV Low-Noise Block (LNB) receiver, a solar panel providing autonomous power supply, a GSM antenna, and a device called Rainbox. The Rainbox incorporates a data logger that enables high-frequency measurements of the signal power received from the satellite and resamples these measurements by averaging them over 15 s intervals. It also contains a SIM card that provides connectivity through multiple mobile operators worldwide. The raw data are transmitted via the GSM network to a central server, where they are processed by a message broker before being stored in a time-series database for subsequent analysis.

The OpenSat4Weather dataset includes measurements from 215 HD Rain stations. Among these, 147 receive the signal from the Astra 19.2° E (Astra 1L) satellite, 67 from Hotbird 13° E (Hotbird 13F), and one from Astra 23.5° E (Astra 3B). Since these three satellites occupy nearby orbital positions, the satellite dishes have similar elevation and azimuth angles (Table ). Two hardware versions are represented in the dataset: RBV2 (23 stations) and RBV3 (192 stations). RBV3 is the latest generation and, while providing the same measurements as RBV2, features updated electronic components and a larger solar panel to improve energy autonomy. The stations are deployed at elevations ranging from 0 to 1622 ma.s.l. (above sea level), with a median elevation of 94 m and an average of 173.3 m. Each station collects data at two frequency bands and two polarizations. For each frequency–polarization combination, the Rainbox module records the RSL. The OpenSat4Weather dataset includes measurements from signals transmitted at horizontal polarization in the upper Ku-band. Specifically, the RSL in the dataset corresponds to the integration of the received satellite signal over the 11.70–12.75 GHz frequency range, which provides the highest RSL for the broadcasting satellites operating over France. Station identifiers follow the format “FRA-NNNNN”, where “FRA” denotes the country code and “NNNNN” is a unique five-digit integer station identifier (e.g. “FRA-00002”).

The dataset consists of RSL time series in dBm recorded at a 1 min temporal resolution with a precision of 0.01 dBm, together with the corresponding time stamps, expressed in UTC. The data cover the period from 1 August to 31 December 2022. Figure a presents a 2D picture of all RSL samples, labeled in three classes: missing data (NA), invalid observations, and valid observations. Figure b reports selected RSL quantiles. Considering all stations and the entire observation period, the RSL values exhibit a median value of -16.4 dBm, with minimum and maximum values of -60.5 and -8.8 dBm, respectively. The absolute RSL value is not a critical parameter provided it remains within an acceptable operating range, as it is directly influenced by the antenna cable length between the dish and the Rainbox unit. However, values below approximately -40 dBm are generally considered suspicious and should be flagged as invalid observations. Such anomalously low values may result from several factors, including excessive cable length, which introduces additional signal loss, inaccurate satellite alignment, or a malfunctioning LNB, among others. In any case, an analysis of the magnitude of the RSL must be always considered in relation to its variability over time. Only five stations in the dataset (FRA-00038, FRA-00309, FRA-00332, FRA-00348, and FRA-00375) recorded RSL values below -40 dBm. The proportion of missing values (NAs) varies between 0.04 % and 20.6 % across stations, with a median of 0.09 % and a mean of 0.90 %, respectively.

The OpenSat4Weather dataset includes ground-based rainfall measurements collected by the operational rain gauge network of Météo-France. These data are freely available through the Météo-France API portal and the open-data platform (http://meteo.data.gouv.fr, last access: 19 May 2026). Rain gauge measurements undergo a data quality control process, which assigns a quality code to each observation as follows; “9 ” denotes filtered data, “0” denotes protected data, that have been validated through manual inspection, “1” denotes validated data either automatically or through manual inspection, and, “2” indicates questionable observations (according to the automatic procedure).

The rain gauge dataset provides rainfall accumulations at a 6 min temporal resolution with a precision of 0.1 mm, covering the same period as the SML dataset (1 August–31 December 2022). A total of 113 rain gauges located within 10 km from at least one SML station were selected for inclusion in the dataset. The rain gauges are installed at elevations ranging from 1 to 1464 ma.s.l., with median and mean elevations of 184 m and 313 ma.s.l., respectively.

Figure  summarizes the statistical characteristics of the rain gauge observations using the same graphical representation as in Fig. . A total of 41 % (46 out of 113) of the rain gauges contain missing or invalid data. The maximum percentage of missing or invalid data for a single sensor was 11.4 %, with an average of 1.1 % across all stations. Zero rainfall was recorded from 86.7 % to 99.0 % of the 6 min intervals, with an average occurrence of 97.5 %. The maximum recorded rainfall accumulation over a 6 min interval was 26.9 mm.

