An EnKF-based reconstruction of rainfall fields using opportunistic satellite MW link signal attenuation: theoretical basis and application to the July 2021 event in the area of Dortmund (Germany)

A reliable retrieval of the actual rain fallen on a given domain is not an easy task, due to its temporal and spatial variability, but its importance is paramount for meteorology, hydrology and for the effects on human lives and the environment. Nowadays there are different solutions to measure rainfall, directly or indirectly, with respect to the reference raingauge method. At present an additional problem is given by the change of the rainfall regimes, almost at every latitude, often with dramatic effects, and with a complex connection to the climate change, in large part to be still understood. Among the emerging methods for rainfall estimation, a specific interest is in the measurements called ‘opportunistic’, because they provide a chance to augment information without adding new infrastructures, so with clear cost advantages, but generally with larger errors than purposely designed rainfall measuring systems. Therefore some smart efforts in devising proper processing are needed to extract the maximum of the geophysical information they can provide. The use of microwave links is among these methods, since they bring information on rainfall rates along their path, through the signal attenuation caused by raindrops. So, broadcast telecommunication satellite signals can be used at the purpose, although rainfall retrieval poses non trivial problems for instance related to the definition of the intercepted precipitation volumes and inhomogeneity of scatterers along the path. The advantages are related to their worldwide availability and to the easiness of data acquisition, natively centralised when using two ways communication receivers. NEFOCAST, a research project funded by the regional administration of Tuscany (Italy), exploited this feature through two-way (transmit-receive) devices named SmartLNB (Smart Low-Noise Block converter), that provide average measurements along quasi-parallel non-nadir paths pointing to an Eutelsat telecommunication geostationary satellite. In order to retrieve ground precipitation, some ancillary information is needed on the structure of the intercepted rainfall system. An experimental network of SmartLNBs was deployed in Italy (namely in Florence, Pisa and Rome), including co-located raingauges and radar measurements, for cal/val objectives. About the developed rain intensity estimation technique, assuming an ideal homogeneous rain layer, the specific MW signal attenuation (k, expressed in dB/km) is related to the instantaneous rain rate (R, in mm/h), by a power-law in the form k=aR^b, where a and b are coefficients that depend on the carrier frequency, that, for broadcast satellites, is typically in the range 10–40 GHz, and on the polarization. A given telecommunication satellite in geostationary orbit (about 36 000 km over the equator) is connected with a set of ground receiving terminals (GTs) via a slanted path which intercepts the precipitation. Each GT yields estimates of the received signal-to-noise ratio, at one sample per minute (or even at higher rates). The start of a rain event produces a sudden drop of the Signal-to-noise ratio (SNR) value which is detected by the algorithm. Then the rain-induced SNR loss is evaluated by comparing the current "wet" SNR reading with a reference level relevant to "dry" conditions. An innovative (patented) algorithm exploits the link geometry and a novel tropospheric model to derive the specific rain attenuation and, eventually, the associated rain rate. When the observed "wet" SNR reaches the "dry" reference, the end of the precipitation is declared. The high rate of measurements provided by the SmartLNBs suggested to approach the retrieval of bidimensional spatialised rainfall maps from along-path averaged rain rates, similarly to a trajectory assessment in a phase space, using an ensemble Kalman (EnKF) filter methodology. Actually such measurements are processed using a spatio-temporal data assimilation framework based on an EnKF, that integrates such peculiar type of observations with a simple storm advection model driven by Atmospheric Motion Vectors (AMV) from Meteosat Second Generation, while initial and boundary conditions are obtained from the MSG Instantaneous rain rate products. In this work, we present the measurement concept, the signal processing algorithm and the method to retrieve the rainfall fields, applied on some significant synthetic studies and on a real one. The real one consists of measurements from 8 SmartLNBs available in an area of about 1000 km^2 surrounding the city of Dortmund (North Rhine-Westphalia, upper basin of Ermscher river), that were used to obtain gridded rainfall fields at fine temporal (5 minutes) and spatial (1km) resolution for the heavy rain event of July 13 and 14, 2021. Such event has been one of the most relevant in Northern Europe in the last years, causing fatalities and damages. Although the Dortmund area was less severely hit compared to other areas in North Rhine-Westphalia, it was interested by intense rainfall especially on July 14. Only one rain gauge is present in the area, so the availability of measurement from other types of sensors may be very useful to detect spatial patterns and localized phenomena. The resulting maps were compared with those provided by the RADOLAN maps (radar based quantitative precipitation products) by the German Meteorological Service. The comparison shows the potential benefit of using the MW-link measurements to improve measurements on a sparse raingauge network, enabling a more detailed spatio-temporal reconstructions of the rainfall fields. However now we are aware that such a benefit could be dramatically enhanced, with some specific software and hardware upgrading of the measuring system. This is the focus of INSIDERAIN, an ongoing project following NEFOCAST, that aims at targeting some main upgrades, overcoming the main limitations intrinsic to the system architecture, emerged during the first experimentations. First of all, measurements of SNR, namely Es/N0, can be collected only when the satellite terminal transmits them to the satellite hub. This means that for satellite terminals used in a non-continuous way (i.e. not communicating over satellite with continuity) these measurements can be missing for long time periods. Another reason for unavailability of measurement data is intrinsic to heavy rain, which causes service outage. Satellite terminals in fact are not able to transmit when they are not able to demodulate the signal received from the satellite network. This means that no Es/N0 measurement will be available in the satellite hub when the link is more perturbed (which is the condition we would like to identify). In order to overcome this remarkable limitation, a store & forward approach for data collection has been implemented. This means that, when the link between the satellite terminal and the hub is not available, signal measurements are collected by the satellite terminal and stored in a local cache, to be transmitted to the hub when the link gets available again. This new feature allows to extend quite much the range of measurable rain rate, without any other change in the overall network architecture. But the most ground-breaking objective of INSIDERAIN is in the design and prototyping of a brand new receiver, capable of measuring rain attenuation affecting several satellite signals, that are simultaneously received from multiple geostationary platforms, seen from different directions. This receiver makes use of standard broadcasting satellite transmissions as signal source, so there is no need for the implementation of a dedicated satellite service. Data are returned to the service centre using any available return link (e.g. LAN, Wi-Fi, 3G/4G/5G, etc.). The receiver performs sequential measurements of the signal transmitted by broadcasting satellites operating in Ku band. The use of a toroidal dual reflector antenna, capable of hosting up to 16 different Low Noise Block (LNB) converters, with a total angular separation of up to 40 degrees, makes this new receiver acting as a multi-directional rain-rate probe. In order to receive from multiple satellites, the system makes use of an electronic switch to select each LNB, then the received signal is measured and delivered to the service centre, which estimates the attenuation and then the rain rate. The new measuring system is capable to detect precipitation simultaneously from many different directions, thus increasing the measuring reliability and enabling the identification and correction of transient satellite-specific effects. In addition it enables the rain-rate measurement up to a threshold 4 times higher than the previous NEFOCAST device. The same EnKF algorithm is applied to generate rainfall maps from all these different sensors and including also raingauge measurements eventually deployed in the target domain. It is also capable to account for the information contained on the link outage and the available tests show very promising performances for the overall measuring system, also in the capability to address different spatial scales, depending on sensor distribution and density.