Advanced method for estimating the number concentration of cloud water and liquid water content observed by cloud particle sensor sondes

A cloud particle sensor (CPS) sonde is an observing system attached with a radiosonde sensor to observe the vertical structure of cloud properties. The signals obtained from CPS sondes are related to the phase, size, and number of cloud particles. The system offers economic advantages including human resource and simple operation costs compared with aircraft measurements and land-/satellite-based remote sensing. However, because CPS systems are limited for data downlink to land stations, the observed information should be appropriately corrected. We launched approximately 40 CPS sondes in 5 the Arctic region between 2018 and 2020 and use these data sets to develop correction methods that exclude unreliable data, estimate the effective cloud water droplet radius, and determine a correction factor for the total cloud particle count. We apply this method to data obtained in October 2019 over the Arctic Ocean and March 2020 at Ny-Ålesund, Svalbard, Norway to compare with a particle counter onboard a tethered balloon and liquid water content retrieved by a microwave radiometer. The estimated total particle count and liquid water content from the CPS sondes generally agree with those data, which exemplifies 10 the promising advantages of this approach to retrieve quantitative and meaningful information on the vertical distribution of cloud microphysics.

dependent (i.e., wind speed) and thus limited to a top height of approximately 1000 m. Unknown particle collection efficiency is also a problem for quantitative understanding. The cost and mobility of observation data are important aspects that should 55 complement existing observation systems, including satellites.
A cloud particle sensor sonde (Meisei Electric, Co., Ltd.; hereafter, CPS sonde) is an observation system used to obtain the vertical profile of cloud information (e.g., total particle count, particle phases, and particle size) (Figs. 1, 2). A CPS connected to a normal radiosonde can obtain cloud parameters and basic meteorological profiles. The observation cost consists of the regular launch of a radiosonde and an additional $ 1200 for the CPS. Although theoretical configurations and laboratory experiments 60 have been intensively reported (Fujiwara et al., 2016), the data require adequate corrections adapted to the individual flight dynamics. The remaining issues are: (1) the relationship between flow speed in the CPS inlet and CPS signal; (2) a theoretical understanding of the time interval of each particle signal; (3) characteristics of the aerodynamic flow pattern around the CPS housing, which determines the sampling volume; and (4) validation of the CPS sonde with other observation systems. In this study, we propose a CPS data correction method using the observation data obtained during three Arctic field campaigns (Fig.

Limitation of data down link
Owing to the downlink capability of the Meisei radiosondes, only 25 byte s −1 can be transferred to the ground-based receiver.
The current CPS provides the following information each second: (i) number of particles (particles s −1 ); (ii) CPS signal voltage for I 55 and I 125p (V) and PSW (ms) for the first six particles entering the instrument each second; and (iii) DC component for the detector no. 1 output. It should therefore be noted that it is impossible to obtain the particle size distribution every second.

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A statistical approach is necessary to estimate the liquid water content (LWC) and liquid water path (LWP).

Detection time for each particle
PSW is considered to be an indicator of particle transit time when I 55 first exceeds 0.3 V and the time when I 55 falls below 0.3 V. According to Fujiwara et al. (2016), a 5 m s −1 flow speed corresponds to a PSW of ∼1 ms for a single particle. They also reported that PWS data can be used to monitor potential particle overlap in dense cloud layers. An excessively long signal 95 width may indicate the overlapping of too many particles in the detection area and thus a substantial loss of particle counts.
In such cases, multiple light scattering can also occur and complicate the particle measurements. As described in section 2.1, however, the detection cross-section is not uniform but rather a parallelogram for each detector with a maximum thickness of 0.5 cm, which allows a wide range of PSWs even under a constant flow speed in the CPS inlet. Fig. 3b reveals the idealized PSW distribution under a flow speed of 5 m s −1 assuming that the shape of the detectable cross-section of detector I 55 is 100 a parallelogram. The PSW value can vary from 0 to 1 ms. Furthermore, if the flow speed slows near the inlet wall owing to frictional forces, the PSW might be large because of the time required to pass the detection area (i.e., slower flow speeds require longer times). under a flow speed (v) of 5 m s −1 . In the case of dense clouds, the PSW might be larger than 1 ms owing to signal overlap and thus lose particle counts. Fujiwara et al. (2016) therefore proposed a correction factor (f ) for the total count of particles per second as f = 4 × (P SW/(5/v)) 3 if the PSW, which is the maximum among up to six values per second, is greater than 5/v; if the PSW is smaller than 5/v, f = 1. The corrected count N cor (s −1 ) can thus be estimated using f and the original count N org (s −1 ) as follows.