We added to OpenSat4Weather the rain gauge-adjusted weather radar product PANTHERE from Météo-France as an additional reference for rainfall estimation. The product is gridded with a spatial resolution of 1 km and a temporal resolution of 5 min. The data are available in near real-time through the Météo-France public API portal (https://portail-api.meteofrance.fr/web/fr/api/DonneesPubliquesPaquetRadar, last access: 19 May 2026). The PANTHERE product is generated from the data collected by ARAMIS, the French operational weather radar network. The network comprises 20 C-band radars, five S-band radars, six X-band radars and two radars deployed at airports in Paris and Nice . A description of the methodology to derive the PANTHERE product is provided in . The radar-derived precipitation fields used in this study contain no missing data during the period covered by the SML observations.

We did not directly include the PANTHERE product in the OpenSat4Weather dataset. Instead, we further processed the data to derive radar-based rainfall estimates along each SML path, as detailed in Sect. , and these estimates were incorporated in the dataset. It is important to note that, as with most weather radar products, PANTHERE provides maps of surface rainfall intensity derived from radar scans acquired at multiple elevation angles. These measurements sample atmospheric volumes located at altitudes ranging from several hundred meters to several kmaboveground. To mitigate this limitation, the PANTHERE product has been corrected using ground-based rain gauge observations. Although gauge-based adjustment reduces uncertainties associated with radar measurements aloft, radar products still are only the best available estimate of the true structure of rainfall, as they are affected by multiple error sources (e.g. refraction, beam blockage, attenuation, and Z–R relationship). For example, weather radar data often underestimate rainfall extremes . Therefore, comparing SML rainfall estimates and radar data, such as the ones provided here, should not be expected to yield perfect agreement.

The knowledge of the 0 °C isotherm is essential for identifying the rain height, defined as the upper limit of the portion of the propagation path where precipitation occurs in liquid form. In this study, we use ERA5, a global atmospheric reanalysis dataset available through the Copernicus Climate Data Store (https://cds.climate.copernicus.eu/datasets, last access: 19 May 2026). ERA5 products are generated using the integrated forecast model, developed by the European Centre for Medium-Range Weather Forecasts (ECMWF), which combines model simulations with the assimilation of meteorological observations from multiple sources. The ERA5 single-layer products provide the 0 °C isotherm height at an hourly temporal resolution and a 0.25° spatial resolution (approximately 28 km). This variable represents the altitude a.s.l. at which air temperature reaches 0 °C. The 0 °C isotherm height is crucial for identifying the melting layer, namely, the vertical region of the atmosphere where solid particles melt into raindrops, as discussed in Sect. .

ERA5 exhibits systematic errors in freezing-level height over complex terrain, primarily due to its limited spatial resolution . Comparisons with aircraft observations show that ERA5 atmospheric temperatures are generally accurate, with maximum biases of approximately 0.4 °C at upper atmospheric levels over the North Atlantic. Direct comparisons of ERA5-derived 0 °C isotherm heights against aircraft measurements in Chile reported mean absolute errors of approximately 133–245 m .

Even though a discussion of the methods for retrieving rainfall intensity from SML raw data is beyond the scope of this paper, nonetheless it is important to understand the role of rain height in SML data processing. The standard conversion formula between rainfall intensity R (in mmh-1) and rain attenuation γ per unit path length is given by 1γ=κRαdBkm-1, where κ and α are coefficients dependent on SML signal frequency and polarization and on the link elevation angle. When the propagation path intersects a rainy layer with a vertical extent of hR km and an elevation angle θ, R can be estimated as follows: 2R=Aκ⋅sin⁡θhR1/αmmh-1, where A is the RSL attenuation (dB) caused by the rainy layer as detected by the SML. Equation () assumes that rain is uniformly distributed along the propagation path up to hR and that no other significant sources of signal attenuation contribute to the observed attenuation. In practice, neither assumption is fully satisfied. Therefore, hR is generally interpreted as an effective rain height rather than the physical altitude up to which liquid particles are present.

