## 2 Materials and Methods
### Metrologies for Measuring Rainfall Rates and Droplet Size Distributions
Because of the low signal-to-noise ratio, the first two diameter classes for the Parsivel\({}^{2}\) (\(D_{i}\) of 0.062 and 0.187 mm) are frequently empty, thus valid data are generally reported for diameter classes with \(D_{i}\) of 0.25 mm and above. Note: The different generations (first and second) of the OTT optical disdrometer are denoted here as Parsivel\({}^{1}\) and Parsivel\({}^{2}\), respectively. Previous research has indicated errors in the OTT Parsivel\({}^{2}\) terminal fall velocities under some atmospheric conditions [106] which may have some implications for the number density estimates reported herein (see Equation (13)). A key aspect of the data analysis framework for optical disdrometer observations pertains to use of screening procedures to exclude droplets reported in the raw measurements as occurring in terminal fall velocities that differ substantially from theoretical estimates of \(v_{t}(D_{i})\). An illustration of this effect is given in Figure 3 for ~14,000 1 min observed hydrometeor counts expressed in diameter and fall velocity classes from measurements with an OTT Parsivel\({}^{2}\) deployed on the campus of Cornell University in upstate New York, US. As shown in Figure 3, while the mean number counts in combined \(D\) and \(v_{t}\) class illustrate the expected monotonic increase of fall velocity with droplet diameter, a non-trivial number of detected hydrometeors exhibit fall velocities below 2 ms\({}^{-1}\) even for \(D>\) 2 mm. These values may reflect the presence of insects and leaves in the instrument field of view, or splintered hydrometeors that strike on the housing of the disdrometer and subsequently enter the field of view. The implication is that it may be appropriate to remove them prior to computing the hydrometeor DSD. For example, in processing of data from optical disformeters operating at US Department of Energy sites, droplets reported in fall velocity classes that differ by >\(\pm\)50% from the terminal velocity for water droplets in stagnant air computed using Gunn and Kinzer [107] are assumed to be in error and are excluded from consideration [101]. This inevitably results in a reduction in \(N(D_{i})\). Currently there is no consensus regarding use of this screening to exclude some count data and/or the specific threshold that should be applied. We recommend best-practice be developed to ensure comparability of observed DSD across different sites and regions. Some droplets pass through the margins of the field of view of the disdrometer. Thus, a further key aspect of the processing of disdrometer data pertains to use of an effective sampling area (\(F_{\mathit{eff}}\)) that scales with the droplet diameter. The following estimate of \(F_{\mathit{eff}}\) has been proposed [108]:  
\[F_{\mathit{eff}}\ =\ L\bigg{(}W_{A}-\frac{D_{i}}{2}\bigg{)} \tag{14}\]  
where \(L\) and \(W_{A}\) are the length (180 mm) and width (30 mm) of the viewing area. Assuming spherical droplets, the precipitation rate (RR in mmhr\({}^{-1}\)) is:  
\[RR\ =\ \frac{\pi}{6}\frac{3.6}{10^{3}}\frac{1}{Ft}\sum n_{i}D_{i}^{3} \tag{15}\]  
The mass-weighted mean diameter (\(D_{m}\) in mm) is computed as the ratio of the 3 rd to the 4 th moment of the measured droplet size distribution as follows [109]:  
\[D_{m}\ =\ \frac{M_{4}}{M_{3}} \tag{16}\]  
where:  
\[M_{n}\ =\ \sum_{i\ =\ 1}^{NB}N(D_{i})D_{i}^{n}\Delta D_{i} \tag{17}\]  
where \(NB\) = number of size bins available from the disdrometer. The Thies Laser Precipitation Monitor (LPM) optical disdrometer [110] works on a similar measurement principle to the OTT Parsivel and also measures hydrometeors as they  
Figure 3: Mean hydrometeor number counts in droplet diameter and fall velocity classes for approximately 14,000 min with RR \(>\) 0 mmhr\({}^{-1}\) from an OTT Parsivel\({}^{2}\) disdrometer deployed at Cornell University (Table 1). Data from a few minutes with WC indicative of snow have been excluded. fall through, and thus break, a series of adjacent horizontal beams.