In order to improve the measurement of precipitation microphysical characteristics sensor (PMCS), the sampling process of raindrops by PMCS based on a particle-by-particle Monte-Carlo model was simulated to discuss the effect of different bin sizes on DSD measurement, and the optimum sampling bin sizes for PMCS were proposed based on the simulation results. The simulation results of five sampling schemes of bin sizes in four rain-rate categories show that the raw capture DSD has a significant fluctuation variation influenced by the capture probability, whereas the appropriate sampling bin size and width can reduce the impact of variation of raindrop number on DSD shape. A field measurement of a PMCS, an OTT PARSIVEL disdrometer, and a tipping bucket rain Gauge shows that the rain-rate and rainfall accumulations have good consistencies between PMCS, OTT, and Gauge; the DSD obtained by PMCS and OTT has a good agreement; the probability of
Measurement of hydrometeors microphysical characteristics, such as size, shape, fall velocity, and their spatial distribution, is of high interest in fields of precipitation physics, numerical weather prediction models, ground validation of satellite remote sensing, electromagnetic wave propagation, and other climatological and hydrological applications [
There are many instruments available to measure the drop size distribution of precipitation, such as the PARSIVEL [
The choice of bin size classes may influence the shape of the DSD fundamentally; a too large bin size may ignore certain small sizes of drops, resulting in that the measured DSD would not represent the underlying DSD; and the bin size cannot be small infinitely because of the limitation of the instrument’s resolution. Furthermore, different bin size classes may cause different representative diameters in the average and integral processes, which influence the results of moments of the DSD; different bin sizes exhibit different scaling relations with respect to the number of samples, sequences, and amplitude of rain-rate. Therefore, the optimal widths of the bin for a certain instrument should be investigated and handled carefully.
We have developed a precipitation microphysical characteristic sensor (short for PMCS, called Video Precipitation Sensor before) based on particle image velocimetry techniques recently [
The PMCS consists of four units: optical unit, imaging unit, acquisition and control unit, and data processing unit, as shown in Figure
The framework of precipitation microphysical characteristic sensor.
The double-exposure in one frame (DEOF) of the PMCS plays a key role in the simultaneous measurement of the size, shape, and fall velocity of precipitation particles, as shown in Figure
The principle of measurement.
In fact, fluctuations in DSD measurements and derived rainfall properties are due to not only the real fine-scale physical variations (called natural variability), but also the statistical sampling errors (called sampling fluctuations) [
Considering the operation principle of PMCS, the effective sampling time is only 10% of the exposure time of each frame; not all particles passing through the sampling area can be double-imaged by camera; the capture probability of a certain particle which can be fully photographed twice by the camera decreases exponentially with its size. Considering this measurement mechanism, the measured DSD might deviate with the real DSD due to unreasonable parameters settings. Therefore, the uncertainty in DSD measured by PMCS with different sampling parameters should be evaluated, and the optimum sampling bin sizes of PMCS should be researched and proposed.
The sampling processes of raindrops by PMCS can be simulated based on a particle-by-particle Monte-Carlo model; the simulation contains
Assuming that the positions of raindrops arriving at the sampling area in space follow the homogeneous Poisson model [
The arriving time (s) and diameter (mm) of
Assuming that
Consider that not all particles that pass through the sampling volume can be double-imaged by PMCS. The probability that a certain raindrop with a certain size and fall velocity can be fully photographed at least once by the camera in the vertical dimension is defined as
Whether raindrops passing through the sampling volume can be fully photographed twice in a single frame can be estimated as follows:
The total number of raindrops can be calculated as follows:
According to (
The simulation parameters consist of raindrop size distribution, sampling time, sampling volume, and bin size and width. The former is related to the natural precipitation itself; the latter three parameters are related to the instrument, in which the sampling time and sampling volume are fixed; considering the effect of capture probability on DSD measurement of PMCS under different rainfall conditions, we focus on the optimization of sampling bin size and width.
Table
Sampling bin size of different disdrometers.
Disdrometer | Bin size [mm] | Bin number |
---|---|---|
OTT PARSIVEL disdrometer (OTT) | | 32 |
2D video disdrometer (2DVD) | | 50 |
Joss-Waldvogel disdrometer (JWD) | | 20 |
Thies disdrometer (Thies) | | 22 |
Taking the above setting modes of bin size and width as references, we propose four schemes of bin sizes for PMCS, as shown in Table
Four schemes of sampling bin size for PMCS.
