Precipitation is the main downward forcing of the water cycle and, consequently, one of the most relevant inputs in hydrological models, which are key tools in early-warning systems for flood risk forecasting and mitigation . However, precipitation exhibits a significant temporal and spatial variation over a catchment area or region , and this is a critical aspect leading to difficulties in reconstructing a reliable rainfall field. In the past, several studies have investigated the effects of spatio-temporal variability in rainfall on the hydrological model outputs e.g., proving that precipitation inputs have a marked influence on the simulated outflow hydrographs. It is also known that the reconstruction of rainfall input is more accurate as the number of rainfall measurements increases over a study area . However, because of economic or geographical factors, an adequate density of rainfall sensors is often not available.

Currently, the most common ground-based technology for rainfall measurement is the rain gauge (RG), which provides single-point measurements . In addition, high-precision ground sensors, namely disdrometers, provide the size and velocity of hydrometeors . One of the major problems encountered when dealing with single-point measurements is the transfer of information to ungauged sites or the reconstruction of the rainfall field over the catchment of interest. Such estimates can be performed by the use of spatial interpolation techniques. Several methods are now available, with different degrees of complexity. They can be either deterministic, such as the inverse distance weighting (IDW) method and the Thiessen polygon method , or stochastic, such as the Kriging technique and co-Kriging . However, the outcome of these techniques has been proven to be highly sensitive to the gauge density , depending on the temporal resolution. Specifically, the shorter the aggregation time, the more critical the rain gauge density. Alternatively, the rainfall field at ground level can be indirectly obtained by weather radars, when available. The radar retrieves the average rainfall intensity across a volume from measurements of reflectivity through power-law formulas, such as the one proposed by . A recent survey of reflectivity-rainfall intensity formulas is given in . and have argued about the purely statistical nature of the reflectivity-rainfall intensity formulas, with important consequences regarding their use where calibration with local data is missing. There are also other drawbacks associated with the use of radar reflectivity, including the problem of spurious echoes, such as ground clutter , which restrict the use of radars to plain areas, and the fact that the radar reflectivity provides only information about precipitable water. Recently, the dual-polarization upgrade of radars has added information about the shape, composition, and phase of the hydrometeors. Hence, quantitative precipitation estimation (QPE) has greatly benefited from such advancements.

For all of these reasons, measuring the spatial distribution of rainfall is still an open issue, which may be tackled through the integration of conventional sensors and/or the implementation of new instruments to complement existing measurements. In this context, the use of opportunistic rainfall sensors, such as commercial microwave links (CMLs), has raised considerable interest. CMLs are the point-to-point radio links connecting the base stations of a mobile network to the core infrastructure. The use of microwave links as opportunistic rainfall detectors was firstly proposed by . The method exploits the relationship between the rainfall intensity and the attenuation (i.e. the loss of signal power) experienced by the electromagnetic wave along the propagation path from the transmitter to the receiver. Later, made use of a mesh of microwave links for the 2D reconstruction of the rainfall field, through simulation. A pioneering experimental campaign was carried out during the Mantissa project . However, at that time, the need to install ad hoc microwave links made the technique impractical. A few years later, the scenario changed following the dramatic expansion of cellular telephony. The use of the ubiquitous CMLs connecting the base stations of cellular networks was first proposed by . Their paper triggered many studies that were conducted worldwide to investigate the potential of CMLs for meteorological and hydrological applications. From a hydrological point of view, CML-based rainfall products were first exploited by to improve urban drainage modelling in a small-scale (2.33 km2) impervious catchment in Prague, Czech Republic. Later, investigated the effects of the use of CML data in discharge simulations, for a natural lowland catchment in the Netherlands, at a small scale (6.5 km2). A further study by used microwave-link-derived precipitation estimates as rainfall input in a distributed hydrological model applied to the Ammer Basin (Germany), with an area of 609 km2. In that work, the authors employed the IDW method for the interpolation of RG and CML rainfall data on a 100m×100 m grid. Another case study to check the potential of a dense CML network for urban drainage management was carried out on an agglomeration of cities (16 km2) in the Czech Republic by . assessed the impact of CML quantitative precipitation estimates (QPEs) on urban drainage modelling. The authors found that the sensitivity of CMLs is the factor that mostly affects the QPEs and that the bias on QPEs propagates throughout rainfall–runoff simulations. Moreover, they showed that the position of CMLs over the drainage area impacts the reconstruction of the runoff dynamic. In Italy, conducted a validation of the CML rainfall estimates in the Po Valley (northern Italy) by comparing them with different data sources (RGs, the ERG5 meteorological data set, and radar products). However, to our knowledge, a hydrological application of CML-based rainfall estimates does not currently exist.

