Abstract. Rainfall is one of the most important environmental variables. However, it is a challenge to measure it accurately over space and time. During the last decade, commercial microwave links (CMLs), operated by mobile network providers, have proven to be an additional source of rainfall information to complement traditional rainfall measurements. In this study, we present the processing and evaluation of a German-wide data set of CMLs. This data set was acquired from around 4000 CMLs distributed across Germany with a temporal resolution of 1 min. The analysis period of 1 year spans from September 2017 to August 2018. We compare and adjust existing processing schemes on this large CML data set. For the crucial step of detecting rain events in the raw attenuation time series, we are able to reduce the amount of misclassification. This was achieved by using a new approach to determine the threshold, which separates a rolling window standard deviation of the CMLs' signal into wet and dry periods. For the compensation for wet antenna attenuation, we compare a time-dependent model with a rain-rate-dependent model and show that the rain-rate-dependent model performs better for our data set. We use RADOLAN-RW, a gridded gauge-adjusted hourly radar product from the German Meteorological Service (DWD) as a precipitation reference, from which we derive the path-averaged rain rates along each CML path. Our data processing is able to handle CML data across different landscapes and seasons very well. For hourly, monthly, and seasonal rainfall sums, we found good agreement between CML-derived rainfall and the reference, except for the winter season due to non-liquid precipitation. We discuss performance measures for different subset criteria, and we show that CML-derived rainfall maps are comparable to the reference. This analysis shows that opportunistic sensing with CMLs yields rainfall information with good agreement with gauge-adjusted radar data during periods without non-liquid precipitation.

Abstract. Quantitative precipitation estimation with commercial microwave links (CMLs) is a technique developed to supplement weather radar and rain gauge observations. It is exploiting the relation between the attenuation of CML signal levels and the integrated rain rate along a CML path. The opportunistic nature of this method requires a sophisticated data processing using robust methods. In this study we focus on the processing step of rain event detection in the signal level time series of the CMLs, which we treat as a binary classification problem. This processing step is particularly challenging, because even when there is no rain, the signal level can show large fluctuations similar to that during rainy periods. False classifications can have a high impact on falsely estimated rainfall amounts. We analyze the performance of a convolutional neural network (CNN), which is trained to detect rainfall-specific attenuation patterns in CML signal levels, using data from 3904 CMLs in Germany. The CNN consists of a feature extraction and a classification part with, in total, 20 layers of neurons and 1.4×105 trainable parameters. With a structure inspired by the visual cortex of mammals, CNNs use local connections of neurons to recognize patterns independent of their location in the time series. We test the CNN's ability to recognize attenuation patterns from CMLs and time periods outside the training data. Our CNN is trained on 4 months of data from 800 randomly selected CMLs and validated on 2 different months of data, once for all CMLs and once for the 3104 CMLs not included in the training. No CMLs are excluded from the analysis. As a reference data set, we use the gauge-adjusted radar product RADOLAN-RW provided by the German meteorological service (DWD). The model predictions and the reference data are compared on an hourly basis. Model performance is compared to a state-of-the-art reference method, which uses the rolling standard deviation of the CML signal level time series as a detection criteria. Our results show that within the analyzed period of April to September 2018, the CNN generalizes well to the validation CMLs and time periods. A receiver operating characteristic (ROC) analysis shows that the CNN is outperforming the reference method, detecting on average 76 % of all rainy and 97 % of all nonrainy periods. From all periods with a reference rain rate larger than 0.6 mm h−1, more than 90 % was detected. We also show that the improved event detection leads to a significant reduction of falsely estimated rainfall by up to 51 %. At the same time, the quality of the correctly estimated rainfall is kept at the same level in regards to the Pearson correlation with the radar rainfall. In conclusion, we find that CNNs are a robust and promising tool to detect rainfall-induced attenuation patterns in CML signal levels from a large CML data set covering all of Germany.