Scheme | Bin size [mm] | Bin number |
---|---|---|
Raw output | | 70 |
Interval 1 | | 25 |
Interval 2 | | 35 |
Interval 3 | | 26 |
Interval 4 | | 25 |
Rain-rate can be seen as the macroscopic expression of the raindrop size distribution; the rainfalls are usually categorized into very light, light, moderate, heavy, very heavy, and extreme rainfalls according to their rain-rate [
The Gamma raindrop size distribution parameters for different rain-rate categories.
Category | | | | Rain-rate [mm h−1] |
---|---|---|---|---|
Light rain | 1.31 × 104 | 2.3 | 4.7 | 1.4 |
Moderate rain | 8.01 × 104 | 3.9 | 5.2 | 7.3 |
Heavy rain | 3.32 × 105 | 6.1 | 6.3 | 15.8 |
Rainstorm | 2.85 × 104 | 3.24 | 3.38 | 55.6 |
Based on the above simulation parameters, we simulate the sampling process of PMCS with a specific DSD in a steady rainfall event, and the rain-rate categories are set to 1.4 mm/h, 7.28 mm/h, 15.81 mm/h, and 58.58 mm/h separately, which is used to evaluate the sampling effect of PMCS in different rain-rate categories. The simulation results of raindrop size distribution are shown in Figure
Real DSD and inversed DSDs under the condition of different rain-rate categories.
For the small raindrops, the raw DSD and inversed DSDs from interval 1, interval 3, and interval 4 agree well with the real DSDs, while the inversed DSDs from interval 2 are lower than the real DSD due to the larger intervals between bin sizes in the small-size range. The median raindrops have the largest number density, which contribute most to rain-rate; the number density and width of median raindrops increase with the increasing of rain-rate, and the raw capture DSD is obviously lower than the real DSD because of the unsteady capture probability, which takes on a nonuniform step downward trend, especially in the light rainfall and rainstorm; there is no significant discrepancy between the inversed DSDs from interval 1, interval 2, interval 3, and interval 4, which agree well with real DSD. The number density of large raindrops determines the final shape of DSD, influenced by the capture probability, the raw capture DSD has a significant fluctuation variation, and a certain number of large raindrops are missed; compared with the raw capture DSD, there are good consistencies between the inversed DSDs from 4 interval schemes and real DSD; the reason is that the appropriate sampling bin size and width can reduce the impact of variation of raindrop number on DSD shape. It should be noted that there are also some certain deviations between the inversed DSD and real DSD, especially for the inversed DSDs from interval 3 in the light rainfall and from interval 2 in the rainstorm.
Considering the different consistencies between the inversed DSDs and the real DSD, each sampling process is simulated 1,000 times, and about 35,000, 86,000, 102,000, and 222,000 raindrops are simulated for 4 rain-rate categories separately. Then the relative deviation
The simulation results of
The mean and standard deviation of relative error of
The simulation results of
The mean and standard deviation of relative error of
Table
Mean relative error of parameters in different rain-rate categories.
| Scheme | | | | | | | |
---|---|---|---|---|---|---|---|---|
1.4 | Interval 1 | 0.94 | 0.13 | 3.00 | 3.67 | 28.72 | 0.87 | 0.94 |
Interval 2 | 1.37 | 1.22 | 2.98 | 5.21 | 40.52 | 2.69 | 2.69 | |
Interval 3 | 1.05 | 0.81 | 2.34 | 3.84 | 34.81 | 2.10 | 2.15 | |
Interval 4 | 1.10 | 0.09 | 2.43 | 3.27 | 28.79 | 1.14 | 0.99 | |
| ||||||||
7.28 | Interval 1 | 1.03 | 0.31 | 3.61 | 5.27 | 7.96 | 1.98 | 0.11 |
Interval 2 | 1.38 | 1.45 | 4.07 | 7.08 | 20.45 | 1.14 | 2.07 | |
Interval 3 | 1.06 | 0.71 | 3.19 | 5.22 | 14.13 | 0.41 | 0.96 | |
Interval 4 | 0.86 | 0.29 | 3.18 | 4.24 | 2.36 | 3.55 | 0.83 | |
| ||||||||
15.81 | Interval 1 | 0.86 | 0.44 | 3.32 | 4.43 | 3.77 | 3.92 | 1.54 |
Interval 2 | 1.19 | 0.88 | 4.01 | 6.43 | 11.26 | 0.83 | 0.73 | |
Interval 3 | 0.85 | 0.04 | 3.04 | 4.46 | 2.94 | 2.33 | 0.53 | |
Interval 4 | 0.54 | 1.08 | 2.87 | 3.14 | 9.35 | 4.81 | 2.37 | |
| ||||||||
58.58 | Interval 1 | 0.34 | 1.63 | 2.75 | 1.88 | 6.70 | 7.59 | 3.10 |
Interval 2 | 0.94 | 0.40 | 3.90 | 4.95 | 0.77 | 5.00 | 1.33 | |
Interval 3 | 0.49 | 1.69 | 2.89 | 2.14 | 6.87 | 8.48 | 3.40 | |
Interval 4 | 0.38 | 0.86 | 2.54 | 2.41 | 3.05 | 4.76 | 1.73 |
The accuracy of DSD measurements varies with the different instruments with different sampling principles and different parameters settings, and there is no ideal reference of rainfall field to test and evaluate them. This method based on sampling process simulation can be applied not only for performance evaluation of existing instruments, but also for optimization of developing instruments. Given the above discussions, based on the scheme interval 4 applied in PMCS, the results of field experiments are shown as follows.
