Prediction of rainfall intensity measurement errors using commercial microwave communication links
TL;DR: In this paper, the root mean squared error (RMSE) expression for path-averaged and point rainfall estimation was derived for microwave radio links forming cellular communication networks, and the dependence of the optimal coefficients of a conventional wet antenna attenuation model on spatial rainfall variability and link length has been shown.
Abstract: . Commercial microwave radio links forming cellular communication networks are known to be a valuable instrument for measuring near-surface rainfall. However, operational communication links are more uncertain relatively to the dedicated installations since their geometry and frequencies are optimized for high communication performance rather than observing rainfall. Quantification of the uncertainties for measurements that are non-optimal in the first place is essential to assure usability of the data. In this work we address modeling of instrumental impairments, i.e. signal variability due to antenna wetting, baseline attenuation uncertainty and digital quantization, as well as environmental ones, i.e. variability of drop size distribution along a link affecting accuracy of path-averaged rainfall measurement and spatial variability of rainfall in the link's neighborhood affecting the accuracy of rainfall estimation out of the link path. Expressions for root mean squared error (RMSE) for estimates of path-averaged and point rainfall have been derived. To verify the RMSE expressions quantitatively, path-averaged measurements from 21 operational communication links in 12 different locations have been compared to records of five nearby rain gauges over three rainstorm events. The experiments show that the prediction accuracy is above 90% for temporal accumulation less than 30 min and lowers for longer accumulation intervals. Spatial variability in the vicinity of the link, baseline attenuation uncertainty and, possibly, suboptimality of wet antenna attenuation model are the major sources of link-gauge discrepancies. In addition, the dependence of the optimal coefficients of a conventional wet antenna attenuation model on spatial rainfall variability and, accordingly, link length has been shown. The expressions for RMSE of the path-averaged rainfall estimates can be useful for integration of measurements from multiple heterogeneous links into data assimilation algorithms.
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TL;DR: In this paper, the authors used a 17-day data set of 57 single-frequency links from 2009 to estimate rainfall in the Rotterdam region, a densely populated delta city in Netherlands (≈1250 km2, > 1 million inhabitants).
Abstract: [1] The estimation of rainfall using commercial microwave links is a new and promising measurement technique. Commercial link networks cover large parts of the land surface of the earth and have a high density, particularly in urban areas. Rainfall attenuates the electromagnetic signals transmitted between antennas within this network. This attenuation can be calculated from the difference between the received powers with and without rain and is a measure of the path-averaged rainfall intensity. This study uses a 17-day data set of, on average, 57 single-frequency links from 2009 to estimate rainfall in the Rotterdam region, a densely populated delta city in Netherlands (≈1250 km2, >1 million inhabitants). A methodology is proposed where nearby links are used to remove signal fluctuations that are not related to rainfall in order to be able to reliably identify wet and dry weather spells. Subsequently, received signal powers are converted to path-averaged rainfall intensities, taking into account the temporal sampling protocol and attenuation due to wet antennas. Link-based rainfall depths are compared with those based on gauge-adjusted radar data. In addition, the rainfall retrieval algorithm is applied to an independent data set of 21 rainy days in 2010 with on average 16 single-frequency links in the same region. Rainfall retrievals are compared against gauge-adjusted radar rainfall estimates over the link path. Moreover, the retrieval algorithm is also tested using high-resolution research link data to investigate the algorithm's sensitivity to temporal rainfall variations. All presented comparisons confirm the quality of commercial microwave link data for quantitative precipitation estimation over urban areas.
130 citations
TL;DR: In this article, a commercial terrestrial microwave link is tested for the first time in Burkina Faso, in Sahelian West Africa, in which the attenuation on a 29'km long microwave link operating at 7'GHz was monitored at 1's time rate for the monsoon season 2012.
Abstract: Rainfall monitoring based on commercial terrestrial microwave links is tested for the first time in Burkina Faso, in Sahelian West Africa. In collaboration with one national cellular phone operator, Telecel Faso, the attenuation on a 29 km long microwave link operating at 7 GHz was monitored at 1 s time rate for the monsoon season 2012. The time series of attenuation is transformed into rain rates and compared with rain gauge data. The method is successful in quantifying rainfall: 95% of the rainy days are detected. The correlation with the daily rain gauge series is 0.8, and the season bias is 6%. The correlation at the 5 min time step within each event is also high. These results demonstrate the potential interest of exploiting national and regional wireless telecommunication networks for monitoring rainfall in Africa, where operational rain gauge networks are degrading and the hydrometeorological risk increasing.
93 citations
TL;DR: In this paper, a spectral time series analysis method was proposed to detect wet and dry periods using spectral signal level (RSL) data from commercial microwave links in the alpine region of Southern Germany.