The physical rain height can be estimated by weather radar measurements. Radars detect the presence and the height of the melting layer, which appears as a thin vertical region of enhanced reflectivity known as bright band, typically located just below the 0 °C isotherm. The bright band is produced by backscattering from snowflakes melting into raindrops . Therefore, the top of the bright band corresponds to the 0 °C isotherm height, while its lower boundary is the physical rain height . The characteristics of the melting layer depend on the precipitation type. Stratiform precipitation is generally associated with large spatial scales, low rainfall intensities and a well-defined vertical structure composed of a frozen layer, a melting layer and a liquid precipitation layer. In contrast, convective precipitation is characterized by vertical winds (downdrafts and updrafts), which generate high-intensity localized phenomena, and it does not exhibit a clear separation between frozen and liquid phase. As a result, mixed type and mixed-phase precipitation coexist and the bright band disappears , which makes rain attenuation difficult to estimate. In addition to radar observations, rain height can be estimated from radiosonde measurements or from NWP model outputs and atmospheric reanalyses, which provide estimates at temporal scales compatible with rainfall variability.

The rain height can also be estimated through models. For instance, provides a statistical formula to retrieve the mean annual rain height a.s.l. from the mean annual 0 °C isotherm height h0: 3hR=h0+0.36km. The output of Eq. () represents an effective rain height intended for the statistical prediction of rain attenuation along Earth–satellite propagation paths. It accounts not only for the attenuation produced by liquid precipitation but also for the melting layer contribution. Moreover, this model provides an average of both stratiform and convective precipitation regimes. proposed a more refined statistical approach deriving separate estimates of hR for stratiform and convective precipitation, while explicitly accounting for the contribution of the melting layer. Their method is based on a weighted average of the monthly mean 0 °C isotherm heights. Statistical methods primarily capture long-term features, such as the seasonal variability of the 0 °C isotherm and rain height, rather than the short-term variability associated with individual precipitation events. Therefore, they are not appropriate for retrieving rainfall intensity from raw SML observations available in real time.

If the actual values of the 0 °C isotherm and of the rain height are known, rainfall intensity can be estimated in real time using electromagnetic models. These models typically represent the atmosphere as a two-layer medium consisting of a melting layer overlying a liquid precipitation layer. A straightforward approach consists of introducing an additional attenuation term analogous to that in Eq. (), which depends on both the rainfall intensity and the thickness of the melting layer, although with coefficients that differ from those of liquid precipitation . Alternatively, the length of the rainy path can be adjusted to incorporate the melting layer contribution . Modeling the melting layer during convective precipitation is considerably more challenging, as updrafts can trasport liquid hydrometeors above their typical equilibrium levels and viceversa for downdrafts with solid hydrometeors. As a result, the contribution of the melting layer contribution becomes more difficult to estimate accurately .

Time series of the 0 °C isotherm height for each SML are included in the OpenSat4Weather dataset. These data were derived from the ERA5 reanalysis and are presented in Fig. . For each SML, the ERA5 grid cell corresponding to the SML receiver location was selected to approximate the atmospheric profile along the propagation path. Nevertheless, the spatial resolution of ERA5 is insufficient to fully capture the fine-scale topographic and meteorological variability of the study area. Consequently, multiple SML receivers may fall within the same ERA5 grid cell and therefore share identical 0 °C isotherm time series despite differences in receiver elevation. As shown in Fig. , the 0 °C isotherm height exhibits significant temporal and spatial variability, primarily driven by seasonal changes and orographic effects. The 0 °C isotherm height progressively decreases from late summer to winter, with peak values exceeding 5000 m above ground in August and minimum values as low as 360 m above ground at winter. This variability is critical for rainfall retrieval from SMLs, as it directly influences the estimation of the effective rain height. The color scale in the figure indicates the elevation of the SML receiver locations. In general, lower receiver elevations are associated with higher isotherm heights a.s.l., reflecting the influence of the regional topography on the atmospheric thermal structure.

We derived the radar-based rainfall intensity estimate in correspondence of each SML propagation path according to the procedure described below. First, we determined the radar grid cells intersected by the SML path using the grid-intersection method implemented in the poligrain package (https://github.com/OpenSenseAction/poligrain, last access: 19 May 2026). As the SML rainfall estimate depends on the melting layer height, we precomputed the intersections between radar pixels and SML paths for melting layer heights between 0–6000 m above ground in 250 m steps. Each radar grid cell intersected by the SML path was assigned a weight proportional to the length of the path segment within that cell. At each time step, the current height of the melting layer was used to calculate the intersected pixels. Finally, the radar-based rainfall intensity estimate along each SML path was computed as the weighted average of rainfall intensity in the intersected radar cells, using the path-length weights.

