The CML dataset was provided by Ericsson and consists of 2777 CMLs spread across Norway. Each CML records the transmitted and received signal strength every minute for data from 2 months: December 2021 and June 2022. The CML signal attenuation, often called total loss (TL), was computed by subtracting the received signal strength from the transmitted signal strength. In our dataset, there were some outliers where the transmitted signal strength was less than -50 dBm. These signals produced negative TL values, likely due to recording errors. We opted to completely remove CMLs with transmitted signal strength less than -50 dBm such that the remaining CMLs did not have any negative TL values. We also removed CMLs with more than 15 % missing values. This resulted in 2179 CMLs for the summer dataset and 2345 CMLs for the winter dataset. Next, as suggested by , we removed erratic CMLs where the 5 h moving window standard deviation exceeded the threshold of 2 dBm more than 10 % of the month and noisy CMLs where the 1 h moving window standard deviation exceeded the threshold of 0.8 dBm more than 33 % of the month. Then CML-derived rain rates were estimated using the pycomlink software and a similar workflow as described in , , and . For the classification of rainy periods, we used the convolutional neural network (CNN) developed by , as this model was trained on hourly data, and this study also evaluates estimates at an hourly resolution. The baseline was estimated by using the average signal attenuation 5 min before a rainy period. Water droplets forming on the antenna cover cause additional attenuation, which we accounted for by using the semi-empirical wet-antenna attenuation model proposed by , with the refined parameters suggested by . Finally, the rainfall rate was computed using the k–R relation, with parameters defined by .

Weather radar data for Norway were downloaded from , a data-hosting platform for gridded meteorological data run by the Norwegian Meteorological Institute. The radar product is developed from 12 weather radars in Norway. These radars are combined using a Constant Altitude Plan Position Indicator (CAPPI). The final result is a grid with a spatial resolution of 1 km × 1 km and a temporal resolution of 5 min. Sea clutter and other large peaks in the data are removed, and ground clutter is identified and corrected using surrounding data. The radar reflectivity (Z [dBz]) is converted to precipitation rates (R [mm h⁻¹]) using the Marshall–Palmer relation . Radar precipitation rates were estimated along all CMLs using the weighted grid approach provided by pycomlink. Then, in line with , time steps with weather radar rainfall rates above 0.1 mm h⁻¹ were considered rainy.

As ground truth for the precipitation type, we used disdrometer data from the Norwegian road authorities. They use two types of disdrometers, namely the OTT Parsivel and OTT Parsivel². The disdrometer data were downloaded from , a data-hosting platform for meteorological observations run by the Norwegian Meteorological Institute. This dataset also contains precipitation type observations from other sensor types, such as the Vaisala PWD12/31 and DRD11A. Using a registry provided by the road authorities, we selected time series that were generated using the OTT Parsivel and OTT Parsivel². This was done to ensure a more controlled comparison between sensors. The disdrometers are placed at least 4 m above the road at automated meteorological stations located along the roads in Norway and provide an estimate of the precipitation type every 10 min. The instruments classify precipitation as light rain, rain, snow, and hail. No precipitation or dry weather is denoted dry in the following. We simplified the classification by merging the classes light rain and rain since they should appear similar in the CML and radar. Additionally, since hail events were rare in the dataset (less than 0.01 %) and were not of interest to our study, we set time steps where the disdrometer recorded hail to dry. This adjustment resulted in negligible error while simplifying the methodology. Thus from the simplifications, the disdrometers only report three classes: dry, rain, and snow. Pairs of CMLs and disdrometers within 8 km of each other were identified using methods from and CMLs longer than 8 km were removed. The threshold of 8 km was a trade-off between getting a large number of CML–disdrometer pairs, while still maintaining a good correlation between the pairs. This resulted in 376 CMLs and 83 colocated disdrometers for December 2021, and 304 CMLs and 60 colocated disdrometers for June 2020. We refer to these as the winter and summer datasets respectively. The CMLs used in the study had signal quantization equal to 0.3 dBm and lengths ranging from 0.4 to 8 km and operated at frequencies between 10 to 40 GHz, with the majority (90 %) operating above 18 GHz (Fig. ).