Total particle count
However, this assumption is only be applicable when the detection area depth is assumed to be uniform in the CPS inlet; however, as described in section 2.3, the PSW will vary widely owing to the inhomogeneous detection cross-section domain ( Fig. 3). This correction method should therefore be validated by other observed products.
To distinguish between cloud ice and cloud water, the degree of polarization (DOP) is defined by Fujiwara et al. (2016) as follows.
When the DOP value is negative, the particle is ice. When the DOP value is positive but less than ∼0.3, the particle is most likely ice. When the DOP value is more than ∼0.3, the particle is water in many cases, but there is a chance that it may be ice 120 because the DOP can take values between −1 and +1 for ice particles. In this study, a stricter DOP threshold of 0.5 is used to focus on the cloud water droplet variables. of which 11 flights are used in this study (Fig. 1a). In addition to the normal CPS sonde observations, the CPS sonde was adiabatic retrieval of LWC when both the cloud radar and lidar detect a liquid layer, and microwave radiometer data are present (most reliable classification). In this study, the LWP data and LWC retrieved by the Cloudnet product are used for comparison with the CPS sonde results.
All soundings consisted of a CPS with Meisei radiosondes (RS-11G). The Vaisala radiosonde (RS41-SGP) was also simultaneously launched by by hanging from the opposite side of a 1-m-long rod in the 2019 and 2020 campaigns (the other side 150 was used for the CPS sonde) (Fig. 1). The balloon-type was a 350-g balloon (TOTEX TA350) in the 2018 and 2019 campaigns and a 600-g balloon (TOTEX TA600) in the 2020 campaign. The detailed data list is shown in Table 1.

Numerical experiments
The simplified three-dimensional computational fluid dynamics (CFD) was simulated using Flowsquare + software (Nora Scientific, https://fsp.norasci.com/en/) to better understand the flow pattern around the CPS housing. Flowsquare + solves for in March 2020 at Ny-Ålesund. The dynamic viscosity µ was fixed at 1.6 × 10 −5 kg m −1 s −1 . The inflow speed was set to 5 m s −1 assuming an ascending speed (exp-5m), whereas the horizontal wind speed was fixed to 0 m s −1 .

quasi-steady state). The list of experiments is shown in
170 4 Data processing 4.1 Relationship between particle signal width and detected particle size voltage To confirm the PSW variability, the accumulated relative PSW frequency is plotted for each field campaign in Fig. 6 when cloud water was detected based on a DOP threshold of 0.5. The approximate thickness of the cloud layer for each case is listed in Table 1. All the CPS profiles contain PSWs smaller than 1.0 ms with 60%-80% relative frequency. There are three hypotheses 175 to account for this small PSW: (1) the detected thickness of the cross-section is thinner than 0.5 cm; (2) the flow speed in the CPS inlet is faster than the ascending speed (typically 5±1 m s −1 ); and (3) a combination of the above two hypotheses.
The first hypothesis is verified in section 2 (Fig. 3). Only 30% of the cross-section of the inlet (magenta area in Fig. 3b) can be used for a detection area with a 0.5-cm thickness, while nearly 70% of the area (other colors in Fig. 3b) can be used for a thinner detection zone. It is therefore natural that the smaller PSW was frequently observed in each CPS flight. 180 We next introduce the possibility of variable flow speeds in the CPS inlet to verify the second hypothesis. Here, we focus on two cases: one with a standard slop curve (NY20-CPS03) and another with a steep slope curve in the smaller PSW range (NY20-CPS09). The mean ascending speeds where liquid clouds were detected was 5.0 and 6.1 m s −1 , respectively (Table 1).
Faster vertical speed might contribute to the steep slope of the PSW frequency. The estimated PSW weighted by the detection thickness in the CPS inlet (0.5 cm: 30%, 0.25 cm: 70%) is 0.65 and 0.53 ms for each case. The difference in the ascending 185 speed therefore has a partial impact on the PSW variability.
Here, we consider the idealized flow distributions in the CPS inlet. The first case is assumed to have a relatively low Reynolds number (Re) with a slow flow speed distribution (relatively laminar flow). The second case is taken to have a relatively high Re with a fast flow speed distribution (relatively turbulent flow). Once the flow distribution is given, the time to pass the crosssection area is calculated (Fig. 7). The low flow speed case allows the large PSW (>1.0 ms), while the high flow speed case 190 allows the small PSW (<0.4 ms). Another important finding in this calculation is that a significantly high-PSW area can exist near the CPS inlet wall owing to the low flow speed. The frequency slope for both cases is reproduced in some sense compared with real cases (Fig. 6d). The observed accumulative relative frequency of PSW would therefore be caused by this non-uniform flow in the CPS inlet and PSW distributions rather than the effect of particle overlapping, as proposed by Fujiwara et al. (2016).
Based on the verification of these two hypotheses, the third hypothesis is also correct. The combination of a non-uniform 195 detection depth and flow distribution can explain the small PSW value.

