Automated precipitation monitoring with the Thies disdrometer: Biases and ways for improvement

The intensity and phase of precipitation at the ground surface can have important implications for meteorological and hydrological situations, but also in terms of hazards and risks. In the field, Thies disdrometers are sometimes used to monitor the quantity and nature of precipitation with high temporal resolution and very low maintenance and thus provide valuable information for the management of meteorological and hydrological risks. Here, we evaluate the Thies disdrometer with respect to precipitation detection as well as the estimation of precipitation intensity and phase at a pre-alpine site in Switzerland 5 (1060 m a.s.l.), using a weighing precipitation gauge (OTT pluviometer) as well as a two-dimensional video disdrometer (2DVD) as a reference. We show that the Thies disdrometer is well suited to detect even light precipitation, reaching a hit rate of around 95%. However, the instrument tends to systematically underestimate rainfall intensities by 16.5%, which can be related to a systematic underestimation of the number of raindrops with diameters between 0.5 and 3.5 mm. During snowfall episodes, a similar underestimation is observed in the particle size distribution (PSD), which is, however, not reflected in 10 intensity estimates, probably due to a compensation by snow density assumptions. To improve intensity estimates, we test PSD adjustments (to the 2DVD) as well as direct adjustments of the resulting intensity estimates (to the OTT pluviometer), the latter of which being able to successfully reduce the systematic deviations during rainfall in the validation period. For snowfall, the combination of the 2DVD and the OTT pluviometer seems promising as it allows improvement of snow density estimates, which poses a challenge to all optical precipitation measurements. Finally, we show that the Thies disdrometer and 15 the 2DVD agree well insofar as the distinction between rain and snowfall is concerned, such that an important prerequisite for the proposed correction methods is fulfilled. Uncertainties mainly persist during mixed phased precipitation or low precipitation intensities, where the assignment of precipitation phase is technically challenging, but less relevant for practical applications. We conclude that the Thies disdrometer is not only suitable to estimate precipitation intensity, but also to distinguish between rain and snowfall. The Thies disdrometer therefore seems promising for the improvement of precipitation monitoring and the 20 nowcasting of discharge in pre-alpine areas, where considerable uncertainties with respect to these quantities are still posing a challenge to decision making.


Introduction
The intensity and type of precipitation falling on the ground surface (e.g. rain, snow, drizzle, or hail) often determines the absence or occurrence of subsequent processes. A detailed knowledge on the nature and intensity of precipitation is therefore decisive in terms of hazards and ensuing risks. For example, for the management of traffic roads, it is important to know 5 whether falling snow or mist will likely hamper road conditions or visibility (Toivonen and Kantonen, 2001). For example, Juga et al. (2012) show that very poor visibility due to intense snowfall combined with reduced road surface friction caused a severe flow of accidents in Helsinki on 17 March 2005. Likewise, the occurrence of freezing rain at the ground surface can lead to the collapse of trees and power supply lines with potentially catastrophic cascading effects, as was experienced during a recent case in Slovenia (Kämäräinen et al., 2017;Schauwecker et al., 2019). Last not least, both precipitation intensity and 10 its phase (i.e. rain or snowfall) are decisive for runoff formation and the occurrence of flash floods in (pre-)alpine catchments (e.g., Fehlmann et al., 2018;Tobin et al., 2012).
To support decision making and intervention in such situations, the Thies Clima laser precipitation monitor (in the following referred to as Thies disdrometer) offers the possibility to measure precipitation intensity and type with a high temporal resolution; the monitor can therefore replace present weather observations from manned stations to a certain degree (Merenti-velocity of falling hydrometeors and has already been used previously as a reference to correct particle size and velocity (Parsivel) distributions of laser disdrometers during either rainfall (Leinonen et al., 2012;Raupach and Berne, 2015) or snowfall (Battaglia et al., 2010), even if the 2DVD seems to underestimate droplets in the lower range of diameters, i.e. below 0.5 mm (Raupach et al., 2019;Thurai et al., 2017;Thurai and Bringi, 2018). In this study, we include both solid and liquid precipitation events and point to differences in resulting correction methods. Furthermore, we develop a hydrometeor classification algo-5 rithm for the 2DVD measurements as a basis for the evaluation of precipitation phase estimates. Whereas other studies have developed such algorithms using bulk variables for the classification (e.g., Grazioli et al., 2014), we have implemented here a particle-by-particle classification method allowing to explore resulting mixing ratios in the case of mixed-phased precipitation.