A joint observation of PMCS, SL-3 tipping bucket rain Gauge (short for Gauge), and OTT PARSIVEL disdrometer (short for OTT) was launched at Nanjing, China, during June 2015; the rainfalls are mainly convective rainfalls when it is plum rain season, and rainfall observations on the 16th, 17th, 25th, 26th, 27th, 28th, 29th, and 30th of June are collected and discussed. The rain-rate resolution and time resolution of PMCS, Gauge, and OTT are 0.001 mm/h and 1 min, 0.1 mm and 1 min, and 0.001 mm/h and 10 sec. For the convenience of comparative analysis, the data of three instruments are processed in the same time resolution of 1 min, and only the rainfalls heavier than 0.1 mm/h from PMCS and OTT are used; after that the rainfalls obtained by all three instruments have 3,618 minutes’ samples.
The rain-rate and rainfall accumulations observed by PMCS, OTT, and Gauge are as shown in Figure
Rain-rate and rainfall accumulations obtained by three instruments.
In order to quantify the discrepancies between three instruments, the relative deviation bias and absolute deviation ab_bias are defined as follows:
Figure
Comparisons of 3 min average rain-rate between three instruments.
In fact, rain-rates measured by different instruments have certain discrepancies in different rain-rate categories, as shown in Table
Discrepancies of rain-rate between three instruments in different rain-rate categories.
Rain-rate category (mm/h) | OTT-PMCS | PMCS-Gauge | OTT-Gauge | ||||||
---|---|---|---|---|---|---|---|---|---|
| Bias | ab_bias | | Bias | ab_bias | | Bias | ab_bias | |
| 0.90 | 18.3% | 26.3% | 0.69 | 4.5% | 54.3% | 0.76 | 22.8% | 50.5% |
| 0.74 | 14.9% | 19.6% | 0.30 | −4.4% | 24.1% | 0.37 | 10.5% | 21.3% |
| 0.89 | 10.2% | 16.0% | 0.67 | −0.2% | 22.5% | 0.82 | 10.0% | 16.1% |
| 0.93 | 9.4% | 15.3% | 0.89 | 6.9% | 17.8% | 0.96 | 16.2% | 17.4% |
All | 0.98 | 11.7% | 17.7% | 0.96 | 3.3% | 25.0% | 0.99 | 15.0% | 22.7% |
The raindrops size distribution can be described by mass-weighed mean diameter
In order to explore the discrepancy of DSD measured by PMCS and OTT thoroughly, the DSD data are divided into four categories according to the rain-rate; the average DSDs are shown in Figure
Average DSDs measured by PMCS and OTT in four rain-rate categories.
To summarize the above, the DSDs obtained by PMCS and OTT have a good agreement, compared with OTT; PMCS can measure more small/median raindrops and less large raindrops (
Based on the DSD measurements, the moment parameters and their deviations are calculated by (
Deviation of moment parameters between PMCS and OTT in different rain-rate.