Relationship between mean PSW and Reynolds number
There is no way to observe the flow speed in the CPS inlet during a normal CPS flight; however, using the observed parameters, the environment characteristics of the flow speed can be estimated. The idealized situations (Fig. 7) are first investigated (assuming cases NY20-CPS03 and NY20-CPS09). A bulk flow speed is defined as 10 −2 /(< P SW > × 10 −3 ) (unit: m s −1 ) to better understand the mean state in the CPS inlet, where f rac is the fraction of the detection area with 0.5 cm, and < P SW > is the spatially and temporally averaged PSW in the detection domain. The v b for low and high flow speed cases is estimated as 3.3 (NY20-CPS03) and 4.7 m s −1 (NY20-CPS09), respectively. These values are roughly similar to the mean flow speed of 3.4 (Fig. 7a) and 5.5 m s −1 (Fig. 7b) for each case simply because the estimated mean PSWs (0.95 and 0.65 ms in low-and high-flow cases, respectively) are very similar to the observed values (0.99 ms in 205 NY20-CPS03, 0.69 ms in NY20-CPS09) ( Table 1). The v b would therefore be a potential indicator as a first approximation of the flow speed in the CPS inlet.
The observed < P SW > and v b are then calculated by time-averaging the observed PSWs in the liquid cloud layer ( Table   1). The v b is generally weaker than the mean ascending speed (v). The question then arises of what controls v b . Based on the By definition, Re decreases with increasing ν. This situation can occur under lower pressure because ρ deceases, which 215 suggests that there is a relationship between ν (= µ/ρ) and v b . The correlation coefficient between the two parameters among all the CPS sondes (except for tethered balloons) is relatively high (0.51, p-value: 0.015). The Re in NY20-CPS09 (3332) is larger than in NY20-CPS03 (2680), which suggests that a more mixed flow regime is expected in the former. The CPS inlet flow characteristics therefore depend on air density (i.e., air pressure) as well as the vertical ascending speed, as discussed in section 6.1; however, v b might be more complicatedly influenced by other factors, as discussed in section 6.2.

Cut-off PSW to reduce the unrealistic data
As shown in Fig. 7, a high PSW (e.g., >2 ms) is observed near the wall of the CPS inlet owing to the slow flow speed. The height where particles are detected under lower flow speed situations thus does not represent the observed height but rather the lower height owing to the time lag. Furthermore, the fact that a higher voltage of I 55 is observed with the higher PSW (discussed later in Fig. 12b) suggests that the threshold PSW value can be useful to reduce unrealistic particle size data. This 225 procedure is thus critical to estimate the effective cloud particle radius.
The PSW cut-off value (hereafter, P SW c ) is proposed as follows.
where P SW c is the difference between the maximum and minimum PSWs (P SW max and P SW min ) counted per unit time (= 1 s). Note that the number of data is six at most second readings. This procedure thus excludes at least one datum among 230 the six recorded values per second. The overbar indicates the time average where a liquid cloud is observed (typically 50-100 s depending on the cloud-layer thickness). If the PSW is recorded randomly in a detection domain, the ratio of rejected data would be approximately 17% and the effective data ratio would be approximately 83%.
As a trial, the relationship between P SW c and accumulative relative PSW frequency is investigated using the idealized cases described in the previous subsection. The sampling points in the idealized CPS inlet (1001×1001 grids: 0.01 mm resolution) 235 are randomly selected (black dots in Fig. 7). The P SW c is calculated using 80 sets of six PSW data, which assumes 80s observations in the cloud layer (a roughly 400-m-thick cloud). The estimated P SW c , shown in Fig. 7 as white contours, heavily depends on the flow speed distribution. The frequency up to P SW c corresponds to 85% and 94% (triangles in Fig. 6d), which suggests that this data screening would be effective despite the limitation of the number of data if the point selection is randomly determined with some time averaging. Using the real cases, P SW c also ranges from 80% to 90% (triangles in 240 Fig. 6a-c: except for NY20-CPS01 owing to the thinner sampling depth of 100 m), which supports the randomness of particle counts in the CPS inlet.