The paper is organized as follows: In section 2, the measurement devices are presented in more detail and the processing of the raw data is described. In section 3, biases and proposed corrections of the Thies disdrometer are presented with respect 10 to precipitation detection as well as the monitoring of precipitation intensity and phase. In section 4, results are discussed and conclusions are drawn with respect to the operational monitoring of precipitation with the Thies disdrometer as well as potential applications in a hydrological context.

Measurement devices 15
The Thies disdrometer is evaluated in this study by using a weighing precipitation gauge (OTT pluviometer) and a 2DVD as a reference. Measurements have been taken over a duration of two years (2017-07-01-2019-06-30). These instruments have been set up at Innereriz, Switzerland (1060 m a.s.l., Fig. 1) and are described in more detail in the following.
The Thies disdrometer is designed to estimate precipitation intensity as well as different types of precipitation (e.g. drizzle, rain, hail, snow or mixed precipitation). Precipitation type and intensity are estimated on the basis of an optical principle, filters are applied to remove spurious measurements due to splashing or margin faller effects (e.g., Chen et al., 2016;Friedrich et al., 2013;Raupach and Berne, 2015;von Lerber et al., 2017). Usually, such filters are based on a validity check of the combined diameter and fall velocity information, e.g. excluding data that are more than 60% above or below the fall velocitydiameter relationship for rain (Jaffrain and Berne, 2011). However, as investigated in detail by Friedrich et al. (2013) for Parsivel disdrometers, such spurious measurements mostly occur at wind speeds exceeding 20 m/s. As our study is extremely 5 wind sheltered, we thus did not see the need of applying such a filter in this study. This is further supported by an exploratory analysis of applying the filter proposed by Chen et al. (2016) to the Thies disdrometer measurements over the full time period, which revealed that the volume contribution of the filtered particles is only very small (in the order of 2-3%) in our case.
The 2DVD, developed by Joanneum research, is able to derive more direct and more detailed information about individual hydrometeors than the Thies disdrometer. Maintenance requirements for the instrument are not negligible and it is mainly 10 used in the research context and in combination with radar observations (e.g., Bringi et al., 2015;Gorgucci and Baldini, 2015;Huang et al., 2010Huang et al., , 2015Thurai et al., 2012). Furthermore, the 2DVD has been used for the correction of laser disdrometers (Raupach and Berne, 2015). As shown in Fig. 2 (right), falling hydrometeors are detected by two optical cameras from two perspectives, which allows to derive more detailed information about the shape and volume of individual particles as well as about their velocity. Information about these quantities is reported for each individual particle, including the exact time of the 15 observation (in ms). Precipitation type is not (yet) reported by the instrument, but can be estimated on the basis of the raw particle data. To validate precipitation type estimates by the Thies disdrometer, a classification algorithm was developed in this study, allowing an estimation of the type of each individual hydrometeor (section 2.2).
The OTT pluviometer is designed to automatically determine precipitation intensities and amounts. Unlike tipping bucket rain gauges, this instrument is based on the weighing of the precipitation amount in a high-precision load cell. Advantages 20 compared to a tipping bucket rain gauge are particularly related to the measurement of solid precipitation amounts, resulting in fewer losses due to the evaporation as well as the avoidance of a temporal lag effect in the measurement (Savina et al., 2012). The instrument is thus able to measure precipitation amounts with high accuracy and is therefore used as a reference for precipitation amounts at the ground surface in various applications, including the validation of disdrometers (e.g., Raupach and Berne, 2015). According to the operating instructions of the OTT pluviometer, the instrument provides the raw precipitation 25 values every 6 seconds using a resolution of 0.001 mm. After the application of special filter algorithms (e.g. a correction for wind effects), non-real time 1-min outputs are available at a resolution of 0.01 mm. Of course, it can be questioned whether very weak precipitation can actually be measured so accurately. For example, Tiira et al. (2016) found in their mass retrieval (performed approximately every 5 minutes) that the output seems to fluctuate and used a threshold 0.2 mm/h for their analysis. Furthermore, a well-known problem when using precipitation gauges mounted above ground is the undercatch due to the 30 influence of wind, which has been extensively studied for rainfall (e.g., Pollock et al., 2018) and in particular for snowfall (e.g., Fassnacht, 2004;Kochendorfer et al., 2017;Yang, 2014;Wolff et al., 2015). The undercatch is thereby found to be larger for snowfall than for rainfall and to increase with increasing wind-speed. In this study, however, we do not explicitly correct for wind effects as wind speeds at the study site are generally very low (on average 0.46 m/s during the investigated time period).