The weather radar (5 min resolution), temperature model (60 min resolution), CML (1 min resolution), and disdrometer (10 min resolution) provide estimates at different locations and with varying time resolutions. This lack of synchronization could potentially lead to erroneous comparisons. To address this issue, we aggregated the precipitation type estimates to hourly intervals to help smooth out these differences.

The “CML–radar” (CR) method uses CML wet periods, as predicted by the wet–dry estimation method, to classify precipitation as rain. Next, since the CMLs are not noticeably attenuated by dry snow, radar precipitation without corresponding CML precipitation is classified as snow. To aggregate the CR estimates to hourly resolution, we classified hours as rainy if the CML rainfall classification algorithm recorded any rainfall, snowy if the radar estimated any precipitation but the CML did not estimate rainfall, and dry otherwise. The “radar–temperature” (RT) method uses surface temperature and weather radar to determine precipitation occurrence and precipitation type. As recommended by , humidity is accounted for by using the dew point temperature. The RT method then works by estimating the average precipitation along the CML and classifying precipitation above a dew point temperature threshold as rain and below the threshold as snow. The dew point temperature was evaluated at the pixel closest to the center of the CML and was, in line with , set to 0 °C. Combining humidity-corrected temperature models with weather radar is a common method and is often used as a reference method . To aggregate the RT estimates to hourly resolution we classified hours as dry if the radar observed no precipitation. If the radar observed precipitation, we classified the hours as rainy or snowy, respectively, based on whether the dew point temperature was above or below 0 °C. For the disdrometers, we classified hours as rainy if the disdrometer recorded any rain during that hour, snowy if the disdrometer recorded snow but no rain, and dry otherwise.

The drawback of the aggregation method is that it overestimates the number of rainfall events, introducing more uncertainties in the results. However, we consider this an acceptable trade-off, as it allows for a more consistent analysis. The effects of the aggregation method are evaluated further in the discussion.

In this study, we consider both binary classification (for instance, rain and not rain) and multiclass classification (rain, snow, and dry). A common tool for visualizing the performance of a classification algorithm is the confusion matrix. It compares the ground truth labels with the predicted labels, allowing us to understand the types of errors made by the classifier. In this study, the classifier is either the CR or RT method, and the ground truth is provided by the disdrometers. In the binary case, the labels are categorized as either negative or positive (Table ).

Using this confusion matrix, several metrics can be defined. We will first consider the accuracy score, which relates the proportion of true results to the total number of cases examined such that 2accuracy=TN+TPTN+TP+FP+FN. Because of its simplicity, accuracy is a widely used metric, but it may not always be the best indicator of a classifier's performance, especially in cases of imbalanced datasets. To better understand the performance of the classifiers, it is therefore common to consider other metrics as well. The precision score focuses on the classifiers' positive predictions and provides the ratio between the false and true positive predictions, such that 3precision=TPTP+FP. It is also common to consider the recall score, which gives the proportion of reference positive cases predicted by the classifier, 4recall=TPTP+FN. Since any classifier typically must strike a balance between false positives and false negatives, improving the precision comes at the expense of the recall. To consider both recall and precision, the F1 score estimates the harmonic mean of the precision and recall, combining these two metrics such that 5F1=2×precision×recallprecision+recall=2TP2TP+FN+FP. We also use the Matthews correlation coefficient (MCC) to quantify the performance of the classification methods. The MCC is a metric that has been shown to outperform the accuracy and F1 score on imbalanced datasets, by indicating a good correlation only when the classifier performs well on both positive and negative cases . The MCC is given by 6MCC=TP⋅TN-FP⋅FN(TP+FP)⋅(TP+FN)⋅(TN+FP)⋅(TN+FN). The accuracy, precision, recall, and F1 score reach their best value at 1 and worst score at 0. The MCC score of 1 indicates a perfect prediction, 0 indicates a random guess, and -1 is a perfect inverse prediction.

In the multiclass case, the hourly predicted estimates compared to the hourly ground truth can be summarized in a multiclass confusion matrix (see Table ).

