Statistic evaluation of low-frequency acoustic wave impact on rainfall stimulation

For securing more water resources, traditional solutions including seawater desalination are limited due to high cost and restricted operating conditions. Thus, acoustic stimulation of rainfall is a potential alternative method due to its low cost and convenient operation. Low-frequency acoustic fields can be used to stimulate rainfall through evoking wavy motion of air particles in clouds which will significantly enhance the process of collision coalescence of cloud droplets and lead to their volume increase. Nevertheless, there is still a lack of rational methods to evaluate the effect of acoustic enhancement of rainfall in field experiments. To this end, in this study, nearly two-month field experiments of acoustic rainfall enhancement with 39 trials were carried out by our research team in the Tibetan Plateau. Statistical analysis was applied to evaluate the effect of acoustic wave on precipitation stimulation. The results of average rainfall intensity distribution using ordinary least square analysis disclose that acoustic interference has a considerable effect on rainfall enhancement. Such a rainfall enhancement effect increases significantly along with the increase of rainfall duration which is the index of cloud precipitation potential. For rainfall events with the duration more than two hours, the average rainfall intensity was improved by 72% with the acoustic wave effect at the experiment site. The phenomena are consistent with the fact that clouds with larger precipitation potential contain more cloud droplets which are beneficial to the acoustic coagulation process.


Introduction
It is expected that the shortage of water resources will be exacerbated due to rapid population growth and climate change in the next several decades . With the advances of meteorological science and technology, artificial rainfall which is part of artificial weather modification has gradually become a promising strategy for increasing challenges remain in selecting suitable operating conditions (Flossmann et al. 2019).
The precipitation process is rather complicated due to intricate microphysics and dynamics of clouds. A significant increase of cloud thickness was observed at 30 min after the seeding of liquid carbon dioxide in the artificial rainfall project at Karatsu, Saga in Japan (Maki et al. 2018). However, for seeding method, the operational effectiveness of artificial rainfall is severally affected by the ambient environment, droplet size distribution, and seeding height. Meanwhile, there are several major difficulties in promoting the seeding technology (Wu et al. 2018), which include the high cost of operation, the risk of pollution (Fisher et al. 2018;Korneev et al. 2017), and the efficient method for evaluating rainfall enhancement. Thereafter, emerging technologies, such as acoustic coagulation (Galechyan 2005), laser-induced condensation (Leisner et al. 2013) and atmospheric ionization (Tan et al. 2016), have attracted more attention. Among them, acoustic coagulation has the advantages of low cost and environment friendly . Notably, the primary application of this acoustic agglomeration technology was mainly focusing on the removal procedure of fine particles of coal-fired ashes (Shen et al. 2018), since traditional dust removal methods, for example bag filter and cyclone, are relatively inefficient for eliminating fine particles (Liu et al. 2009;Zhou et al. 2016).
The mainstream method to evaluate the efficiency of artificial rainfall projects is using regression analysis based on years of historical precipitation data. Cheng et al. (2021) applied the regional historical regression test of ten years of precipitation data recorded in the Hexi Corridor in Northwest China to assess the rainfall enhancement; the results suggested that the average growth rate of monthly rainfall in the Shiyang river basin be about 17.5% with seeding operations. A randomized crossover experimental design was conducted in the Weather Modification Pilot Project in Wyoming, USA, and Breed et al. (2014) selected the 4-h accumulation of precipitation as response variable and the root regression ratio as test statistic to estimate the effectiveness of seeding silver iodide. It is observed that the expected increasing rate of accumulated precipitation is ranged from 10 to 15% based on a 5-6-year program (Breed et al. 2014;Wu et al. 2015) employed the "bootstrap" statistical simulation method to analyze the natural rainfall variability and concluded that the average seeding effect is about 11.95% in Jilin Province in China. Traditional cloud seeding project has the characteristics of large operation area and wide influence range. Due to the impact of terrain and atmospheric circulation, the boundary of the actual sphere of artificial influence may be tens of kilometers away from the initial seeding location (Maki et al. 2018). Thus, to avoid the errors caused by uneven rainfall distribution, to accumulate multiple years of rainfall data is necessary to assess the effectiveness of cloud seeding technology. Notably, the acoustic rainfall technology differs from the seeding one significantly, resulting in a different method for evaluating effectiveness.