The maintenance requirements of the instrument are relatively low -only the container, which holds 750 mm for the model used, must be emptied regularly. Precipitation intensity and amount are reported every minute.
Finally, temperature and wind measurements of a LUFFT weather sensor are used in this study. This sensor was located at the same measuring station (Fig. 1, left) and provided corresponding measurements every minute. Temperature is measured by way of a highly accurate NTC-resistor in a ventilated housing with radiation protection in order to keep the effects of external 5 influences (e.g. solar radiation) as low as possible. The wind meter uses 4 ultrasonic sensors which take cyclical measurements in all directions. The resulting wind speed and direction are calculated from the measured run-time sound differential.

2DVD classification algorithm
As precipitation type is not reported by the 2DVD by default, a classification algorithm was developed in this study, to assign one of the following precipitation types to each observed hydrometeor: hail, rain, melting snow, graupel or snow. Unlike other 10 algorithms (e.g., Grazioli et al., 2014), the algorithm used here is based on a particle-by-particle classification rather than on bulk information, which even allows for the explicit quantification of hydrometeor mixtures during a given time period. For the validation of the Thies disdrometer, the dominant precipitation type during 1-min observations was then estimated on the basis of these mixing ratios.
Similar to the Thies disdrometer, the classification algorithm is based on the empirical relationship between particle diameter 15 D and fall velocity V, which varies among different types of precipitation. The equations used (equations 1-5) are based on literature (Gunn and Kinzer, 1949;Locatelli and Hobbs, 1974;Mitchell, 1996) as well as measurements and analyses conducted by Joanneum Research.
A particle is considered for classification only if its diameter D and velocity V lie within a valid range (0.6 mm < D < 9 mm, V < 17 m/s) and if no major differences exist in particle size between the two cameras (0. and H B denote the particle height in camera A and B, respectively). For each valid particle, theoretical fall speeds for different precipitation types are calculated according to its diameter and equations 1-5. The estimated values are then compared to measured velocity, whereas precipitation type is determined according to the closest match between these values. In addition, snow or melting snow above 10°C is reclassified as rain -a plausibility check which is also applied by Thies Clima for the processing of Thies disdrometer data. An example of the resulting particle-by-particle classification is given in Fig. 3 for a 30 transition from rain to snowfall during 6 h.
After the inspection of 1-min mixing ratios of different precipitation types obtained by this classification algorithm (not shown here), we determined the dominant precipitation phase during 1 min as follows (Table 1): Rain is considered dominant if more than 70% of the particles are classified as rain, whereas snow and/or graupel are considered dominant if more than 80% of the particles are classified as snow, melting snow or graupel. Furthermore, hail is already assigned for mixing ratios greater than 1% as the chance of (larger) hailstones being captured by the relatively small measuring area is quite small. In the 5 remaining cases, mixed-phased precipitation is assigned.
To investigate the effect of applying different classification methodologies on obtained results, the classification algorithm described above was also applied to Thies data. Given the binned data, the mean velocity and diameter of each V-D class were used for the classification rather than information about individual particles.

Comparison of measurements and performance measures 10
The Thies disdrometer is evaluated by using the OTT pluviometer as a reference for precipitation detection and intensities and the 2DVD as a reference for PSD and precipitation type. The following comparisons refer to a time period of two years  When comparing the Thies disdrometer with the OTT pluviometer, corresponding 1-min observations are merged. Although both instruments are measuring with a resolution of 1 min, they have not been set up to measure synchronously. To avoid mismatches due to temporal shifts between observations, the minimum integration time considered for the evaluation of precipitation detection and precipitation intensities was set to 5 min. As the effect of increasing integration time on the reliability of measurements can be of interest for operational applications, we also report results for integration times up to 4 h (i.e. 5, 10, 20 20, 30, 60, 90, 120 and 240 min). Intensities for different integration times are calculated based on the cumulative precipitation sum, which is given by both instruments. For all correction methods applied, the variable of interest is first integrated over the considered integration time before any correction is applied.