Estimation of effective particle size
Fujiwara et al. (2016) conducted laboratory experiments to measure the particle voltage (I 55 : V) for known particle diameter sizes (d: µm) between 1 and 100 µm. Table 2 summarizes their results. However, they did not provide an empirical equation for 245 estimating particle size and some approximations are required to estimate LWC and LWP. Based on the quadratic regression between log 10 (d) and log 10 (I 55 ) (correlation coefficient = 0.983, p-value: 7.28 ×10 −5 ), the following empirical equation is proposed: log 10 (d) = log 10 (I 55 ) + 0.13303 0.4257 + 0.09831, where d is the diameter that corresponds to the observed voltage (I 55 ) of a particle. Considering that the number of I 55 data 250 is six per second at most and one of which will be excluded where P SW max is larger than P SW c , only five data sets are available to estimate the particles sizes. Although random sampling is assumed, as discussed in section 4.3, time-averaging in a certain thickness would better represent the section of cloud layers. Here, the averaging time is set to ±2 s, corresponding to a 25-m-thick cloud layer. The effective radius (r e : µm) of the cloud droplets is estimated by considering volume averaging as follows: where n is the number of observations in the target cloud layer (typically 5 particles s −1 × 5 s = 25 particles) and d n is the nth particle diameter estimated by Eq. (5).

Correction factor of total particle count
Once the r e and total particle count are determined at each level, the LWC and LWP can be estimated as the integrated LWC.

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Although the observed total particle count should be corrected owing to sampling overlap, as proposed by Fujiwara et al.
(2016), the sampling overlap might be a minor factor because most PSW are smaller than 1.0 ms with 70% of the accumulative relative frequency. Instead of this issue, sampling loss should be considered as a major factor because the CPS inlet flow dynamics during ascent have large uncertainties. In particular, there is no conclusive evidence that the ascending speed equals the CPS inlet flow speed.

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Here we consider the shape of the CPS housing with a radiosonde. The flow at the top of the housing during ascent (assuming 5 m s −1 ) would be modified and aerodynamically slowed (<5 m s −1 ). This reduced inflow into the CPS inlet leads to a loss 9 https://doi.org/10.5194/amt-2020-476 Preprint. Discussion started: 8 January 2021 c Author(s) 2021. CC BY 4.0 License.
of cloud particle counts. Furthermore, the bulk flow speed v b in the CPS inlet estimated by < P SW > is generally slower than the ascending speed v (Table 1) For this purpose, we calculated the flow pattern around the CPS housing using Flowsquare + . Fig. 8 shows the flow pattern assuming an ascending speed of 4, 5, and 6 m s −1 . As expected, the flow speed is reduced at the top of the housing for 275 each case. The minimum flow speed at the entrance of the CPS inlet is 0.69, 0.87, and 1.04 m s −1 for each case, which is 17.2%±0.04% of the initial flow speed (Fig. 9a), which suggests that the chance that the air mass can enter the CPS inlet in a unit of time is reduced to 17.2%. The remaining air mass turns aside from the CPS housing by the divergent flow (Fig. 8). The correction factor for total particle counts is therefore proposed as 5.8 (= 1/0.172). Under a minimal ascending speed (exp-1m) and assuming the tethered balloon measurements (green line in Fig. 9a), the reduction ratio is 16.7% (i.e., correction factor of 280 6.0).
An additional remarkable feature is that the flow speed in the CPS inlet is recovered to the ascending speed with approximately 10% loss (Fig. 9a). Figs. 8 and 9 indicate that the flow speed in the CPS inlet increases with increasing ascending speed.
Compared with the three cases, the pressure gradient between the top and bottom sides (i.e., pressure drag) regulates the flow speed in the CPS inlet (Fig. 9b). The flow speed near the bottom side decreases, which is consistent with the results of Fujiwara 5 Comparison with other data sources

Total particle count by a tethered balloon in the Arctic Ocean
The OPC's vertical profiles on the tethered balloon are used to evaluate the corrected total particle count by the CPS sonde.