Literature review of acoustic wave impacts on precipitation
Micron particles in acoustic fields can be evoked to vibrate at different amplitudes due to the combined effect of inertial force and viscous force (Zhou et al. 2017). Thus, the particles with different sizes in acoustic fields will have different vibration amplitudes, and agglomeration process due to acoustic stimulation occurs (Bai et al. 2021).
The application of acoustic coagulation in artificial precipitation was first proposed by Russian scientists in the 1950s (Mednikov 1965). However, the technology could not be widely used in the last century due to some insurmountable limitations (Galechyan 2005;Tulaikova and Amirova 2015). Those limitations mainly are (1) knowledge shortage of physical mechanism of acoustic wave impact on precipitation stimulation, (2) manufacture of the devices for providing strong acoustic waves which can propagate to the high sky with an altitude of several hundred or even 1 to 2 km, (3) a cloud and precipitation monitoring system for obtaining acoustic impacts on clouds and then precipitation, and (4) an effective method to evaluate the efficiency of acoustic wave impacts on stimulation of precipitation quantitatively. To overcome those limitations, in recent years, the feasibility of the technology has been explored through numerical modeling analysis (Markauskas et al. 2015;Shi et al. 2020) and indoor cloud chamber experiments (Bai et al. 2021). Meanwhile, the field experimental explorations of acoustic wave impacts on the natural cloud of precipitation processes were widely conducted to evaluate the efficiency of precipitation enhancement Wei et al. 2021).
However, due to the complexity of the precipitation process and the uncertainty in natural rainfall (Wen et al. 2020), the evaluation of acoustic effect in previous research was mainly based on remote sensing cloud observations and related statistical analysis. Wei et al. (2021) disclosed that there is the trigger and periodic effect of the acoustic interference process on clouds based on the analysis of radar echo intensity and microphysical characteristics of clouds.  studied two cloud microphysical parameters, liquid water content and raindrop diameters at different atmospheric heights, and found that both parameters increase under the influence of acoustic waves. Those study results confirmed that the acoustic wave effect has significant impacts on rainfall stimulation. However, the analysis of remote sensing data is not a direct evaluation of the acoustic impacts and might be disturbed by environmental factors and instrumental errors (Guo et al. 2014;Tessendorf et al. 2012). In other words, the current evaluation of acoustic impacts on rainfall stimulation remains vague. Thus, it is necessary to conduct analysis of the ground-based rainfall measurements.
For acoustic rainfall, the influence space range is relatively small due to the rapid decay of sound strength in the atmosphere; however, regarding field operation, the mobility is improved, and the cost is reduced notably . Meanwhile, since the impact range of acoustic rainfall technology is usually concentrated within a space of a few kilometers around the operation point, the evaluation of artificial effectiveness could be performed with short sequences and small sample sizes ) developed a time-structuralized method to analyze the rainfall process variation with the impact of acoustic fields, and it was concluded that the rainfall intensity is relatively larger when the acoustic devices are turned on.
However, to date, because there are few field experiments on acoustic precipitation enhancement conducted Wei et al. 2021), studies on acoustic effects are not systematically developed, and, specifically, the efficient analysis using rain gauge observations has not been available yet. To this end, in this study, a statistical analysis was proposed and implemented through using the field data obtained from a rainfall enhancement project to evaluate the influence of acoustic waves on rainfall stimulation. In the analysis, the average rainfall intensity of each rainfall event was adopted as dependent variable. Then acoustic interference and several environmental factors were considered to assess the effectiveness of acoustic impacts. The study would mainly contribute to relax the fourth limitation of applying acoustic technology, development of an effective method to evaluate the efficiency of acoustic wave impacts.