When comparing the Thies disdrometer (or the OTT pluviometer) with the 2DVD, 1-min observations can be used and the 2DVD data is aggregated accordingly. When comparing the PSD between the two disdrometers, the number of particles is 25 normalised by the so-called effective measuring area. This area slightly deviates from the actual measuring area (being 45.32 cm 2 for the Thies disdrometer and 109.39 cm 2 for the 2DVD) as a function of particle diameter. Essentially, the effective measuring area decreases for larger particles due to the increasing non-recognition of partially observed particles at the border of the measuring area. Whereas the effective measuring area is reported by the 2DVD for each observed particle, it is calcu- separately calculated for rain and snowfall. For the consistent comparison of precipitation phase between the two disdrometers, certain precipitation types were aggregated according to Table 1. Furthermore, we only consider pairwise complete (1 min) observations of both instruments with either rain, snow or mixed precipitation, resulting in a time series of 2,533 h of precipitation.
For the evaluation of categorical variables, i.e. precipitation detection (yes/ no) and precipitation phase (rain/ mixed/ snow), 5 hit and false alarm rates with respect to the reference instrument are calculated according to Jolliffe and Stephenson (2012). In the case of precipitation detection (yes/ no), we further investigate the effect of minimum precipitation thresholds applied to measurements of the Thies disdrometer on hit and false alarm rates by investigating the so-called Receiver Operating Characteristic (ROC) curves (e.g., Jolliffe and Stephenson, 2012). A ROC curve thereby depicts the variation of hit and false alarm rates with the variation of such a threshold. For example, using a threshold of 0 mm/h for precipitation detection (i.e. always

Precipitation detection
The capability of the Thies disdrometer to detect precipitation is assessed using the OTT pluviometer as a reference. After exploring the full time series, data from the first year of measurements was used to optimize precipitation detection by establishing minimum precipitation thresholds. The application of these thresholds was then evaluated during the second year of 25 independent measurements.
The capability of the Thies disdrometer to distinguish precipitation from no precipitation is described in terms of its hit and false alarm rate when using the OTT pluviometer as a reference. In a first step, hit and false alarm rates are calculated over the whole time series and are indicated with circles in Fig. 4 (left) for different integration times. Thereby, hit rates are stable and reach values between 95.2 and 95.9%. False alarm rates are low for short integration times (e.g. 5.1% for periods of 5 min) but 30 tend to increase with increasing integration time (e.g. 14.1% for periods of 4 h).
In a second step, we tested the application of minimum precipitation thresholds to the Thies disdrometer observations in order to reduce false alarm rates for longer integration times. The ROC curves shown in Fig. 4 (left) thereby depict all possible combinations of hit and false alarm rates that can be achieved by the introduction of such a threshold. The application of a minimum threshold will generally reduce both false alarm as well as hit rates. Therefore, an optimal threshold was defined for each integration time by minimising the Euclidean distance to the upper left corner in the ROC diagram (i.e. to the theoretical 5 optimum with a hit rate equal to 1 and a false alarm rate equal to 0), resulting in a balanced solution between the two measures.
This optimization was applied to the first year of measurements and the resulting thresholds are listed in Table 2 for each integration time. Noteworthy, these thresholds (expressed in mm/h) are quite stable for different integration times with a mean of 0.04 mm/h.
The effect of applying the proposed thresholds on hit and false alarm rates during the second year of measurements is de-10 picted in Fig. 4 (right) and Table 2. The application of such thresholds is particularly beneficial for integration times exceeding 20 min, as they allow to effectively reduce false alarm rates by up to 8.9 % (for periods of 4 h). For integration times shorter than 20 min, the application of a minimum precipitation threshold only has a negligible effect. Furthermore, by applying the proposed thresholds, a balanced solution with respect to hit rates and false alarm rates can be found for all the integration times considered, resulting in a relatively similar distance to the theoretical optimum in the ROC diagram.

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Finally, by applying the proposed minimum precipitation thresholds in Table 2, we analyze missed events as well as false alarms produced by the Thies disdrometer in the validation period in more detail, i.e. with respect to precipitation intensity and phase. Whereas precipitation intensities measured by the OTT pluviometer were of interest during missed events, precipitation While precipitation intensities during missed events are very similar above and below the temperature threshold of 1.2°C, the relative frequency of missed events seems to be slightly higher below this temperature threshold. Precipitation intensities 25 indicated by the Thies disdrometer during false alarms are very low, ranging from 0.12 mm/h for 5-min periods to 0.02 mm/h for 4-h periods, with no remarkable differences above and below the temperature threshold of 1.2°C.