The accuracy score can be extended to the multiclass case as follows: 7accuracy=true dry+true rain+true snowtotal number of instances. The precision, recall, and F1 scores are slightly more complicated to generalize, as they involve selecting specific parts of the binary confusion matrix. In this work, we generalized the precision, recall, and F1 scores using macro averaging, which works by evaluating each class (dry, rain, and snow) individually and then averaging them into a single number.

Following , the MCC metric can be generalized to n classes, providing a balanced metric that uses the full confusion matrix . The MCC between the reference x and the predictions y for the multiclass case is given by 8MCC=cov(X,Y)cov(X,X)⋅cov(Y,Y), where 9cov(X,Y)=1N∑k=1Ncov(Xk,Yk). Here, N is the number of classes, and cov(Xk,Yk) is the covariance between the reference Xk and the predictions Yk for class k. All metrics were computed using scikit-learn .

To illustrate the RT and CR methods, we first focus on a case study performed over a large area in mid-Norway, covering 36 CML–disdrometer pairs over 2 d from 18 to 20 December 2021 (Fig. ). The area spans the Trondheim fjord and Norwegian coast in the north and west to the Dovre mountain in the south. For each CML, we counted the number of snowy and rainy hours estimated by the RT method (a, d), the CR method (b, e), and the nearby disdrometer (c, f). The total snowy and rainy hours were then interpolated using inverse distance weighting, with the midpoint of the CML indicating its position. We observe that, at the location of CML1 and CML2 (mountainous areas), the RT and CR methods estimate more snow and less rain compared to the disdrometers. At the location of CML3, the RT method estimates more snow and less rain compared to the CR method and disdrometers.

Examining the time series for CML1 and CML2 (Figs.  and ), we observe that before 18:00 UTC (for all times throughout the text) on 18 December, the dew point temperature (b) is mostly above 0 °C, and the CML signal level fluctuates markedly (c), especially during periods when the weather radar estimates rainfall. After 18:00, as the temperature drops well below 0 °C, the CML signal loss shows a different pattern, with much less fluctuation. At the same time, the CR and RT methods estimate snow, while the disdrometer shifts between rain and snow. Before 18:00, the RT method estimates some rainfall, while the CR method estimates snow, possibly because the rainfall event was not strong enough for the CML wet detection algorithm to identify it as rainfall.

The time series for CML3 indicate a different climatological pattern compared to CML1 and CML2, with temperatures above 0 °C before 18:00 on 18 December and hovering around 0 °C afterward (Fig. ). Observing the CML time series, we see that the signal loss fluctuates during all time steps when the radar estimates precipitation. The disdrometer primarily indicates rainfall, except for a period from 00:00 to 09:00 on 19 December, when it shows a mixture of rain and snow. In contrast, the RT method indicates a longer snowy period, lasting from 19:00 on 18 to 14:00 on 19 December. The CR method primarily estimates rainfall but identifies short snowy periods around the disdrometer's snow period, and estimates rainfall when the disdrometer indicates snow.

To get an overview of the full dataset used in the study, we counted the total number of rainy and snowy hours estimated by the disdrometers, RT method, and CR method for dew point temperature intervals of 1 °C between -20 and 20 °C (Fig. ). Our data cover the full temperature range, with most observations concentrated between -10 and 10 °C. The disdrometers record snow mainly below 0 °C (a), with some snow events slightly above 0 °C. Most rainy hours recorded by the disdrometers occur above 0 °C, but there are also a substantial number of rainy hours recorded below 0 °C. The CR method also estimates rainy hours below 0 °C, though less frequently than the disdrometers, and it estimates a significant number of snowy hours above 0 °C (c). The RT method, by definition, predicts rainy hours above 0 °C and snowy hours below 0 °C  (b). Additionally, we observe that the RT method estimates fewer rainy hours than the CR method, even above 0 °C.