Field experiments
The experiment site is located at Nyingchi City, Southeast of the Tibet Autonomous Region, China, with the central coordinates of 29°98´ N and 93°82´ E ( Fig. 1(a)). The average altitude of Nyingchi City is about 3100 m, and the annual precipitation is mainly concentrated in summer from May to September. During the rainfall season, the cloud has the characteristics of a lower base and a broad range of droplet size distribution (Fu et al. 2020), which are rational conditions for acoustic enhancement operation ). Thus, the study selected the site for conducting the field experiments for the period from May to July in 2020. Figure 1(a) shows the major equipment for the field experiments. The strong acoustic wave field was generated by the fluidic air-modulated speaker (FAS) . The maximum sound intensity measured near the center of the horn outlet was about 150 dB with a frequency range from 20 ~ 250 Hz, which maintained the same condition throughout the experiment period. A portable weather station (PWS) was installed for monitoring wind condition, relative humidity, temperature and air pressure during the experiment period. A panoramic camera was installed to monitor the variation of clouds. The rainfall data were recorded by the automatic rain gauges with the resolution of 0.2 mm. Totally 30 rain gauges (RS) were installed within a range of 3 km around the FAS as the center; however, 4 of them were damaged during the experiments. Thus, the rainfall data collected from the remaining 26 rain gauges were analyzed (see the following section for the method of analyzing the rainfall data). Figure 1(b) shows the spatial distribution of those rain gauges.
The non-randomized experimental plan was designed, and the experiment period was divided into two parts. From May 18, 2020 to June 19, 2020, experimental operations only took place on Monday, Wednesday, and Friday when it was likely to rain. From June 20, 2020 to July 21, 2020, there was no limit on the date in conducting field experiments. Generally, the FAS would be turned on when the experimental site sky was filled with clouds during daytime (from 9:00 to 21:00) on experiment days. Notably, for the safety reasons of the panel involving in the field experiments in the remote mountainous area ( Fig. 1(a)), the daily operation period was from 9:00 to 21:00. The experiment start time was decided mainly based on the meteorological observation by the experienced field panel who participated in preliminary experiments Wei et al. 2021). After the FAS was turned on, it would be turned off when one of three circumstances appeared: (1) There was no rain for half an hour after the operation. (2) The rainfall process occurred and ended more than 10 min later. (3) The time passed 21:00.
During the data analysis, two adjacent rainfall events were identified when the duration of recorded-zero rain gauge data between them is longer than 30 min (Chang and Guo 2016). Then, totally there are 183 rainfall events identified during the experiment period from May 18, 2020 to July 21, 2020. Among them, 39 events are classified as an experimental group (EG) with the influence of the acoustic fields, and the remaining ones without acoustic interference are regarded as a control group (CG) according to the naming rules for reference trials in scientific experiments.
rule that for a continuous rainfall event, any intermittent intervals of no rainfall would not be longer than 30 min and at least three rain gauges have recorded no-zero data in the same period.
Secondly, we computed the total rainfall depth and average rainfall intensities. For an individual rainfall event, the rainfall duration was obtained through calculating the time interval between the first and last rain gauge data of all the available rain gauges in the field experiments. Then, the total rainfall depth at each rain gauge was computed. Notably, we divided the rain gauges into 7 groups according to their locations next to the FAS (see Fig. 1(b)), and the total rainfall depth for each group was represented by the mean value of the total rainfall depths of those rain gauges within the group. Lastly, the total rainfall depth is the mean of the 7 groups, and the average rainfall intensity was calculated by the total rainfall divided by the rainfall duration. The relationships among total rainfall depth, average rainfall intensity and rainfall duration were analyzed to identify the

Analysis method
In this study, to evaluate the acoustic impacts, the average rainfall intensity of each rainfall event was used as an independent variable. The impact of acoustic interference and meteorological conditions were analyzed. Figure 2 shows the study framework, and the following provides the details of those processes.