Precipitation intensities
The capability of the Thies disdrometer to measure precipitation intensities is assessed with the OTT pluviometer as a reference for precipitation intensities as well as with the 2DVD as a reference for the PSD. After exploring error patterns in the entire 30 time series, the first year of measurements was used to establish corresponding correction methods. The application of the established correction methods was then evaluated with independent data from the second year of measurements. Figure 6 depicts the cumulative precipitation sums of the Thies disdrometer over the full investigation period as compared to the OTT pluviometer. Precipitation sums for both instruments are separated into rain and snow according to 1-min precipitation type estimates of the Thies disdrometer. As rain and snowfall events represent 89.5% of the total precipitation sum, we restrict analysis to these two precipitation types in the following. Total precipitation after two years of measurements is underestimated by 12.4% by the Thies disdrometer. This systematic underestimation is almost entirely related to rainfall events, during which the total precipitation sum is underestimated by even 16.5%. The underestimation during snowfall events is much smaller (4.0%) and seems to be less systematic, but rather related to individual events during the second year of measurements.

5
As a first approach to improve precipitation intensity estimates by the Thies disdrometer, we tested a direct adjustment to the measurements of the OTT pluviometer. A comparison of precipitation intensities between these instruments during the full investigation period is shown in Fig. 7 for an integration time of 30 min; it confirms the error pattern described above: whereas a systematic underestimation of rainfall intensities is visible, almost no systematic error can be seen with respect to snowfall intensities. Furthermore, the systematic underestimation of precipitation intensities seems to be well captured by a constant 10 factor (i.e. independent of integration time or precipitation intensity). We thus propose to use the ratio of the OTT pluviometer to the Thies disdrometer precipitation sum as a correction factor and to distinguish between rain and snowfall. Using the first year of measurements, the resulting correction factors for rain and snowfall intensities are 1.20 and 0.96, respectively.
As a second approach to improve precipitation intensity estimates by the Thies disdrometer, we tested an adjustment of the PSD to the measurements of the 2DVD. A comparison of the summed PSD between these two instruments is shown in Fig.   15 8 for all rain and snowfall events during the whole time series (two years). The separation into rain and snowfall events is based on the recorded dominant precipitation type by the Thies disdrometer (1 min). Although the overall shape of the PSD is similar for both instruments, systematic deviations seem to exist during both rain and snowfall events. During rainfall events, the number of particles with diameters between 0.5 and 3.5 mm (classes no. 4-12) is systematically underestimated, whereas the number of smaller and larger particles is overestimated by the Thies disdrometer as compared to the 2DVD. When looking 20 at the monthly variability of the resulting correction factors (Fig. 8, right), the overestimation seems to be less stable than the underestimation. During snowfall, the number of particles with diameters exceeding 0.75 mm is overestimated, whereas the number of smaller particles is underestimated as well. Noteworthy, the underestimation (classes no. 4-12 for rainfall and 5-22 for snowfall) will affect resulting estimates of precipitation intensity in particular. In the case of rainfall and assuming the mean PSD obtained by the Thies disdrometer, particles between 0.5 and 3.5 mm (classes no. 4-12) are contributing to 25 90% of the total rainfall volume. The smallest and largest particles are almost negligible for total volume due to their small volume (smallest particles) and number (largest particles), respectively. Nevertheless, we propose to apply correction factors for the number of particles in each diameter class, and to further distinguish between rainfall and snowfall. Using the first year of measurements, the resulting correction factors for rain and snowfall are listed in Table 3. Given the corrected PSD, rainfall intensity is calculated by assuming a density of 1 g/cm 3 . For snowfall, a relationship between particle diameter and density is 30 established by comparing 1-min accumulated volumes (measured by the 2DVD) to the corresponding mass (measured by the OTT pluviometer) and is shown in Fig. 9.
The effect of both correction methods proposed here was subsequently tested during the second year of measurements. The resulting biases of the Thies disdrometer before and after the correction are given in Table 4 for different integration times.
These biases are thereby calculated for the whole dataset as well as for all rain and snowfall separately. An example for the 35 integration time of 30 min is further given in Fig. 10. As can be seen in Table 4 and Fig. 10, the most robust result is achieved by the adjustment of rainfall intensities to the OTT pluviometer, which successfully reduces the underestimation of liquid precipitation in the validation period. The adjustment of rainfall intensities to the 2DVD, however, results in a positive bias in the validation period. For snowfall, both correction methods have a smaller impact and even result even in slightly higher negative biases than are present without any adjustment.