The difference between the estimated CML rainfall amounts and the radar rainfall amounts is plotted as a function of dew point temperature (Fig. a). For dew point temperatures below -2 °C, there is a positive bias where the radar generally estimates more precipitation. Between 0 and 2.5 °C, there is a stronger negative bias, where the CML estimates more precipitation. For dew point temperatures above 4 °C, the CML and radar estimates show a similar spread. In panels (b) and (c), the color of each cell indicates the proportion of rainy or snowy hours over total hours for the corresponding cell in panel (a). Generally, there is more rainfall in observations above -2.5 °C and more snow in observations below 2.5 °C. Additionally, for events where the CML estimates more rainfall (i.e., negative bias), more rainy hours are observed by the disdrometer.

The performance of each CML–disdrometer pair for the RT and CR methods is compared on the summer and winter datasets using scatter density plots (Fig. a–e). In the lower row (f–j), the mean dew point temperature of each CML disdrometer pair is shown. Note that some cells consist of several CML–disdrometer pairs and that the indicated temperature then is the average of all pairs in the cell. In terms of accuracy (a, f), both the CR and RT methods perform similarly well, with a few CMLs performing less well using the CR method. For precision (b, g), we observe that, on average, the RT method outperforms the CR method, indicating that the RT method's positive predictions are more trustworthy than those of the CR method. However, the CMLs for which the CR method performs less well tend to have an average temperature above 5 °C, while at colder temperatures, the RT and CR precision scores are more similar. In terms of recall (c, h), the CR method performs slightly better than the RT method, indicating that the CR method is better at correctly identifying the disdrometer precipitation type. Looking at the F1 score (d, i), which combines the precision and recall score, we observe that the CR method performs worse on average when the temperature is above 5 °C, but better when the temperature is below 5 °C. Lastly, looking at the MCC score (e, j), the CR method outperforms the RT method for most CML–disdrometer pairs.

To investigate the effect of temperature on the CR and RT predictions we plotted the multi-label confusion matrix of the two methods for the three temperature intervals -20 to -2 °C (a, d), -2 to 2 °C (b, e), and 2 to 20 °C (c, f) (Fig. ). The corresponding accuracy, precision, recall, F1, and MCC scores for the individual classes (rain and snow), as well as the multiclass score, are shown in Table . We can observe that, compared to the RT method, the CR method generally identifies more correct rainfall events. It also identifies more snowfall events in the temperature interval -2 to 2 °C.

The disdrometer data suggest that rain is more frequent below 0 °C than snow is above 0 °C (Fig. ), which could indicate that the disdrometer overestimates the number of rainy hours. For example, looking at the CML time series (Fig. ), the disdrometer shows a mix of rain and snow, while the CR and RT methods indicate only snow. This discrepancy could be due to the spatial distance between disdrometers and CMLs, with temperature differences at these locations possibly causing rain to be recorded at colder temperatures. However, if this effect were significant, we would also expect to see more snow recorded at temperatures above 0 °C, which we do not observe. Another explanation for these discrepancies could be the aggregation method, where rainy hours are given priority over snowy hours, creating the impression that there are more rainy hours below 0 °C. However, if the disdrometer was correct and 10 min of an hour were indeed rainy, this would still represent a significant amount of rain during that hour. Moreover, comparing the CR rain distribution with the disdrometer rain distribution (Fig. ), we can see that the CR method observes fewer rainy hours below 0 °C, indicating that the disdrometers overestimate the number of rainy hours below 0 °C.

One explanation for this overestimation could be that wet snow makes the disdrometer alternate between snow and rain, creating the impression that there is more rain below 0 °C. Moreover, different precipitation type sensors are also known to disagree during mixed precipitation events , indicating that these events are hard to classify. However, while wet snow could explain some of the rainfall events below 0 °C, the large proportion of rainy hours below -10 °C remains puzzling, as wet snow is not expected at such low temperatures. Another explanation could be misclassification by the disdrometer due to factors such as strong winds and particles falling through the edges of the sampling area and splashing. Although correction algorithms exist , they typically require the full velocity-drop size distribution matrix, which our disdrometers do not provide. This limitation may lead to less accurate classifications. Additionally, cars spraying water from salted roads could contribute to the high number of rainfall events recorded below 0 °C. Consequently, while the disdrometers provide valuable estimates, they do not perfectly represent the ground truth, especially during mixed precipitation events.