Firstly, we conducted the rainfall data quality check and rainfall event identification. It is necessary to check the rain gauge data quality since some rain gauges might be blocked or destroyed during the field experiments, and then some records were missing. During a rainfall event, a rain gauge only recorded zero rainfall depth, and meanwhile the surrounding gauges recorded non-zero data; then, we can identify the data quality problem of the rain gauge and need to use the data with a certain caution. After the data quality check, we need identify those rainfall events in terms of the events occurred at night time of CG events for comparison study, we conducted the t-test to check whether the rainfall period of daytime, or nighttime, of CG rainfall events influence the average rainfall intensity or not (see Sect. 4.2 for further information).
It is worth noting that most of the rainfalls occurred in Tibetan Plateau (TP) region have the characteristics of low intensity, short duration, and uneven spatial and temporal distribution (Guo et al. 2014). The trigger effect of acoustic wave on cloud microphysical characteristics might only take few minutes . Therefore, considering rational indicator for evaluating the acoustic influence on rainfall.
Thirdly, we classified those rainfall events as EG or CG in terms of with or without acoustic influence during rainfall periods. Furthermore, we divided the CG into daytime or nighttime rainfall events according to the rainfall period whether it was daytime or nighttime. Then, the average rainfall intensity distributions of both groups are compared to evaluate the variation tendency. Since the acoustic operations were conducted during the daytime from 9:00 to 21:00, in order to determine whether we need use the rainfall Fig. 2 The flowchart of conducting data analysis in the study Chang and Guo (2016) that the rainfall on the south TP usually has weak intensity and prolonged rainfall occurs mostly at night.
We conducted the simple linear regression for total rainfall depth and average rainfall intensity relative to rainfall duration with the intercept set as zero. Table 1 lists the analysis results, indicating that both the total rainfall depth and average rainfall intensity has a positive relationship with the rainfall duration (P < 0.01). The adjusted R 2 and coefficient of total rainfall depth are larger than those of average rainfall intensity, which means during the experiment period, the lasting time of rainfall has more influence on total rainfall depth than the average rainfall intensity. As shown in Fig. 3, the prediction bands of those two regressions are much broader than the confidence bands and most of the data are out range of the confidence bands, which indicates that the total rainfall depth and average rainfall intensity with same duration varied in wide ranges. Notably, the prediction and confidence bands were used to evaluate the uncertainty of the regression analysis; the prediction band represents the uncertainty in the new data-point value on the curve, and the confidence band indicates the uncertainty in the curve fitting based on limited data. In the following parts, we selected the average rainfall intensity as evaluation index for assessing the acoustic impact.

The distribution of average rainfall intensity
According to the national classification standard of rainfall intensity (General Administration of Quality Supervision & Committee, 2012), we grouped the rainfall events into 5 classes (namely, light, moderate, heavy, torrential, and torrential downpour), and Table 2 lists the statistics of occurrence frequency of different rainfall intensity level for the recorded rainfall events. From the table, we can observe that nearly 65% of the events are classified as light or moderate rain. This is consistent with the finding reported by Chang and Guo (2016) that the major rainfall process is short-duration and showery with an average rainfall intensity around 1.2 mm/h during the summer season in TP. Due to the influence of high-altitude terrain, the water drop size distribution inside the clouds varies significantly along with short distance at the vertical direction, which would lead to the appearances of the low intensity and short duration of rainfall (Fu et al. 2020).