Abstract: Measuring rain rates over complex terrain is afflicted with large uncertainties, because rain gauges are influenced by orography and weather radars are mostly not able to look into mountain valleys. We apply a new method to estimate near surface rain rates exploiting attenuation data from commercial microwave links in the alpine region of Southern Germany. Received signal level (RSL) data are recorded minutely with small data loggers at the towers and then sent to a database server via GSM (Global System for Mobile Communications). Due to the large RSL fluctuations in periods without rain, the determination of attenuation caused by precipitation is not straightforward. To be able to continuously process the RSL data from July 2010 to October 2010, we introduce a new method to detect wet and dry periods using spectral time series analysis. Its performance and limitations are presented, showing that the mean detection error rates of wet and dry periods can be reduced to 10% for all five links. After, the wet/dry classification rain rates are derived from the RSL and compared to rain gauge and weather radar measurements. The resulting correlations differ for different links and reach values of R 2 = 0.81 for the link-gauge comparison and R 2 = 0.85 for the link-radar comparison.
86 citations
TL;DR: In this article, the authors used the countrywide commercial microwave link (CML) networks for rainfall estimation by exploiting the measurements of rain-induced attenuation along these CMLs.
Abstract: Funding information German Research Foundation Accurate observation of the high spatio-temporal variability of rainfall is crucial for hydrometeorological applications. However, the existing observations from rain gauges and weather radars have individual shortcomings that can introduce considerable errors and uncertainties. A fairly new technique to get additional rainfall information is the usage of the country-wide commercial microwave link (CML) networks for rainfall estimation by exploiting the measurements of rain-induced attenuation along these CMLs. This technique has seen an increasing number of applications during the last years. Different methods have been developed to process the noisy raw data and to derive rainfall fields. It has been shown that CMLs can provide important line-integrated rainfall information that complements pointwise rain gauge and spatial radar observations. There exist several limitations, though. Robustly dealing with the erratic fluctuations of the CML raw data is a challenge, in particular with the growing number of CMLs. How to correctly compensate for the biases from the effect of wet antenna attenuation for different CMLs also remains a crucial research question. Progress is additionally hampered by the lack of method intercomparisons, which in turn is hampered by restricted data sharing. Hence, collaboration is key for further advancements, also with regard to extended interaction with the CML network operators, which is a prerequisite to achieve increased data availability. In regions where rain gauges and weather radars are available, CMLs are a welcome complement. But in developing countries, which are characterized by weak technical infrastructure and which often suffer from water stress, additional rainfall information is a necessity. CMLs could play a crucial role in this respect.
79 citations
TL;DR: The goal of this article is to present a critical survey of the existing papers and works relating to precipitation monitoring to multidimensional signal processing, and emphasize the works relating this topic to multi-dimensional signal processing.
Abstract: Accurate measurements of precipitation are essential for many applications, ranging from flash-flood warnings to water resource management. However, the accuracy of the existing tools is limited by various technical and practical reasons. Percipitation monitoring has traditionally been known to rely on gauges, weather radars, and satellites. Recently, a new approach has begun to be examined, the usage of commercial wireless communication networks (CWCNs), which enjoys the lack of any need for deployment procedures or costs, and which is already widely spread across countries.
58 citations
Cites background from "Prediction of rainfall intensity me..."
...[30] showed that the most dominant source of error (assuming an effect called the wet-antenna effect, which we discuss in the following paragraph, is corrected for) is the spatial nature of the rain, surpassing the errors that are caused by quantization, zero-level uncertainty, DSD variability along the link, and others....
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References
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TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
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12,407 citations
11,285 citations
"Prediction of rainfall intensity me..." refers background in this paper
...(26) and the rest of non-linear minimization problems in this study are solved using simplex optimization (Press et al., 1992); preliminary coarse grid search has been done to find optimal initial values, likely leading to a global minimum....
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27 Jan 2017
TL;DR: In this article, the effects of correlation on statistical inference have been investigated in the context of spatial analysis. But the authors focus on the use of non-Euclidean distances in Geostatistics.
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1,022 citations
"Prediction of rainfall intensity me..." refers methods or result in this paper
...This assumption is similar to the one of ordinary kriging (Schabenberger and Gotway, 2005); in the climatological scale, the expected rainfall intensity in an area depends on the location (constant per link-gauge pair and over the studied area) and the area size (determined by the link length and…...
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...This assumption is similar to the one of ordinary kriging (Schabenberger and Gotway, 2005); in the climatological scale, the expected rainfall intensity in an area depends on the location (constant per link-gauge pair and over the studied area) and the area size (determined by the link length and the linkgauge distance, constant per link-gauge pair as well)....
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...To compare path-averaged rainfall with the point scale rain gauges, one can address modeling of rainfall spatial variability through the use of geostatistics methods (Schabenberger and Gotway, 2005) to obtain an MSE expression for rainfall estimation at an arbitrary point in space....
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TL;DR: In this article, a compromise between maximum path-averaged rainfall rate sensitivity and minimum sensing errors may be achieved by the use of one-way methods between the transmitter and the receiver, with a wavelength of 1.5 to 2.0 cm.
Abstract: At a wavelength of about 0.9 cm, microwave attenuation is demonstrated to be linearly related to rainfall rate and independent of drop size distribution and temperature. In addition, practical methods for measuring path- and area-averaged rainfall rate are reviewed. A compromise between maximum path-averaged rainfall rate sensitivity and minimum sensing errors may be achieved by the use of one-way methods between the transmitter and the receiver, with a wavelength of 1.5 to 2.0 cm. Corrections for nonspherical drops and for multiple scattering are also discussed.
510 citations