The resulting radar-derived rainfall estimate is consistent with the SML measurement geometry, as it represents the path-averaged rainfall between the SML receiver and the point at which the propagation path intersects the melting layer. An example of the radar-based rainfall intensity along an SML path is shown in Sect. .

A major challenge associated with opportunistic data is the lack of standardized procedures for generating, formatting and storing the data. This issue has recently been addressed by , who proposed a set of data format conventions for several types of opportunistic data, including SMLs. These recommendations are the outcome of the activities of the COST Action OpenSense (Opportunistic Precipitation Sensing Network), which aims to improve access to opportunistic precipitation observations (https://opensenseaction.eu/, last access: 19 May 2026). recommended the use of the NetCDF format for data storage, because of its flexibility and portability. They also defined a set of conventions for variable names and for data and metadata structure, distinguishing between required and optional elements, to ensure consistency and interoperability across datasets. The OpenSat4Weather dataset adopts these recommendations, including all the required SML variables and data specified by .

The dataset includes the following three NetCDF files:

SML_data_2022.nc: stores SML data;

In particular, the SML_data_2022.nc file hosts the following variables:

The main variable is rsl, stored in the file with the dimensions sml_id and time;

The radar-derived rainfall estimates along the SML path are stored using the same dimensions, format and naming convention as the SML data. The corresponding SML metadata are not included and radar-derived rainfall is stored in the variable rainfall_amount. The rain gauge dataset contains the variable rainfall_amount together with the corresponding time, coordinates and elevation a.s.l. All timestamps in the three datasets are UTC. For the rain gauge data, each timestamp corresponds to the end of the 6 min accumulation interval. Similarly, the time stamps of radar data are the end time of each 5 min radar volume scan. Since the available radar product is rainfall intensity, the time stamp should be interpreted as a nominal time rather than the exact acquisition time, because rain estimation is based on sweeps at different elevations that generated data before the time stamp.

Figure  presents descriptive statistics of the RSL measurements for the individual SML stations. In each boxplot, the box extends from the 25th to the 75th percentile (interquartile range), while the vertical lines indicate the 5th and 95th percentiles. The stations are ordered from left to right according to increasing elevation a.s.l. Figure a reports the boxplots of the RSL (dBm) over the observation period with the median values highlighted in orange. No clear relationship is observed between RSL and SML elevation. Instead, the median RSL exhibits substantial variability across the network, ranging from -24 to -10 dBm. Although unusually low RSL values may, in some cases, indicate malfunctioning, the dominant factor affecting the median RSL is the length of the coaxial cable connecting the satellite dish to the Rainbox unit. Longer cables introduce greater losses, resulting in lower median RSL values. Consequently, SML data analysis should focus primarily on relative changes in the received signal (e.g. due to rain) rather than on the absolute values, which are strongly influenced by installation-specific characteristics.

Figure b shows the normalized RSL, defined as the difference between the 1 min time series and the corresponding mean RSL value over the observation period. For the vast majority of SMLs, the boxplots are centrered around 0 dB and exhibit a dynamic range within 1.5 dB (difference between the 5th and 95th percentiles). This indicates that rainfall, and, particularly moderate-to-heavy precipitation, is only marginally represented within the selected percentile range, as rain attenuation typically exceeds 1 dB during intense precipitation events. Indeed, the radar-derived rainfall estimates along the SML propagation paths indicate that rainfall occurs during only 3.2 %–7.4 % of the 5 min radar time intervals. Consequently, most rainy periods lie near or beyond the tails of the boxplot distribution. Furthermore, a large portion of these rainy periods corresponds to light rainfall, which generally produces attenuation values within 1 dB. For example, only 26 % of the 5 min rainy intervals in the radar dataset are associated with rain intensities above 2 mmh-1. A small number of stations exhibit anomalous boxplots characterized by median values shifted away from 0 dB (indicating a few extreme values that affect the mean value but not the quantiles) or by a large variability, which is an indicator of unstable or malfunctioning links.

The boxplots in Fig. c show the normalized RSL, conditioned on the occurrence of rainfall, as identified by the radar-derived rainfall intensity along each SML path. In contrast to Fig. b, the effect of rain is clearly visible. Although the median RSL is only slightly reduced (generally between -1 and 0 dB), the lower quantiles (corresponding to 25th and 5th percentiles) drop significantly for nearly all stations. The spread of the distributions also increases, consistent with the spatial variability of rainfall observed by the radar, whose total accumulation ranges from approximately 230–727 mm. Again, no clear altitude effect is observed.