Herein, the analysis aims at investigating and validating the potential of a CML network, located in Lombardy (northern Italy), exploited for hydrological purposes. Specifically, relying on a semi-distributed hydrological model, we assessed whether rainfall data collected by a large CML network of 50 links may be used to provide a reliable reconstruction of the hydrological process in a medium-sized basin and if the reconstruction is comparable with those achieved with a well-designed RG network. We investigated a set of summer and autumn precipitation events, both convective and stratiform, that occurred over the Lambro Catchment during the years 2019 and 2020. The analysis of events taking place in different seasons allowed us to point out some limitations of CMLs with respect to detecting specific types of precipitation. In this work we firstly focused on the spatial interpolation of rainfall observations, comparing results from conventional (RGs) and unconventional (CMLs) instruments and their combined use. In fact, the issue of spatial interpolation is crucial when dealing with point (RG) or linear (CML) measurements used as input for a semi-distributed hydrological model, especially when the study area is quite large (in the order of 100 km2 or even larger). We relied on the traditional IDW method to spatially interpolate precipitation measurements/estimates from RGs/CMLs. Secondly, we implemented a semi-distributed rainfall–runoff model using three types of input: (1) RG measurements, (2) CML estimates, and (3) a combination of RG and CML data. Given the different nature of rainfall input, we also assessed three calibrations of model parameters. We then compared results in terms of river discharge.

The remainder of this paper is structured as follows. In Sect. , we present the case study, the experimental set-up, and the features of the networks of conventional and unconventional sensors. Section  includes a description of all methods implemented for the analysis, and Sect.  reports the results, including a comparison of rainfall spatial interpolation carried out with the different data types and of streamflow simulations against hydrometric measurements. Discussion and conclusions are given in Sects.  and respectively.

The case study was carried out in the Lambro Catchment, a peri-urban catchment that is a northern tributary of the Po River, as shown in Fig. a. It is located north of the Milan metropolitan area and covers three different provinces: Como, Lecco, and Monza and Brianza. The Lambro River, at the Lesmo River section (shown in purple in Fig. a), drains an area of 260 km2 that can be mainly divided in two zones based on different morphology and land use. The northern zone is the pre-Alpine region, where the Lambro River originates, at 944 ma.s.l. In contrast, the southern zone, between Pusiano Lake (in sub-basin 6 in Fig. ) and the outlet section, at 178 ma.s.l., is a flat area subjected to massive urbanization, which results in large impervious surfaces and, consequently, fast runoff processes with a lag time of few hours. The catchment includes the presence of two lakes: Pusiano Lake (which is the biggest one) and Alserio Lake (in sub-basin 8 in Fig. ), both located in the middle part of the catchment. According to the climate classification, the northern inland portion of Italy belongs to the humid subtropical climate (Cfa) zone. Heavy convective precipitation cells characterize the basin, while the highest monthly rainfall accumulation occurs in spring and autumn. The local meteorological drivers, along with urban sprawl, lead to the hydrological vulnerability of the region. In order to mitigate hydrological risk in the Monza and Milan urban areas (downstream of our case study region), structural works have been carried out along the Lambro River in past years. Moreover, great efforts have been made in the implementation and development of non-structural measures e.g., including a dense monitoring system managed by ARPA Lombardia (the regional agency for environmental protection). From this, we exploited 10 min resolution rainfall depths and temperatures from 13 tipping-bucket RGs and eight thermometers (THs) respectively, for the years 2018 and 2019 as well as for the first 6 months of the year 2020. In addition, we used 10 min resolution water level measurements of a flow gauge (FG), located at the outlet section of the Lambro Basin in the municipality of Lesmo. All of these meteorological and hydrological data are available at https://www.arpalombardia.it (last access: 10 March 2022). A rather dense CML network, owned by Vodafone Italia S.p.A., covers the central and southern catchment area and its surroundings. In contrast, the northernmost portion of the Lambro Basin is covered by few and unevenly distributed CMLs, given that it is thinly populated and characterized by higher altitudes. A total of 50 CMLs are available over the above-mentioned area. The key features of CMLs as rainfall sensors are the operation frequency and the path length. Regrouping the available CMLs according to the frequency:

5 links are in the frequency range [11.4,13.1] GHz, with a path length between 3.5 and 8 km;

We investigated 12 storm events and the associated floods, in the period from June 2019 to June 2020. The RG- and CML-based precipitation data sets, aggregated at an hourly timescale, cover a wide range of rainy events, from summer thunderstorms to low-intensity autumn events. In Table , we reported some features characterizing the 12 selected events, namely the initial date, the final date, and time; the accumulated precipitation averaged over 13 RG measurements; the total volume of precipitation that fell on the basin area; the 1 h maximum rain rate; the observed total flow volume; and the peak flow. We defined a storm event as the time lapse where at least one RG, available in the area, detected precipitation with possible dry intervals no longer than 5 h. An hour is considered dry when the detected rainfall depth is lower than 1 mm and wet otherwise. The beginning of the flood event is conventionally set at the hour in which the flow rate experienced a sudden deviation from the average. The end is instead set when the flow rate reverts to the initial condition, at the end of the depletion curve. According to the maximum observed rain rates, we classified events as low-rain-rate and high-rain-rate events, adapting the classification reported in to our specific case study. The former group includes storm events 5, 6, 7, and 12, for which the maximum rain rate was lower than 15 mmh-1, whereas the latter covers the remaining events, for which the maximum rain rate was higher than 15 mmh-1.

In order to implement the hydrological model (see Sect. ), the catchment area is divided into 15 sub-basins (as shown in Fig. a), with areas ranging from 1.15 km2 (HRU 7) to 42.6 km2 (HRU 10). Hereinafter, the sub-basins will be referred to as hydrological response units (HRUs). In particular, the semi-distributed model adopted here requires, as input data, rainfall depths estimated in the HRU centroids. The estimates were gathered using the IDW technique (see Sect. ), and a different number of sensors was exploited for each HRU, according to a defined maximum distance of 10 km from the HRU centroid. Figure  shows some features of the rainfall sensors used for spatial interpolation in each HRU: the number of exploited RGs, CMLs, and their sum; the ratio between the number of CMLs and RGs; the mean distance between rainfall sensors and HRU centroids; and the mean length of CMLs. Please, note that the CML–HRU centroid distance is calculated considering the CML middle point. It is also worth mentioning that the number of available CMLs was less than 50 for some events due to instrument maintenance or malfunction. Hence, the numbers in Fig.  are averaged over all of the events. Figure a highlights a significant increase in the exploited CMLs from HRU 1 to 6. This could be a potential problem and could lead to more inaccurate estimates, at the stage of spatial interpolation, for the northern HRUs with respect to the southern ones. On the other hand, the number of RGs undergoes minor variation from one HRU to another. In Fig. b, we can see that the lowest ratios between CMLs and RGs correspond to HRU 1 to 5 and HRU 10. Moreover, Fig. c shows that, considering HRUs 1 to 9, the mean distance between sensors and HRU centroids is always higher when CMLs are considered. The opposite trend, with a single exception for HRU 12, occurs for HRUs located further downstream. Lastly, the mean CML length, in Fig. d, has a decreasing trend from upstream to downstream.

In this section we firstly describe the data processing algorithms. While the procedure is simple for conventional sensors (RGs, THs, and the FG), it is not straightforward to extract quantitative rainfall information from CML raw data, which are generated for network monitoring purposes. Second, we discuss the semi-distributed hydrological model and its calibration/validation procedures. Finally, we illustrate the methods for the spatial interpolation of RG- and CML-based rainfall data.

The results are presented in the following two subsections. Section  provides a comparison of rainfall depths interpolated at the HRU centroids, by using data either from conventional or opportunistic sensors. Both accumulated rainfall values and hourly rainfall depths are considered at the basin and sub-basin scale, for the 12 events. Therefore, we investigate whether there are some critical issues that might help to explain differences in the rainfall–runoff model outputs. Section  analyses discharge performance by comparing RG-, CML-, and RG+CML-driven simulations with the observed flow rates.

The analysis of interpolated rainfall data carried out in Sect.  reveals that CML and RG estimates of accumulated areal-averaged rainfall depths are comparable. However, two issues emerged.