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The OPC's count is based on a 5-s suction (L −1 ), whereas the CPS's count is based on a 1-s interval. Thus, the CPS count is averaged by 5 s. The data in which the DOP values are larger than 0.5 are used for comparison, focusing on the liquid cloud.
The CPS count unit (s −1 ) is standardized to that of the OPC (L −1 ) by the ascending speed at each level (typically ∼1 m s −1 ) and cross-sectional area of the CPS inlet (1 cm 2 ). Based on the extra simulation assuming an ascending speed of 1 m s −1 , the correction factor of the CPS total count of 6.0 is applied to this case. 295 Fig. 10 shows the vertical distribution of the number concentration of particles larger than 2 µm obtained by the OPC and CPS sonde. A 50-m-thick cloud layer characterizes case 1 at 400 m height where the OPC detected a peak value of around 10,000 L −1 , whereas the CPS significantly underestimates this value. This discrepancy arises from the low cloud cover of the thin stratus clouds (Fig. 5a), introducing horizontal and vertical heterogeneity in the measurements because of the vertical distance between both systems of 5 m with a slight tilting. Sunlight (Fig. 5a) might affect to count of the signal (the DOP among the three (Fig. 5b). The observation terminates at 750 m height, but the moist layer (relative humidity > 95%) continues until approximately 1200 m, as confirmed by a regular-time Vaisala RS-41 radiosonde observation (not shown). A cloud bottom height of 600 m with 97% relative humidity matches well where the number concentration starts to increase. The rapid 305 increase in concentration where the relative humidity is 100% is also very similar. Although both sensors detect a lower number concentration up to 700 m height, the remarkable difference between the two occurs at heights between 700 and 750 m. The OPC value continuously decreases, whereas the CPS value rapidly increases. This discrepancy arises from the detectable range of the sensors because the CPS has a wider particle size range, which suggests that larger cloud particles dominate at this level.
The averaged I 55 voltage at 600-650 and 700-750 m corrected by P SW c is 0.61 V and 1.27 V, respectively, which corresponds 310 to ∼2 and ∼25 µm in diameter ( Table 2). The former particles are detected by the OPC, whereas the latter are likely out of range. The third case is the intermediate case in terms of the cloud layer (120 m thick) (Fig. 5c). The two concentration peaks at heights of 690 and 730 m are well-matched despite the CPS underestimation. The third peak in the CPS sonde at 760 m height is characterized by the larger particles out of the OPC range.
The total particle count corrected by the factor proposed by Fujiwara et al. (2016) is nearly the same as the raw particle count, 315 leading to a significant underestimation (green line in Fig. 10). Because the slow ascending speed promotes 5/v larger than the PSW, the factor is frequently unity (i.e., 1.0) by the definition of Fujiwara's factor. A correction factor of 6.0 proposed in this study assumes that the ascending speed is 1.0 m s −1 ; however, the speed is typically decreasing (e.g., 0.1-0.5 m s −1 ) at the beginning of the launch and before reaching the maximum height owing to operational procedures. The correction factor may therefore be larger than 6.0, which would be in better agreement with the OPC results. Despite the difference in the detectable 320 particle size range and sampling method (suction vs. natural ventilation by the ascending motion) between the OPC and CPS sonde, the correction factor for the CPS's total particle count proposed in this study offers a promising advantage to provide meaningful physical information for the quantitative analysis of cloud microphysics processes.

LWC and LWP by microwave radiometry at Ny-Ålesund, Svalbard
Using the land-based remote sensing product at Ny-Ålesund, r e and P SW c are applied to estimate and validate LWC and LWP.

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The Cloudnet product is only available for a portion of the March 2020 data set to retrieve the LWC. Only the NY20-CPS03 case is available for comparison. Because this case is the single-layer cloud case (400 m water cloud depth) and the LWP from the Cloudnet product is 30.4 g kg −1 at 17:10 UTC on the measurement day, which is larger than the typical uncertainty of the HATPRO (20-25 g m −2 ), comparison with the CPS sonde is feasible. Although two more cases might be available (NY20-CPS09 and NY20-CPS14), they are multiple-layered clouds with thinner water cloud layers of less than 200 m depth.

