1616 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 4, APRIL 2009 Rain Rate Estimation Using Measurements From Commercial Telecommunications Links Oren Goldshtein, Hagit Messer, Fellow, IEEE, and Artem Zinevich Abstract—In this paper, we propose a novel method for esti- mating the rain rate at any given point within a two-dimensional plain using measurements of the received signal level extracted from power control records of an existing deployed fixed wireless communication network. The path-average rainfall intensity along each microwave radio link is estimated from the rainfall-in- duced attenuation using an empirical relationship. The proposed algorithm consists of appropriate preprocessing of the links data, followed by a modified weighted least squares algorithm to infer on the rain level at any given point in space. The algorithm can be used to interpolate measurements onto a regular grid to construct a two-dimensional rainfall intensity field. The novelty of the pro- posed estimation method comes from its ability to be applied on an arbitrary geometry network comprising different microwave links lengths and frequencies and allowing easy integration of rain gauge observations into the model to improve estimation accuracy. The technique has been applied to an existing fixed wireless communication network comprising 22 microwave links covering an area of about 15 15 km and operating at carrier frequencies of about 20 GHz. The resulting rainfall field estimates have been compared to rain gauge stations in the vicinity and to weather radar data, showing good agreement. Index Terms—Environmental monitoring, rain rate estimation, received signal level (RSL) measurements, wireless microwave radio networks. I. INTRODUCTION T HE problem of accurate measurements of rainfall amounts has been intensively investigated worldwide and has important implications in meteorology, hydrology, agriculture, environmental policies, and weather forecasting. Several techniques have been developed for monitoring rainfall; the prevailing methods use a network of rain gauge stations or weather radar. Rain gauge stations are considered to be accurate ground point measurements (though they are prone to errors due to wind, calibration error, etc.), but they do not provide high spatial resolution data. It is generally not practical to install and maintain a large number of closely spaced rain gauge stations to monitor highly variable distribution of rainfall. Weather radar, on the other hand, estimates rainfall field over a large contiguous areas and provides high temporal data resolution Manuscript received November 20, 2007; accepted October 20, 2008. First published January 13, 2009; current version published March 11, 2009. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Zhi Tan. The authors are with the Department of Electrical Engineering-Systems, Tel Aviv University, Ramat Aviv 69978, Israel (e-mail: orengoldi@gmail.com; messeryaron@gmail.com; zinevich@gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2009.2012554 but is affected by a high degree of uncertainty and does not provide a good ground-level measurement [1]–[3]. Rapid growth of cellular communications and global spread of fixed microwave radio networks bring about great opportu- nity for their use in environmental studies in general, and pre- cipitation monitoring in particular. In [4] and [5], it has been demonstrated that received signal level (RSL) measurements from fixed terrestrial line-of-sight microwave links, deployed by cellular operators, can be used to estimate space–time rainfall intensities. The microwave signal attenuation caused by scattering and absorption by rain drops has been extensively studied for years and modeled by telecommunications engineers in order to provide reliable microwave communication system design. This is particularly true for electromagnetic signals traveling at frequencies above 10 GHz, where the wavelength inside the raindrops is of the same order of magnitude of the drops size, causing a large variation in the received signal power. This work is based on a well-known power law relation, con- necting rainfall-induced attenuation along a microwave link path with rainfall intensity; see Olsen et al. [6]. The advantage of microwave links for high temporal resolution measurements over conventional rain gauges was demonstrated by Minda and Nakamura [7]. A technique that uses microwave attenuation measurements from several microwave links for estimating rainfall rate over a specific limited local area has been proposed by Giuli [8], [9]. Giuli has suggested a tomographic reconstruction technique to be applied on a hypothetical, specifically designed multiple path attenuation measurement system, composed of fixed microwave point-to-point links. The system geometry, placement, measure- ment paths, frequencies, and other parameters were optimized for the best quality. A nonlinear tomographic technique, partic- ularly applicable for dense urban microwave networks, has been suggested in [10]. The Microwave Attenuation as a New Tool for Improving Storm-water Supervision Administration (MANTISSA) project involving a few European universities has explored the use of designated dual-frequency microwave links to estimate path-in- tegrated rainfall along a link; see [11], for example. It was shown that for certain combinations of frequencies and polarizations, the difference in microwave attenuation between two frequen- cies along a terrestrial link is less sensitive to the drop size dis- tribution (DSD) variations along a link and can give better esti- mate of path-averaged rain rate than can be obtained from single frequency. The use of dual-frequency links for reconstruction of rainfall spatial distribution, in conjunction with rain gauges and radar, was demonstrated in [12]. 1053-587X/$25.00 © 2009 IEEE