Rain-rate | PMCS-OTT | M0 | M1 | M2 | M3 | M4 | M5 | M6 |
---|---|---|---|---|---|---|---|---|
| | 0.63 | 0.67 | 0.76 | 0.78 | 0.73 | 0.63 | 0.52 |
Bias | 22.0% | 20.5% | 19.8% | 22.2% | 29.5% | 42.7% | 62.3% | |
ab_bias | 37.8% | 34.1% | 32.9% | 35.8% | 43.9% | 57.8% | 78.2% | |
| ||||||||
| | 0.55 | 0.68 | 0.76 | 0.75 | 0.69 | 0.62 | 0.57 |
Bias | 2.9% | 6.0% | 8.9% | 13.7% | 21.8% | 33.6% | 49.1% | |
ab_bias | 26.7% | 22.5% | 22.6% | 27.1% | 36.0% | 49.2% | 66.8% | |
| ||||||||
| | 0.34 | 0.54 | 0.69 | 0.76 | 0.74 | 0.71 | 0.67 |
Bias | −10.1% | −2.9% | 2.1% | 8.2% | 17.5% | 31.1% | 49.5% | |
ab_bias | 34.0% | 24.0% | 20.7% | 22.4% | 29.4% | 41.5% | 59.0% | |
| ||||||||
| | 0.43 | 0.54 | 0.67 | 0.76 | 0.78 | 0.75 | 0.71 |
Bias | −25.8% | −15.9% | −5.8% | 6.7% | 22.5% | 41.9% | 64.3% | |
ab_bias | 48.1% | 34.1% | 25.1% | 23.2% | 31.4% | 47.0% | 67.8% | |
| ||||||||
All | | 0.66 | 0.81 | 0.90 | 0.92 | 0.91 | 0.88 | 0.82 |
Bias | −1.7% | 0.9% | 4.0% | 10.5% | 21.8% | 38.2% | 59.1% | |
ab_bias | 36.7% | 28.8% | 24.7% | 25.4% | 32.9% | 46.8% | 66.4% |
Considering that M2, M3, and M4 from PMCS and OTT have better correlation, the M234 order moment method is used to calculate
Peak values, median values, and corresponding probability of probability distributions of
Gamma parameter | Peak value | Probability of peak value | Median value | Probability of median value | ||||
---|---|---|---|---|---|---|---|---|
PMCS | OTT | PMCS | OTT | PMCS | OTT | PMCS | OTT | |
| 4.8 | 4.3 | 0.11 | 0.15 | 6.3 | 5.3 | 0.06 | 0.09 |
| 4.5 | 3.5 | 0.08 | 0.13 | 8.5 | 5.5 | 0.06 | 0.08 |
| 5.5 | 3.5 | 0.10 | 0.13 | 8.5 | 6.5 | 0.05 | 0.07 |
Probability distribution of
Expression of
Instrument | Fitted equation | |
---|---|---|
PMCS | | 0.911 |
PMCS | | 0.969 |
OTT | | 0.914 |
OTT | | 0.931 |
Sampling parameters of different disdrometers have various impacts on the rainfall properties estimation. Aiming at the self-developed precipitation microphysical characteristics sensor (PMCS), the sampling process of raindrops by PMCS based on a particle-by-particle Monte-Carlo model was simulated, the sampling effect of different bin sizes on DSD measurement of PMCS was discussed, and the optimum sampling bin sizes were proposed.
The simulation results of five sampling schemes of bin sizes in four rain-rate categories (light rainfall, moderate rainfall, heavy rainfall, and rainstorm) show that the raw capture DSD has a significant fluctuation variation influenced by the capture probability, and a certain number of large raindrops are missed; compared with the raw capture DSD, there are good consistencies between the inversed DSDs from 4 interval schemes and real DSD; the reason is that the appropriate sampling bin size and width can reduce the impact of variation of raindrop number on DSD shape. The scheme interval 4 has the minimum relative error and absolute error on the whole; therefore, the scheme interval 4 is adopted as the optimal sampling bin sizes of PMCS.
The field measurement of a PMCS, an OTT PARSIVEL disdrometer, and a tipping bucket rain Gauge shows that the rain-rate and rainfall accumulations have good consistencies between PMCS, OTT, and Gauge; the DSDs obtained by PMCS and OTT have a good agreement, compared with OTT, and PMCS can measure more small/median raindrops and less large raindrops (
The authors declare that they have no conflicts of interest.
All authors were involved in designing and discussing the study. This research idea was conceived of by Xichuan Liu and Taichang Gao. The experiments were designed and performed by Xichuan Liu and Xiaojian Shu. The data were analyzed and interpreted by Xichuan Liu and Yuntao Hu. The manuscript was written by Xichuan Liu and Xiaojian Shu.
This work is supported by the National Natural Science Foundation of China (Grant nos. 41327003, 41505135, and 41475020) and the Natural Science Foundation of Jiangsu Province (Grant no. BK20150708). The PMCS was developed with support from Ying EnTe Environment Technique Co., Ltd., Nanjing, China.