In Table 2, we can find that for each proportion level of the first four rainfall intensity categories, the ratio of the experimental group showed a generally increasing trend with the increase of rainfall intensity level. This phenomenon may indicate that the acoustic interference should have a positive effect on enhancing rainfall intensity. Notably, during the acoustic device operation, there was no torrential that the acoustic interference on clouds is a continuous process for a certain period, we selected the rainfall events with a certain duration for the following quantitative analysis to effectively evaluate the acoustic interference. The tippingbucket rain gauge used has a resolution of 0.2 mm, and then it involves large uncertainty in estimating the rainfall duration of light rainfall events as their starting and end times are difficult to define (Habib et al. 2001;Shi et al.2021;Wang et al. 2008). Thus, the study adopted the minimum rainfall depth of 0.6 mm as the screening threshold for a rainfall event to make sure the rain gauges have at least 3 non-zero data logs, and the recorded events with the rainfall depth less than 0.6 mm were removed in the subsequent statistical analysis.
The duration of a low intensity rainfall is difficult to estimate accurately due to the uneven spatial rainfall distribution. To avoid the errors caused by the rainfall uneven distribution, in this study, the rainfall duration was identified when at least 5 rain gauges recorded non-zero data. For regression analysis, a dummy variable that takes only the value of 0 or 1 is extensively employed to distinguish the categorical effect (Chelani and Gautam 2022;He et al. 2014). In the study, the interference of acoustic field was regarded as a dummy variable, and the widely used ordinary least square method (OLS) (Kim et al. 2018;Li et al. 2021;Zhang et al. 2021) was applied to analyze the dependence relationship of average rainfall intensity with acoustic interference and meteorological variables.
In the analysis, the rainfall duration is a key factor in computing the rainfall intensity and is closely related to evaluating the acoustic impacts. Therefore, to assess the impact efficiency of acoustic interference on rainfall with different durations, the single-factor analysis of variance model (ANOVA) (Ohn et al. 2021;Zhao et al. 2012) was employed, because the acoustic rainfall enhancement is a continuous process. Figure 3 shows the relationship between total rainfall depth and average rainfall intensity related to rainfall duration for those recorded events. The total rainfall depth ranges from 0.02 to 32.23 mm, the average rainfall intensity ranges from 0.04 to 5.52 mm/h and the rainfall duration ranges from 0.10 to 14.92 h. Compared with the average rainfall intensity, the total rainfall depth has a wider range of variation. The samples with larger rainfall depths usually have longer duration and mostly belong to the nighttime rainfall group. Those rainfall features are consistent with the previous finding by assess the effect of rainfall period on average rainfall intensity, Fig. 4 shows the distribution of daytime and nighttime natural rainfall intensity (namely, CG rainfall events). In general, compared with the daytime group, rainfall that occurred at nighttime had a broader range of intensity, while the mean values of the two sample groups are near the same. To further confirm the result, the two-sample t-tests were conducted on the two groups (see Table 3), and we can observe that there was no significant difference between the mean value of average rainfall intensity between daytime and nighttime rainfall events since the t value is smaller than t critical (two tailed). Thus, the influence of rainfall period on average rainfall intensity is not significant.

Rainfall characteristics in the experimental site
Further, we excluded the rainfall events with total rainfall depth less than 0.6 mm and redefined the lasting time of each rainfall event to avoid the error caused by the temporal and spatial heterogeneity of rainfall. Figure 5 shows the new average rainfall intensity probability distributions and normal fitting curves of both groups. From the figure, we can find that rainfall with relatively large intensity is more likely to occur in the EG rainfall events, and this is further confirmation of the finding presented in Table 2. This fact downpour. This is mainly due to its low occurrence rate, only 1% (namely, two events) during the entire period, which occurred in nighttime (see Fig. 1; Table 2).