Precipitation phase
The capability of the Thies disdrometer to detect the predominant precipitation type is assessed using the 2DVD as a reference.
We thereby focus on the precipitation phase, i.e. the distinction of rain and snowfall, which has been shown above to be an important criterion for the proposed correction methods. Table 5 shows the agreement of precipitation phase estimates between the Thies disdrometer and the 2DVD during the full 10 time series, while Fig. 11 depicts the relative frequency of observations as a function of temperature for both instruments, including an indication of the mixing ratios obtained by the 2DVD. Thereby, the Thies disdrometer agrees well with the 2DVD insofar as the classification of rain and snow is concerned. By contrast, larger differences exist with respect to the classification of mixed precipitation. Regarding the detection of rain, the Thies disdrometer reaches an almost perfect hit rate (99.7%).
However, the overall frequency of rain is slightly overestimated by the Thies disdrometer, being reflected by a false alarm rate 15 of 9.9%. Regarding the detection of snow, the overall frequency of detected cases is almost equal for both instruments. The hit and false alarm rate of the Thies disdrometer with respect to the 2DVD is reaching 95.3 and 1.3%, respectively, reflecting a good agreement between the two instruments. Finally, the Thies disdrometer classifies much less cases as mixed precipitation (1%) than the 2DVD (4.3%), resulting in both a low hit and false alarm rate for these cases.
Most misclassifications are related to cases during which the Thies disdrometer indicates rain, whereas the 2DVD indicates 20 mixed precipitation or snow. As can be seen in Fig. 11, such cases occur at both temperatures above and well below 0°C.
Thereby, the Thies disdrometer seems to overestimate cases of rain below 0°C and to underestimate cases of snowfall or mixed precipitation above 0°C as compared to the 2DVD. At least during distinct misclassifications, i.e. in cases where the Thies disdrometer indicated rain while the 2DVD indicating snow, it can be shown that precipitation intensities are very small, i.e. their mean being 0.19 mm/h (while being 0.93 mm/h for all cases).

Discussion and Conclusions
In this study, we have shown that the Thies disdrometer is well suited for precipitation detection, reaching hit rates of around 95% with respect to the OTT pluviometer. The false alarm rate, which indicates the probability of the Thies disdrometer detecting precipitation during a dry period, is increasing with increasing integration time. This can be somewhat expected, as the chance of misinterpreting a signal or disturbance as precipitation is increasing with increasing duration of this period.

30
Furthermore, false alarm rates might be affected by the sensitivity of the reference instrument, but are comparable to findings of Bloemink and Lanzinger (2005) who use human observations as a reference.
We have further demonstrated that the Thies disdrometer systematically underestimated rainfall intensities at the study site by 16.5% during two years of measurements, which we explain to be related to an underestimation of drop concentrations for drop diameters ranging between 0.5 and 3.5 mm. At the same time, larger and smaller drops are overestimated by the instrument; this is, however, less relevant for the resulting estimates of rainfall intensities. Other studies have reported similar patterns in terms of bias in the PSD and while analyzing other disdrometers, such as the Joss-Waldvogel (Leinonen et al., 5 2012) or the OTT Parsivel disdrometers (Raupach and Berne, 2015). However, the deviations in the PSD and implications for rainfall intensity estimates can be different between different types of instruments. For example, the OTT Parsivel 1 disdrometer only underestimates drops with sizes ranging between 0.8 and 1.6 mm and only during periods of higher rainfall intensity.
In addition, the device tends to even overestimate rainfall intensities (Raupach and Berne, 2015). Interestingly, an overestimation of rainfall intensities is also reported for the Thies disdrometer at the intercomparison site Wasserkuppe in Germany 10 (Lanzinger et al., 2006). Supposedly, this contrary result to our study is due to differences in wind exposure. While our study site in Innereriz is extremely wind sheltered (average wind speeds being 0.46 m/s during the investigation period), the site at Wasserkuppe is strongly exposed to wind, average wind speeds being 6.4 m/s from 1999-2018 (data obtained by German weather service DWD). Finally, when compared the OTT Parsivels, Guyot et al. (2019) found that the Thies disdrometer starts to underestimate the number of droplets from 0.75 mm onwards towards larger diameters when compared to Parsivel 1 and 15 also underestimates liquid precipitation compared to both Parsivel 1 and Parsivel 2 . To reduce the underestimation of rainfall intensities by the Thies disdrometer found at our study site, we established an adjustment to 2DVD measurements following the methodology of Raupach and Berne (2015). However, when applying the resulting adjustment in the validation period, we introduce a positive bias, which could indicate a slight overestimation of liquid precipitation by the 2DVD when compared to the OTT pluviometer. A more stable correction is achieved by applying a linear adjustment to the OTT pluviometer. This 20 method is thus proposed as the preferred correction method in this study, especially when the PSD itself is not of interest to the user. It should be noted further that the overestimation of smaller drops by laser disdrometers with respect to the 2DVD is also found in other studies (Krajewski et al., 2006;Raupach and Berne, 2015), but can at least partly be related to unreliable estimates by the 2DVD for small drops (Tokay et al., 2013). As rainfall intensity or radar reflectivity are not strongly affected by the concentrations of small drops, no further adjustment of the PSD is considered in this study. For the reconstruction of 25 the drizzle mode of the PSD, Raupach et al. (2019) present a method being able to correct for this deficiency and to further improve rainfall intensity estimates for light rain.
