# Real-Time Rain Rate Evaluation via Satellite Downlink Signal Attenuation Measurement
## 1 Introduction
### Ground-Based Instruments  
Several ground-based instruments exist [3] which take advantage of different rainfall characteristics and various physical principles of measurements. There are some systems that directly measure the amount of rainfall by observing the increase in the volume and the weight of the water in a collection container, using mechanisms based on float (float gauges), springs or system balance (weigh gauges) or mechanical parts driven by a known amount of water (tipping bucket gauges). Other types of systems are the disdometers that measure the drop size distribution and, in some cases, also the terminal velocity of falling hydrometeors, and can help to distinguish different types of precipitation as rain, graupel, hail or snow. Various types of technologies are employed for implementing disdometers systems [4]. The kinetic energy of falling drops can be measured by means of acoustic or displacement methods. Optical disdometers employ imaging (2-3D video disdometers) or laser technologies to measure raindrop microstructure by means of non-catching methods, reducing the effects of splashing and drops break up during the measurement process. Finally, the use of active microwave sensors pointing in the vertical direction constitutes an additional type of disdrometer that exploits Doppler power spectra of power received from falling drops. Regarding the types of error sources, the main problem for point measurements is the difficulty of extrapolating the representativeness to an area, due to the high spatial variability of rainfall. During the measurement process, both systematic and random errors can occur. Errors due to the effect of wind, the evapotranspiration losses, the site-dependent instrument exposure, and the incorrect calibration fall within the first type. Malfunctioning problems, instrumental errors and observational effects can vary depending on the specific case, and therefore produce random effects. Some solutions exist for reducing the errors of the measuring instrument and the correction accuracy can be dependent on the observed phenomena [3]. Tipping bucket rain gauges (TBRs) are widely used, due to their simplicity and reliability, which reduces installation and maintenance costs. Several networks have been deployed around the globe for monitoring rainfall for a series of applications spanning from hydrogeological vigilance to agronomic management practices and to provide ground validation products for radar and satellites rainfall estimation systems. An in-depth literature review of the issues and problems pertaining to the use of TBRs, featuring laboratory testing and field evaluation, is reported in [5]. Tipping-bucket data are rather inaccurate and their readings require thus some adjustment [6] or cumbersome correction procedures [7]. The accuracy of some types of TBRs is experimentally evaluated in [8] and [9]. The major problems of the TBRs are that they cannot measure instantaneous rainfall, but provide, at discrete-time instants, measurements of the water quantity relative to a time interval. For this reason, the information about rainfall spikes and peaks, essential in hydrological applications to solve water balance, is not given in the raw measurements. This is particularly critical, especially in very small catchment areas, such as urban ones, which are vulnerable from the hydrological point of view, as the hydrological processes develop very fast. In order to have continuous-time rain-rate estimates, algorithms must be applied to the measured data for the reconstruction of an instantaneous rain rate from the tipping bucket measurements. The simplest way is a linear interpolation based on the ratio between the bucket size and the time intervals between two tips. Unfortunately, this method only provides an averaged value and cannot reconstruct the instants of zero rain. In [10], a cubic spline, constructed of third-order polynomials, is used to interpolate discrete TBR tip records into one-minute rain rates during a rain event.