Abstract. Quantitative precipitation estimation with commercial microwave links (CMLs) is a technique developed to supplement weather radar and rain gauge observations. It is exploiting the relation between the attenuation of CML signal levels and the integrated rain rate along a CML path. The opportunistic nature of this method requires a sophisticated data processing using robust methods. In this study we focus on the processing step of rain event detection in the signal level time series of the CMLs, which we treat as a binary classification problem. We analyze the performance of a convolutional neural network (CNN), which is trained to detect rainfall specific attenuation patterns in CML signal levels, using data from 3904 CMLs in Germany. The CNN consists of a feature extraction and a classification part with, in total, 20 layers of neurons and 1.4 x 105 trainable parameters. With a structure, inspired by the visual cortex of mammals, CNNs use local connections of neurons to recognize patterns independent of their location in the time-series. We test the CNNs ability to generalize to CMLs and time periods outside the training data. Our CNN is trained on four months of data from 400 randomly selected CMLs and validated on two different months of data, once for all CMLs and once for the 3504 CMLs not included in the training. No CMLs are excluded from the analysis. As a reference data set we use the gauge adjusted radar product RADOLAN-RW provided by the German meteorological service (DWD). The model predictions and the reference data are compared on an hourly basis. Model performance is compared to a reference method, which uses the rolling standard deviation of the CML signal level time series as a detection criteria. Our results show that within the analyzed period of April to September 2018, the CNN generalizes well to the validation CMLs and time periods. A receiver operating characteristic (ROC) analysis shows that the CNN is outperforming the reference method, detecting on average 87 % of all rainy and 91 % of all non-rainy periods. In conclusion, we find that CNNs are a robust and promising tool to detect rainfall induced attenuation patterns in CML signal levels from a large CML data set covering entire Germany.

Abstract. Rainfall is one of the most important environmental variables. However, it is a challenge to measure it accurately over space and time. During the last decade commercial microwave links (CMLs) operated by mobile network providers have proven to be an additional source of rainfall information to complement traditional rainfall measurements. In this study we present the processing and evaluation of a German-wide data set of CMLs. This data set was acquired from around 4000 CMLs distributed across Germany with a temporal resolution of one minute. The analyzed period of one year spans from September 2017 to August 2018. We compare and adjust existing processing schemes on this large CML data set. For the crucial step of detecting rain events in the raw attenuation time series, we are able to reduce the amount of miss-classification. This was achieved by a new approach to determine the threshold which separates a rolling window standard deviation of the CMLs signal into wet and dry periods. For the compensation of wet antenna attenuation, we compare a time-dependent model with a rain-rate-dependent model and show that the rain-rate-dependent method performs better for our data. As precipitation reference, we use RADOLAN-RW, a gridded gauge-adjusted hourly radar product of the German Meteorological Service (DWD), from which we derive the path-averaged rain rates along each CML path. Our data processing is able to handle CML data across different landscapes and seasons very well. For hourly, monthly and seasonal rainfall sums we found high agreement between CML-derived rainfall and the reference, except for the cold season with non-liquid precipitation. This analysis shows that opportunistic sensing with CMLs yields rainfall information with a quality similar to gauge-adjusted radar data during periods without non-liquid precipitation.

Microwave radiation is attenuated by hydrometeors through scattering and absorption processes. For raindrops an advantageous relationship between specific attenuation k in dB km −1 and rainfall rate R in mm hr −1 exists. This power law known as the k-R relation is close to linear at frequencies between 20 and 35 GHz (Chwala & Kunstmann, 2019). Commercial microwave links (CMLs) use frequencies from 7 to 80 GHz and thus can be used to derive path averaged rainfall intensities by comparing transmitted and received signal levels (TSL and RSL) (Uijlenhoet et al., 2018). In theory, the k-R relation is valid for arbitrary rainfall intensities occurring in the underlying drop size distribution simulations. In practice, the measurement of high attenuation values at a given transmitted signal level has an upper bound when the signal cannot be distinguished from the receiver's background noise. CML rainfall estimates were derived for many countries around the globe, for example,