The case study indicated that the CR and RT methods estimated a similar number of snow events in the mountains, while along the coast (for instance, at CML3), the CR estimates were more in line with the disdrometer estimates, suggesting an advantage of using the CR method in certain climatic zones. This could be due to the warmer conditions along the coast, which keep the temperature around 0 °C, a range where the RT method has more uncertainties. However, looking at the time series of CML3 (Fig. ), we see that the CR method estimates rainfall during the true snow event, lasting from 00:00 to 10:00 on 19 December. It also wrongly estimates snowfall before and after the true snowfall event. Thus, while the case study map suggests a better agreement between the CR and disdrometer estimates (Fig. ), there is still a significant discrepancy between the CR and disdrometer estimates in the hourly time series (Fig. ). This discrepancy could be due to the spatial difference between the CML and disdrometer, or disdrometer misclassification, as discussed above. Another explanation could be that the disdrometers classify mixed precipitation, such as wet snow, as snow, while the CMLs classify wet snow as rainfall, leading to a misclassification by the CMLs. This phenomenon is clearly observable during the true snowfall event lasting from 00:00 to 10:00 on 19 December (Fig. ), where the CML estimates a long rainy period and the disdrometer estimates a mixture of rainfall and snow.

For snowfall classification at temperatures between -2 and 2 °C, the CR method holds a slight advantage over the RT method, as reflected in a slightly higher MCC (0.3 vs. 0.27) and recall score (0.63 vs. 0.61) (Table ). This indicates that the CR method is slightly better at identifying true snow events (higher recall) while maintaining reliable estimates (equal precision of 0.67). Looking at the confusion matrix for the same temperature interval, we observe that, compared to the RT method, the CR method correctly identified 2986 true snowy hours, an increase of 453 h, while wrongly classifying 3731 h as snow, an increase of 434 h (Fig. ). In other words, the CR method identifies more true snowfall events, while also wrongly classifying rainy and dry events as snow. The large number of false snow events estimated by the CR method, also observable above 2 °C (Fig. ), might be due to several factors. Low-intensity rainfall events could fail in triggering the CML rainfall detection algorithm, for instance, due to the quantization of the CML signal. Further, due to the spatial difference between the radar beam and the CMLs, the precipitation might hit the radar, but miss the CML, triggering the CR method to estimate snow. Finally, hardware issues with the CML, or database errors, could result in a flat signal level, causing the CR method to misinterpret conditions and estimate snow. Better quality control of the CMLs, for instance, by checking their correlation against the weather radar during rainfall events, could improve the CR estimates. Next, at temperatures below -2 °C (Fig. ), both the CR and RT methods snow classification produced recall scores of 0.65, indicating that the weather radar misses many of the snowfall events recorded by the disdrometers. This could be due to the spatial difference between the CML and disdrometer or disdrometer misclassification, as discussed above. Another explanation could be that blowing winds or road traffic transport snow horizontally, causing the disdrometers to detect snow that does not originate from the sky.

In terms of rainfall classification, the CR method performs as well as, or outperforms, the RT method for all temperatures above -2 °C (Table ). For instance, for temperatures above 2 °C, the binary accuracy score for rainfall increases from 0.85 with the RT method to 0.88 with the CR method, and the binary MCC for rainfall increases from 0.34 to 0.52. However, both the RT and CR methods still miss many of the rainfall events observed by the disdrometer, which is evident in their recall scores of 0.66 and 0.77, respectively. As discussed above, this could be due to the spatial difference between the CML and disdrometer, or, for instance, splashing from the roads, leading the disdrometers to estimate rainfall that is not detected by the CML or weather radar. The increased performance of the CR method, compared to the RT method, could be due to radar overshooting or the radar beam being blocked by mountains.

For classifying snowfall and rainfall, both methods have their own strengths and weaknesses. The CR method shows a better ability to classify precipitation in the interval -2 to 2 °C (MCC = 0.39) but falsely estimates a large number of snowfall events above 2 °C. The RT method, on the other hand, provides reliable precipitation classification below -2 °C (MCC = 0.30) and above 2 °C (MCC = 0.34), while its performance is not as good within the interval -2 to 2 °C (MCC = 0.28). Consequently, combining the RT and CR methods would be optimal. This could, for instance, be done by using the CR method in the interval -2 to 2 °C and the RT method below -2 °C. Above 2 °C, precipitation could be classified as rainfall if either the RT or CR method detects rainfall.

