*2.2. Calculation of AV*

The calculation of AV is crucial for classification of hydrometeor species (Hclass, Section 2.3) because the classification is mainly based on their terminal velocity (TV). The cloud radar measures composed velocity (DV) of TV and air velocity (AV), such as DV = TV + AV. When calculating AV, the AV is oriented towards the radar (downward) in accordance with basic processing of measured data by the IDL software used by the radar manufacturer. At the end of our calculation of AV, however, the AV orientation is reversed and we present all outputs of AV with upward orientation.

AV calculation is based on very small particles in Doppler spectra that are assumed to be so light that their TV is very close to zero, i.e., they are carried solely by air, and thus their velocity defines the AV. This is a common approach that was detailed by Kollias et al. [29], Gossard [30] and Shupe et al. [31], and conducted by, e.g., Zheng et al. [32] or Sokol et al. [33]. In this study, we innovated the algorithm used by Sokol et al. [33] to derive AV from variances caused by turbulence, wind shear, particle size distribution, and finite radar beam width.

We found that the original algorithm used for AV calculation, which performs de-aliasing of the Doppler spectra, can lead in some cases to significant and unrealistic temporal changes of AV, which then result in erroneous hydrometeor classification. That is why our new de-aliasing algorithm uses three methods of AV calculation, compares the result of each of them (AV1, AV2 and AV3) with the result of the two others and also compares the three calculated AV with the AV calculated for the previous cloud radar recording, i.e., 2 s back in time, approximately (AVL).

Any Doppler spectrum is stored for each gate in intervals beginning with a component ia and ending with a component ib, where ia corresponds to lower speed and ib to higher speed. The intervals, which are identified by the algorithm of the manufacturer of the cloud radar, represent continuous parts of a Doppler spectrum which are ordered from the lowest speeds. Note that for a gate, we can obtain multiple intervals. Components, which are not part of any determined interval, are considered to have zero amplitude. In this study, we consider not only the interval with the lowest magnitude of velocity corresponding to ia in the first interval (Sokol, Z. et al. [33]), but also the ia from the second interval.

We assume that measured values might be aliased. Therefore, in addition to recorded values Vori, we also consider Vori ± Vd values, where Vd = VNyquist + VNyquist (for VNyquist value see Table 1). We use parameters qtol = 3 and qmax1 = 5 in the following calculations of AV. The calculations of AV consist of steps provided below, which are performed for individual gates (ig) from the bottom (ig = 4) to the top (ig = 512) because AV is not affected by aliasing in the lowest gates as updrafts cannot be that strong (>VNyquist) near the ground. We calculate AV1, AV2, AV3 and AVL and assign the resulting AV to the value (i.e., among AV1, AV2, AV3 and AVL) that best corresponds to conditions described in the next paragraph. In the de-aliasing algorithm, we also use a reference value Vref, which is define in steps 7, 8 and 9 in the procedure described below.

The procedure of AV calculation consists of following steps:

1. For an ig (ig = 4 at first), we define de-aliasing function (DAL) calculating velocity Vcor using original and reference velocities Vori and Vref, respectively:

$$\text{V}\_{\text{cor}} = \text{DAL}(\text{V}\_{\text{ori}}, \text{V}\_{\text{ref}})\_{\prime} \tag{1}$$

where Vcor corresponds to one of the values (Vori, Vori + Vd or Vori − Vd) that is closest to the value Vref.


AV2cor(ig) = DAL(AV2(ig), AV(ig − 1))

AV3cor(ig) = DAL(AV3(ig), AV(ig − 1))

If |AV2cor(ig) − AV(ig − 1)| < qtol, then AV(ig) = AV2cor(ig), stop

If |AV1cor(ig) − AV(ig − 1)|, then AV(ig) = AV1cor(ig), stop

$$\text{If } |\text{AV3}\_{\text{cor}}(\text{ig}) - \text{AV(ig} - 1)| \text{, then } \text{AV(ig)} = \text{AV3}\_{\text{cor}}(\text{ig}) \text{, stop}$$


It should be noted that the applied procedure determining AV based on very small particles (tracers) is limited by how well very small particles are identified in the Doppler spectra. It may happen, especially in the case of heavy rain, that smallest particles with negligible terminal velocity are not detected anymore due to extinction or that in the radar volume of some gates, there are only larger droplets likely due to size sorting. This is related to spots in thunderclouds with high LWC, which make the larger droplets arrive earlier to lower gates. However, our experience suggests that these are very rare cases and their effect is marginal.

Calculation of AV precedes the classification of hydrometeor species (Hclass) because AV cannot be neglected in summer thunderstorms that are under investigation in this paper. Thunderstorms are a convective phenomenon for which (strong) updrafts and downdrafts are typical.