As shown in Fig. 3, most of the rainfall events in EG occurred in the daytime due to the acoustic operation schedule. However, in a few prolonged nighttime rainfall events, the acoustic interference was only applied in the early stage (acoustic equipment was shut down at 21:00), but the rainfall lasted for few hours and mainly in the night. Those rainfall events are classified as nighttime rainfall in EG. To 1.464*** 0.236*** The symbols: *** mean the coefficients are significant at the level of 1% Fig. 3 The distribution of total rainfall depth and average rainfall intensity of each rainfall event versus rainfall duration

Influence of meteorological condition
Since rainfall is influenced by the surrounding environment and terrain, the OLS method was applied here to evaluate indicates that the rainfall intensity frequency distribution was considerably changed due to acoustic interference.   . 4 The distribution of natural rainfall intensity during daytime and nighttime was improved when rainfall duration and meteorological variables were included. Among the other 5 predictor variables, only the coefficient of T is significant. Figure 6 shows the scatter plot of rainfall intensity vs. temperature. With the increase in temperature, the distribution of rainfall intensity presented a decreasing trend. This might be coincidence with the finding of Fu et al. (2020) that the precipitation of TP has a strong diurnal variation. In summer over TP, due to the growth of local thermal-forcing convection, the intensities of convective clouds and precipitation became strongest around 18:00 and the convection dissipated completely until next morning (around 06:00) (Chang and Guo 2016;Fu et al. 2020). Since the temperature was relatively low during that period, the average rainfall intensity was negatively correlated with the temperature.

Evaluation of rainfall enhancement
To quantitatively evaluate the acoustic influence on rainfall intensity, all rainfall events with a total rainfall depth greater than 0.6 mm were countered as group A. Further, the study divided group A into two parts according to the precipitation duration: group A1 with their rainfall durations less than 2 h and group A2 including the remaining ones with their durations more than 2 h. The classification attribute of 2 h was selected because the cloud and weather conditions were different for showers and prolonged rainfall in TP (Chang and Guo 2016). Figure 7 shows the rainfall intensity distribution of those three groups. Take the dummy variable acoustic interference as the predictor variable and rainfall intensity as the dependent variable. The ANOVA model was applied to the three sample groups and Table 6 lists the regression results.
According to the regression results of group A, the mean value of average rainfall intensity for natural precipitation during the experiments is 1.50 mm/h, while this value the correlation between rainfall intensity and surrounding meteorological conditions. Considering the average rainfall intensity as dependent variable, in addition to the acoustic field (namely, acoustic wave), rainfall duration (Duration) and mean value of four other environmental variables, temperature (T), atmospheric pressure (P), relative humidity (RH) and wind speed (Wind), were selected as independent variables. Acoustic interference is a dummy variable that used to describe the presence or absence of the acoustic field during each rainfall event. In the study, this parameter was set to 1 if there was acoustic wave influence and otherwise it is 0. Notably, there are totally 64 rainfall events with meteorological data. Table 4 lists the descriptive statistics results of those variables. We can find that among different rainfall events, the atmospheric pressure and relative humidity were relatively stable while the temperature, wind speed and rainfall duration varied widely. For comparison, the linear regression between rainfall intensity and the single variable of acoustic interference was also performed. Table 5 lists the regression results. From the table, we can observe that for acoustic interference, both regressions have positive coefficients, which means the acoustic interference has a positive effect on rainfall intensity. Meanwhile, the level of significance  The symbols: ***, ** mean the coefficients are significant at the level of 1%, 5% respectively are more large agglomeration nuclei in clouds which are favorable for application of the acoustic impacts to rainfall enhancement. As the primary mechanism of the acousticinduced rainfall technology is orthokinetic agglomeration, which is caused by the relative movement of droplets of different sizes in the acoustic field (Bai et al. 2021;. The collision process of cloud droplets would be significantly accelerated with sufficient large droplets and the exist of the intense acoustic field (Pruppacher and Klett 2012;Shi et al. 2020Tulaikova and Amirova 2015;Yan et al. 2018). Then, the rainfall intensity would increase accordingly. The other reason would be the delay time between the effect of acoustic interference on cloud droplets and precipitation occurrence. Since the strength of acoustic wave decreases significantly along with the increase of distance from the acoustic devices to the clouds, its influence on cloud droplets agglomeration might be effective only for those with moderate sizes (Bai et al. 2021;Shi et al. 2020). Then, for those enlarged droplets, more micro droplets and is increased by 0.52 mm/h with the influence of acoustic interference (P < 0.1). Therefore, it would be concluded that for the rainfall events with the rainfall depth greater than 0.6 mm, the average rainfall intensity was improved by 34%. Comparison of the regression models for groups A1 and A2 shows that the significance of R 2 and coefficients were considerably increased when the rainfall duration is more than 2 h. For group A2, the mean values of average rainfall intensity with or without acoustic interference are 2.37 mm/h and 1.38 mm/h, respectively; thus, it would be argued that the average rainfall intensity was improved by 72% with acoustic interference. In general, acoustic interference might be more effective for rainfalls with longer durations.