Figure  presents time series of indicators aggregated across all SML stations and derived from SML and radar data. The top panel shows the mean of the normalized RSL across all SML stations (green), together with the 95th percentile (blue), and the 5th percentile (orange). For comparison, the mean radar-derived rainfall along SML paths is also shown (black). The distance between the blue and the orange curve measures the difference between the strongest and weakest RSL across all SMLs at each time stamp. The two lower panels in the figure provide views of two selected 10 d periods.

During dry weather, the normalized RSL exhibits a pronounced diurnal cycle, which will be discussed later. This pattern is particularly evident during the summer months. Rainfall events are also clearly visible, especially in the 5th percentile time series. In the September zoom-in, the 5th percentile drops sharply to approximately -3 dB, while the 95th percentile remains essentially unchanged and the mean slightly decreases. This behavior is consistent with heavy but spatially localized precipitation affecting a subset of SMLs across the French Mediterranean arc. In contrast, during the December period, the 5th percentile is less affected (1.5 dB). However, a slight decrease is observed also in the 95th percentile, indicating the presence of widespread but less intense precipitation.

The spatial distribution of rain gauges relative to SML sensors is a key factor for effectively leveraging opportunistic data, as the distance to the nearest rain gauge directly influences the reliability of validation analyses. Figure  shows boxplots of the distribution of the distances between each of the 215 HD Rain SML stations and its three nearest rain gauges. The mean distance to the closest rain gauge is 5.87 km, with an interquartile range of 5.16 km (25th percentile: 3.13 km, 75th percentile: 8.29 km). Distances range from a minimum of 0.06 km to a maximum of 19 km. The mean distances to the second and third nearest rain gauges are 10.43 and 13.93 km, respectively, with interquartile ranges of 5.10 and 6.76 km, respectively. Overall, 43 % of SMLs have a rain gauge within 5 km, and 87 % are within 10 km, indicating a relatively homogeneous distribution of both rain gauges and HD Rain stations across the study area.

Figure  illustrates the evolution of the 0 °C isotherm height from August to December 2022 (bottom panel), together with the RSL of a representative SML (top panel), and nearby rain gauge and radar-based rainfall intensity along the SML path (middle panel). The ERA5-derived 0 °C isotherm height exhibits a large temporal variability, ranging from almost 5000 ma.s.l. in August to less than 1000 ma.s.l. in December. It usually lies above 2000 ma.s.l. from August to mid-October. Consequently, the average SML propagation path of the SML signal below the melting layer is about 6 km. From November onward, the path length decreases to generally less than 3 km.

Large signal attenuation values (up to about 12 dB) are observed during the summer in correspondence of heavy precipitation events (rainfall intensities exceeding 75 mmh-1), while the 0 °C isotherm height remains around 4 kma.s.l. A similar situation occurs between late October and early November (rainfall intensity peaks higher than 40 mmh-1, attenuation around 10 dB, and 0 °C isotherm height around 3500 m). As the atmosphere cools later in the observation period, rainfall events become less intense and the 0 °C isotherm height decreases to 1500–2000 m. The observed signal attenuation is substantially reduced, reaching only about 2 dB. These results highlight a clear seasonal pattern, typical of temperate regions. During the warmer months, rainfall events tend to be more intense and the 0 °C isotherm is located at higher altitudes, resulting in stronger signal attenuation, due to both the higher specific attenuation and the longer propagation path through the liquid precipitation layer. Conversely, winter precipitation is generally weaker and predominantly stratiform, which, combined with the lower 0 °C isotherm height, produces substantially lower attenuation.

This seasonal variability has important implications for rainfall retrieval from SML data. During summer, strong attenuation may cause the RSL to decrease to the minimum detectable level of the LNB or result in complete signal loss, thereby limiting the ability to quantify heavy rainfall. Conversely, in winter, the weak attenuation and low variability in the signal can make rainfall detection and estimation more challenging, as identifying the baseline signal level becomes more difficult. However, these seasonal patterns have exceptions. In Mediterranean regions, for example, intense convective events may also occur during the colder months, while stratiform precipitation can occasionally be observed in summer.

Finally, it is important to note that the 0 °C isotherm height exhibits substantial variability, not only on seasonal time scales but also over much shorter periods: fluctuations of 1–2 km can occur over a few days. For instance, Fig.  shows that the 0 °C isotherm raises occasionally above 3000 m in late December, while dropping below 2500 m in early October.