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As seen in the previous subsection, the CPS sonde tends to underestimate the total particle count, presumably causing an underestimation of LWC and LWP. Additionally, the LWP observed by HATPRO on those days is 12.0 and 3.4 g kg −1 , which suggests that these observed values also contain considerable uncertainty.
To estimate LWC, r e is calculated at each level by satisfying the P SW c threshold value to Eqs. 5 and 6. The LWC can be estimated assuming the cloud droplet shape is a sphere and water density is 1000 kg m −3 . Fig. 11 shows the vertical profiles of 335 air temperature, relative humidity, I 55 voltage, DOP value, total particle count, P SW c , r e , and LWC. This case is characterized by mixed-phase clouds where the lower layer up to 500 m is filled by cloud ice or snow (i.e., the DOP value is small; blue dots in Fig. 11), whereas the upper layer from 500 to 900 m is dominated by cloud water (e.g., the DOP is larger than 0.5; red dots in Fig. 11).
Based on the vertical distribution of the I 55 voltage, r e increases from ∼10 to 25 µm with two peaks at 700 and 830 m.

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P SW c ranges between 1 and 5. The I 55 voltage sometimes exceeds 7 V, which suggests that P SW c appropriately reduces the samples larger than the CPS detection limit or solid cloud phase. The LWC increases up to 850 m with a maximum of 0.25 g m −3 . This peak value does not depend on the total particle count but rather the size of r e . These characteristics generally agree with the adiabatically retrieved LWC by the Cloudnet product, which linearly increased up to the cloud top. The vertical integration of LWC, namely LWP, shows that the CPS sondes (21.6 g m −2 ) tend to underestimate the LWP by the Cloudnet 345 (30.4 g m −2 ). A possible reason might be cloud ice contamination. The DOP threshold between cloud ice and cloud water is set to 0.5 in this study. If a more strict DOP threshold is applied, the LWP increases (e.g., to 27.9 g m −2 for a DOP threshold of 0.7); however, the number of samples for the r e calculation decreases with considerably higher uncertainty of the LWC calculation. It should also be noted that the LWP data from the Cloudnet product also have a given uncertainty, as previously mentioned before. In other words, the LWP value by the CPS sonde falls within the range of the Cloudnet product uncertainty.

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If the correction factor by Fujiwara et al. (2016) is applied to this case, the total particle count (∼10 4 L −1 : green dots in Fig.   11) is one order larger than our corrected value (∼10 3 L −1 ), and thus overestimates LWP (506 g m −2 ). Although the true r e is unknown, a combination of corrected total particle count and r e using P SW c can provide new insight into understanding the vertical structure of liquid phase clouds. topographic effects at Ny-Ålesund in ERA5. Fig. 12a shows a scatter plot between LW P ERA5 and LW P CP S . Several outliers show a common feature: a mean r e larger than 20 µm (gray dots). By excluding these five cases, the correlation coefficient between LP W ERA5 and LW P CP S is 0.55, with a p-value of 0.082. LW P CP S is almost twice as much as LW P ERA5 because ERA5 uses a coarser vertical resolution (seven layers below 850 hPa). The cloud microphysics without solving each hydrometeor number concentration would be the other factor. Of course, several error sources can arise from the corrected CPS 365 sonde data. In any case, abnormal LW P CP S values would occur in the case of relatively large particle sizes, which are larger in I 55 .
The MR19-CPS06 case (largest r e case: 31 µm) reveals that the voltage in I 55 frequently reaches the maximum regardless of the degree of PSW (red circles in Fig. 12b), whereas the MR19-CPS07 case (normal r e case: 14 µm) does not exhibit such a condition (blue squares in Fig. 12b). The former case has a larger P SW c of 2.75 ms (red dashed line Fig. 12b), which cannot 370 correctly exclude the saturated voltage data and thus causes unrealistic r e and LW P CP S . The latter case successfully leaves the data via P SW c (blue dashed line in Fig. 12b). In the intermediate P SW c case with 2.07 ms, the number of saturated I 55 voltage is reduced (MR19-CPS09: green dashed line in Fig. 12b); however, the LW P CP S is still seven times larger than LW P ERA5 with r e = 22 µm. Extra caution is therefore needed for high P SW c (e.g., >2.0 ms).

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The simulations show that the flow speed in the CPS inlet becomes fast with increasing ascending speed (v) (Fig. 8), leading to a decrease in P SW c under relatively high Re conditions (turbulent flow). The correlation coefficient between v and P SW c is −0.58 (p-value: 0.0023) if the tethered balloon cases are included. The pressure height (p) is another factor to modify P SW c (correlation coefficient = 0.57, p-value: 0.0027). The multiple linear regression correlation coefficient to predict P SW c with v and p is 0.71 with an F-value of 0.0003. Therefore, both v and p are important environmental parameters for determining 380