Regarding the measurement of snow, we show that the number of particles with diameters exceeding 0.75 mm is slightly underestimated by the Thies disdrometer. However, this bias is not reflected in intensity estimates. Although not systematically biased, a more detailed analysis of the correlation coefficient (not shown here) revealed that uncertainty in snowfall intensity 30 estimates is higher than for rainfall. This is most likely related to some of the underlying assumptions (e.g. about particle orientation, shape or density) being less appropriate for solid than for liquid precipitation (Yuter et al., 2006;Battaglia et al., 2010). Regarding snow density, we propose a simple parametrization of particle density as a function of particle diameter, which is similar to other studies (e.g., Fabry and Szyrmer, 1999;Brandes et al., 2007) and found here to substantially improve intensity estimates as compared to a constant density assumption. By applying the proposed adjustment of the PSD and this 35 snow density parametrization to Thies disdrometer measurements, correlation of the resulting snow intensity estimates with respect to the OTT pluviometer can be slightly improved. Given the still high uncertainties in the snow density parameterization (apparent in Fig. 9), we further tested the inclusion of information about particle velocity and temperature but could not thereby improve resulting intensity estimates. The analysis of the correlation coefficient for snowfall intensities further revealed that correlations generally increase with increasing integration time (particularly up to 20 min). This indicates that at least some 5 uncertainties in estimates of snowfall intensities including small time shifts between observations are averaged out over longer integration times.
The distinction between rainfall and snowfall is not only an important prerequisite for the proposed correction methods, but also relevant with respect to hydrological applications in alpine or pre-alpine areas. In this study, we show that the Thies disdrometer is well suited for a distinction of rainfall from snowfall (hit rates reaching 99.7% for rainfall and 95% for snowfall 10 using the 2DVD as a reference). Larger differences between the two disdrometers exist for mixed precipitation and particularly small precipitation intensities. As such, our results are in line with other studies in which precipitation phase estimates from disdrometers (including the Thies disdrometer) have been compared to human observations (Bloemink and Lanzinger, 2005;Merenti-Välimäki et al., 2001). In particular the underestimation of mixed phased precipitation by the Thies disdrometer is consistent with results of Bloemink and Lanzinger (2005). At the same time, a recently reported case study suggests that the 15 instrument is able to accurately signal mixed precipitation during changes between snow and rain (Pickering et al., 2019). In this context, we would like to point out that the agreement of the dominant precipitation type during mixed precipitation with any reference observation will depend on the range of mixing ratios implicitly or explicitly considered as mixed precipitation.
Our analysis indicates that the distinction between liquid and mixed precipitation is particularly sensitive to the choice of such a threshold. Furthermore, the application of the proposed classification algorithm to both disdrometers indicates that a reasonable 20 choice of these thresholds might differ between different instruments. In addition to the validation of dominant precipitation type estimates, the particle-by-particle classification algorithm presented in this study can provide a basis for the validation of explicitly characterized hydrometeor mixtures as for example in polarimetric radar observations (e.g., Besic et al., 2018) or atmospheric models (e.g., Forbes et al., 2014).
The Thies disdrometer has the advantage of low maintenance requirements and allows not only the estimation of precipitation 25 intensity but also precipitation type. The reliable distinction between rainfall and snowfall is considered here as an advantage for hydrological applications in mountainous environments, where local estimates of precipitation phase are still uncertain.
We therefore see a potential in installing disdrometers at sensitive elevations in mountainous catchments complementary to precipitation gauge and weather radar data to improve precipitation monitoring and short-term flood forecasting in these areas.