The above result would be caused by two possible reasons. Firstly, according to Fig. 3, rainfalls with longer durations would likely have more precipitable water in the related atmospheric column than those with shorter durations in the experimental area (Xie et al. 2020). Therefore, there  Wei et al. 2021). However, since the physical mechanism of the technology is differed from that of the traditional seeding method, both the operation plan and efficiency assessment method need to be investigated . In this study, non-randomized acoustic wave experiments for a period of two months were conducted at Nyingchi City in TP, and several statistical methods were adopted here to evaluate the effect of acoustic interference on rainfall enhancement based on the field rain gauge data.
Totally, 183 rainfall events were collected during the experimental period from May to July in 2020. The study time are needed for them to grow up. Thus, with the increase of rainfall duration, the effect of acoustic wave on rainfall intensity would become significant (Rosenfeld et al. 2008;Shi et al. 2020;Wei et al. 2021).

Conclusions
As a potentially applicable emerging artificial rainfall technology, acoustic wave stimulation of droplet coagulation is promising because of its flexibility and low cost (Shi The symbols: ***, **, * mean the coefficients are significant at the level of 1%, 5% ,10% respectively Fig. 7 Rainfall intensity distribution of Group A, A1 and A2; Group A includes all the rainfall evens, Group A1 has the rainfall durations smaller than 2 h, and Group A2 has the remaining events disclosed that both total rainfall depth and average rainfall intensity of each rainfall event were positively correlated with the rainfall duration. The average rainfall intensity presents an increasing trend for the rainfall events with acoustic interference. To further analyze the influencing factors of rainfall intensity, the OLS method was adopted to analyze six variables: acoustic interference, rainfall duration, air temperature, atmospheric pressure, relative humidity, and wind speed. The results showed that only acoustic interference and air temperature are significantly associated with the rainfall intensity. The correlation coefficient between acoustic interference and rainfall intensity is positive, and this is consistent with the previous findings Shi et al. 2020). Based on the ANOVA analysis of rainfall groups with different sample sizes, which were classified by rainfall duration, the positive impact of acoustic interference on rainfall enhancement is more significant when rainfall durations are longer than 2 h. As long-lasting rainfalls at the experimental site usually have more agglomeration nuclei and precipitable water (Chang and Guo 2016), those specific cloud circumstances are more conducive to the acoustic coagulation process.
In summary, the method of using acoustic wave to stimulate rainfalls is a cutting-edge technology; however, the method still needs more exploration due to complicated circumstances of the nature in association with rainfall processes. Thus, in addition to investigating the physical mechanism and numerical simulation of acoustic interference induced agglomeration of water droplets, field experiments and acoustic interference evaluation in natural cloud-precipitation processes are also valuable for further research. However, the great variance existed in the cloud characteristics and natural rainfall distribution makes it difficult to explicitly assess the effect of acoustic interference. Even though the average rainfall intensity of independent rainfall events presented a growing tendency when acoustic devices were turned on in this study, the impact of strong acoustic wave interference on total rainfall depth, spatial and temporal rainfall distributions are still vague. Further field experiments with more precise cloud and precipitation monitoring instruments should be used to comprehensively investigate the influence of low-frequency and strong acoustic waves on cloud-precipitation development process. Meanwhile, field experiments under different terrain conditions should be conducted to verify the universality of this artificial rainfall technology.