The impact of mixed precipitation, such as wet snow, on the observation methods (disdrometers, CR method, and RT method) remains a significant source of uncertainty in this study. This uncertainty arises from the fact that none of the observation methods can reliably classify mixed precipitation. Additionally, accurately classifying hours that may contain both snow and rain when aggregating the data to hourly intervals poses a challenge. One solution is to introduce a mixed class, classifying hours with both snow and rain as mixed precipitation. However, it remains unclear whether true mixed precipitation, like wet snow, would consistently cause the disdrometer, CR, and RT methods to alternate between detecting rain and snow, which could make the mixed class less physically meaningful and lead to inconsistent representations across different estimation methods. While other studies, such as , aggregated multiple precipitation type data from different sensors to longer periods using a Boolean algorithm, we found that the sensors used in our study differed too much for a similar approach. For instance, the RT method uses temperature data with hourly resolution, which complicates accurately capturing hours with both wet and solid precipitation types. While some studies introduce mixed precipitation estimates by classifying precipitation within a fixed temperature interval as mixed , the true precipitation type within this interval could still be purely rain or purely snow, leading to inaccurate classifications. Furthermore, since the radar might estimate precipitation slightly before the CML, the CR method is prone to estimate snow before rainfall events, leading to an overestimation of mixed precipitation. This could be addressed by aggregating the CML wet period, so that the radar precipitation estimates fall within the wet period, but this would require further tuning to avoid estimating too many rainfall events at the expense of fewer true mixed events. This work uses a simplified aggregation method in order to avoid introducing too many parameters. We found that, while this approach produces a higher rain-to-snow ratio for negative temperatures, the assumptions are stated more explicitly, and the final results and conclusion remain similar to what we got using other aggregation methods.

Around 0 °C, the CMLs estimate larger rainfall amounts compared to the weather radar (Fig. ). The same temperature interval is also characterized by the disdrometers observing both rainfall and snow. This suggests that significant discrepancies between the CML and radar estimates around 0 °C may be attributed to wet snow. This effect has been observed before in previous studies, such as and , where a marked positive CML bias during the winter months was observed. Further, Fig.  reveals that the CML bias as a function of temperature, follows a smooth transition. This indicates that wet snow, as observed by the CML, does not belong to a homogeneous group, but instead follows a gradual transition from snow to rainfall while melting.

Another source of uncertainty lies in the temperature data used for the RT method. The temperature data are a downscaled version of ERA5 data that are combined with ground observations. found that the expected RMSE of the temperature data ranged between 1–2 °C in observation dense areas and 2–2.5 °C in observation sparse regions. The RT method performance could thus be worse in areas with complex terrain and sparse ground observations.

While studies such as , , and have evaluated the performance of temperature-based precipitation-phase classification methods, these studies typically vary in methodology, terrain complexity, radar technology, and the instruments used to estimate the ground truth. This variability introduces challenges when comparing results across different studies. Although the disdrometers used in this study provide a large dataset, they have some limitations; in particular, the large number of rainy events recorded below 0 °C and the lack of mixed class classification introduce uncertainties specific to this study. Further, any type of wet precipitation can cause the CML signal level to drop, potentially leading to precipitation being falsely classified as rainfall. Another source of uncertainty is the spatial distance between the disdrometer and the CML, where, for instance, temperature variations due to elevation and spatial differences can affect precipitation classification. Moreover, the temperature model used is based on model data and could be improved by using ground-based sensors. Combined, these factors introduce large uncertainties in this study and further make it challenging to directly compare the CR and RT estimates in this study to those from similar studies.

Nevertheless, our study demonstrates that CMLs can be used to enhance the classification of snow and rainfall around 0 °C, which are useful for hydrological applications such as in predicting hydropower production, flooding, avalanches, and slush avalanches.