First, CMLs exhibit a different behaviour depending on the event intensity, as their sensitivity varies with length and frequency. Specifically, they return lower values of rainfall depth and rainfall accumulation in connection with low-rain-rate events. This aspect becomes evident at either different spatial scales (sub-basin and basin scales) or different temporal scales (hourly and event-based timescales). In fact, due to a coarse quantization of the raw data, CMLs are not sensitive to low rain intensity; hence, when the rainfall depth value over a certain lapse of time is required (in our case 1 h), this limitation may lead to large errors, especially when light rain goes on for a long time. Despite some discrepancies in the behaviour of single CMLs with respect to their nearby RGs, as highlighted in Appendix , we observed a good agreement between CML- and RG-based estimates in HRU centroids for high rain rates due to spatial interpolation which could mitigate such biases.

The second issue is the different CML density over the HRUs. It is well known that spatial interpolation methods are sensitive to sensor density ; consequently, the relatively large distance of the available CMLs from the HRU centroids in the most scarcely populated areas (northern HRUs) may lead to a loss of reliability in the estimated rainfall depths. However, such an aspect appears to be less relevant when compared with the first issue outlined above, at least when dealing with quite large HRUs (dozens of square kilometres). In fact, a careful comparison of Figs.  and  does not show an evident correlation between the mean CML–centroid distances and ΔE values.

Last but not least, model performance is influenced by the calibration process of model parameters. Similar model performance, in terms of the NSE index, can be achieved with all three types of input data (RGs, CMLs, and CMLs+RGs) if the calibration is carried out with the respective data inputs. This means that, after a proper calibration, opportunistic sensors could be exploited in semi-distributed hydrological models, as well as RGs. In particular we found that, after calibration, the RGs+CMLs data set provides the highest median NSE. However, it is worth highlighting that we calibrated the parameters on the basis of only 12 flood events. In order to assess a robust calibration and the associated validation, a larger data set of CML-based rainfall events should be processed.

In this work, we assessed the use of commercial microwave links (CMLs) as opportunistic rainfall sensors within hydrological modelling. We focused on Lambro, a peri-urban catchment, 260 km2 in area, located north of Milan (Italy) and covered by 50 CMLs that are part of the network owned by a major mobile operator. The Lambro Catchment area is also covered by 13 rain gauges (RGs), which we used both as an independent rainfall data set and in combination with CMLs. We implemented a semi-distributed hydrological model and carried out two types of comparison between CML and RG data. First, we considered rainfall data (hourly rainfall depths, the input of the hydrological model, and total accumulations at the storm end, for a sample of 12 storm events) interpolated at the HRU centroids. We then compared river discharge simulations (model output) from RGs, CMLs, and RGs+CMLs against flow measurements.

Concerning the comparison of the two sources of rainfall data, we found that high-intensity events detected by CMLs are in accordance with RG measurements. On the other hand, we came across a critical aspect with respect to the inability of CMLs to detect low rain rates, due to the coarse 1 dB quantization step of raw data (i.e. received power levels). The minimum detectable rainfall intensity depends on the operation frequency of CMLs as well as on their length; for the available set of CMLs, the minimum detectable rainfall intensity ranges from 1 to 10 mmh-1. Such a limitation results in the underestimation of rainfall depths interpolated in the HRU centroids for low-intensity storm events, when compared with RG-based rainfall data.

The hydrographs simulated by the hydrological model perform better in terms of the Nash–Sutcliffe efficiency (NSE) and relative error on flow volume (Dv) in the case of RGs compared with CMLs. This result is not surprising, as the model was calibrated using RG data for 1 year. Nevertheless, satisfactory values of relative error on peak discharge (REP) are achieved through the use of CML and CML+RG data as inputs to the RG-based calibrated model.

By calibrating the model with CML data and by using the same as input, it is possible to improve the model performance, which becomes comparable with the case of RG calibration and RG input. Even a slightly better performance can be gathered with a CML+RG-based calibration and CML+RG data as input.

Despite the lack of sensitivity of the CMLs that we relied on, this analysis proves that rainfall estimates based on CMLs could be exploited in hydrology, with a certain confidence, for river discharge simulations. These results show that the use of opportunistic sensors could support hydrological modelling, especially in areas lacking traditional monitoring systems. Furthermore, in the regions already equipped with traditional rainfall sensors, the integration of existing instrumentation with CMLs could also provide advantages for hydrological applications, as this increases the number of reliable rainfall measurements.