The 2DVD was particularly useful in this study to further investigate the biases of the Thies disdrometer, to establish a 30 parametrization of snow density and to provide a reference for the estimation of precipitation phase. Future studies may focus on a refinement of the proposed snow density parametrization and hydrometeor classification algorithm by taking other parameters such as particle orientation or shape (e.g. roundness, oblateness) into account.
In this study, we could not clarify how the relevant underestimation for liquid precipitation is depending on wind or other influences. We suggest to investigate this dependence in further studies.
Author contributions. MF designed the framework of the study and evaluation strategy with help from all coauthors. MF processed the data obtained by the measurement devices (i.e. the Thies disdrometer, the two-dimensional video disdrometer, the OTT pluviometer and the LUFFT weather sensor) and implemented the presented evaluation methods. MF, MR, AvL and MS participated in writing and editing the 5 manuscript, as well as investigating and interpreting the results.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. This work has been supported by the European Horizon 2020 research project ANYWHERE (EC-HORIZON2020-PR700099-ANYWHERE). The authors acknowledge the Canton of Bern for the purchasing of measurement devices, the Federal Office for the Environment for financial support and Geopraevent for technical support in the field. Also, we would like to thank Joanneum Research and Thies Clima for providing information about data processing algorithms of their instruments (i.e. the Thies disdrometer and the twodimensional video disdrometer) as well as for the valuable discussion of the obtained results. Thanks also to Alexis Berne, the two anonymous reviewers and to Adrien Guyot for their very constructive feedback during the peer review process of this article.  Thurai, M., Bringi, V. N., Carey, L. D., Gatlin, P., Schultz, E., and Petersen, W. A.: Estimating the accuracy of polarimetric radar-based retrievals of drop-size distribution parameters and rain rate: An application of error variance separation using radar-derived spatial corre-Thurai, M., Gatlin, P., Bringi, V. N., Petersen, W., Kennedy, P., Notaroš, B., and Carey, L.: Toward completing the raindrop size spectrum: Case studies involving 2D-video disdrometer, droplet spectrometer, and polarimetric radar measurements, Journal of Applied Meteorology and Climatology, 56, 877-896, https://doi.org /10.1175/JAMC-D-16-0304.1, 2017. Tiira, J., Moisseev, D. N., von Lerber, A., Ori, D., Tokay, A., Bliven, L. F., and: Ensemble mean density and its connection to other microphysical properties of falling snow as observed in Southern Finland, Atmospheric Measurement Techniques, 9, 4825-4841,  Table 2. Minimum precipitation thresholds established in the calibration period to optimize precipitation detection for different integration times. The thresholds are chosen to minimise the distance to an ideal point in a receiver operating characteristic (ROC) diagram (i.e. a hit rate equal to 1 and a false alarm rate equal to 0, Fig. 4). The corresponding reduction in hit and false alarm rates as well as the resulting distance to this point are given for the independent validation period.   Table 4. Biases in precipitation intensity measurements of the Thies disdrometer during the second year of measurement using the OTT pluviometer as a reference. The absolute bias B (equation 6) of the uncorrected measurements is given for all events as well as for rain and snowfall separately (left value). Furthermore, the effect of the two proposed correction methods is shown, i.e. the adjustment to the OTT pluviometer (middle value) and the two-dimensional video disdrometer (right value). The correction methods are thereby established during the first year of measurements.
∆t (min) All events Rain Snow  . In this study, the Thies disdrometer is evaluated using both the OTT pluviometer as well as a two-dimensional video disdrometer as a reference during two years of measurements.    . Relationship between snow particle density and mean particle diameter based on 1 min observations during the first year of measurements. Snowfall events are identified based on the recorded dominant precipitation type by the Thies disdrometer. Snow particle density is then calculated by comparing the precipitation volume measured by the two-dimensional video disdrometer (2DVD) and precipitation mass measured by the OTT pluviometer, and related to mean particle diameter as measured by the 2DVD. The fitted curve is used to translate Mixing ratios (10 th and 90 th percentile) 2DVD Figure 11. Relative frequency of the observed dominant precipitation phase by the Thies disdrometer (left) and the two-dimensional video disdrometer (2DVD, right) as a function of air temperature during two years of measurements (2,533 h of precipitation). For the 2DVD, the mixing ratio of liquid precipitation obtained at different temperatures is indicated by the 10 th and 90 th percentile of its distribution (dashed lines).