A method for retrieving atmospheric precipitation particle size distribution

Abstract

This invention discloses a method for inverting atmospheric precipitation particle spectra, belonging to the field of inversion technology. It addresses the limitations of existing technologies in accurately obtaining inversion parameters for ground and atmospheric microphysical parameters, thus hindering understanding of the formation, development, and variation mechanisms of atmospheric cloud precipitation and consequently preventing accurate prediction and interpretation of atmospheric processes and meteorological disasters. The method includes: acquiring the observed power spectrum using C-band frequency-modulated continuous wave radar and employing denoising methods to remove noise levels; constructing the atmospheric power spectrum based on horizontal wind data acquired from wind profiler radar; constructing the raindrop spectrum using ground raindrop data acquired from a ground raindrop spectrometer and a standardized gamma distribution; and performing ground and atmospheric microphysical parameter inversion based on the above results. This invention is used for inverting and obtaining ground and atmospheric microphysical parameters.

Description

Technical Field

[0001] A method based on the inversion of atmospheric precipitation particle spectrum is used to invert and obtain ground and atmospheric microphysical parameters, belonging to the field of inversion technology. Background Technology

[0002] The atmospheric precipitation particle spectrum typically refers to the size distribution of precipitation particles such as raindrops, snowflakes, and ice pellets in the atmosphere. Changes in the atmospheric precipitation particle spectrum are the most direct description of the complex interactions between precipitation particles in clouds. Furthermore, as the most direct observation target of weather radar, precipitation particles are subject to varying sensitivities from different radar detectors to different sizes of raindrops due to limitations in radar detection principles. Differences in the distribution of the precipitation particle spectrum directly affect the accuracy of radar precipitation estimation. However, existing technologies suffer from the following technical problems:

[0003] Without the ability to accurately obtain inversion parameters of ground and air microphysical parameters, it is impossible to understand the formation, development and change mechanisms of atmospheric cloud precipitation, thus making it impossible to accurately predict and explain atmospheric processes and meteorological disasters. Summary of the Invention

[0004] To address the problems mentioned above, the present invention aims to provide a method based on the inversion of atmospheric precipitation particle spectra, which solves the problem that existing technologies cannot accurately obtain the inversion parameters of ground and atmospheric microphysical parameters, that is, cannot understand the formation, development and change mechanism of atmospheric cloud precipitation, and thus cannot accurately predict and explain atmospheric processes and meteorological disasters.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method based on the inversion of airborne precipitation particle spectra includes the following steps:

[0007] Step 1: Obtain the observed power spectrum based on C-band frequency modulated continuous wave radar, and use a denoising method to remove noise levels. The observed power spectrum refers to the Doppler power spectrum.

[0008] Step 2: Construct the atmospheric power spectrum based on horizontal wind data obtained from wind profiler radar;

[0009] Step 3: Construct raindrop spectra based on ground raindrop data acquired by a ground raindrop spectrometer and standardized gamma distribution;

[0010] Step 4: Based on the results obtained in Steps 1-3, perform ground microphysical parameter inversion and airborne microphysical parameter inversion.

[0011] Furthermore, the specific steps of step 1 are as follows:

[0012] Step 1.1: Obtain the observed power spectrum based on C-band frequency-modulated continuous wave radar, which is the Doppler power spectrum of precipitation particles and atmospheric turbulence after convolution operation. The formula for the Doppler power spectrum is:

[0013] S obs (v, r) = S dsd (vw, r)*S air (v, r) + S noise (v, r)

[0014] Among them, S obs (v, r), S air (v, r), S dsd (vw, r) and S noise (v, r) are the measured Doppler power spectrum, atmospheric turbulent motion Doppler power spectrum, precipitation particle Doppler power spectrum and noise level of the measured Doppler power spectrum, respectively. v, r and w represent radial velocity, Coulomb number and atmospheric vertical motion velocity, respectively.

[0015] Step 1.2: Use denoising methods to remove noise levels from the observed power spectrum. Denoising methods include segmentation, wavelet denoising, and local time-frequency analysis.

[0016] The segmentation method assumes that the noise of the C-band frequency-modulated continuous wave radar follows a central χ distribution with 2N / k degrees of freedom. The observed power spectrum is divided into k segments, the average power spectrum of each segment is calculated, the minimum value is taken as the noise level and removed, thus obtaining the denoised observed power spectrum.

[0017] Wavelet denoising removes wavelet coefficients from the observed power spectrum that contain more than a given amount of noise by wavelet decomposition and filtering, and then recombines the obtained coefficients into a time domain signal to obtain the denoised observed power spectrum.

[0018] Local time-frequency analysis involves analyzing the characteristic histogram and cumulative distribution function of the LT region in the observed power spectrum, and filtering noise in small time-frequency regions that clearly distinguish noise from signal to obtain the denoised observed power spectrum. Here, LT refers to local time-frequency.

[0019] Furthermore, the specific steps of step 2 are as follows:

[0020] Step 2.1: The wind profiler radar uses a 5-beam detection mode to obtain vertical beams, with beams in the north, east, south, and west directions, all tilted at 15°. The vertical beams include wind speed and wind direction components perpendicular to the ground, and the beams in the north, east, south, and west directions respectively obtain the wind speed and wind direction components in the corresponding directions.

[0021] Step 2.2: Based on the average value of the acquired sample data and the horizontal wind obtained in Step 2.1, compare the components of wind speed and wind direction at adjacent times or adjacent heights, regard the data with a difference exceeding a predetermined threshold as outliers, and then replace them with the average value. That is, by judging whether the vertical velocity difference between the vertical beam and the four inclined direction beams and the difference between the two sets of corresponding horizontal winds exceed a given threshold. If the difference exceeds the preset threshold, limit or exclude the abnormal data; otherwise, retain it.

[0022] Step 2.3: Construct an atmospheric power spectrum based on the quality-controlled horizontal wind obtained in Step 2.2.

[0023] Furthermore, the specific steps of Step 3 are as follows:

[0024] Step 3.1: The ground rain gauge obtains rain drop data, including the size of ground rain drops, the falling velocity, and the number of rain drops passing through the sampling area within the unit sampling time.

[0025] Step 3.2: Based on the acquired size of ground rain drops, perform correction on it. The correction formula is:

[0026]

[0027] In the formula: D is the diameter of the corrected ground rain drop, D par is the measured diameter of the ground rain drop;

[0028] Step 3.3: After removing the rain drops with a corrected diameter of 6 - 8 mm, construct a rain drop spectrum based on the standardized gamma distribution. The formula is:

[0029] N(D) = N0D μ exp(-ΛD)

[0030] where, N0 represents the intercept parameter, μ represents the shape factor, and Λ represents the slope parameter.

[0031] Furthermore, the specific steps of Step 4 are as follows:

[0032] Step 4.1: Based on the rain drop data and the rain drop spectrum, perform inversion of ground microphysical parameters to obtain ground microphysical parameters, including ground rain drop number concentration, ground rainfall intensity, ground liquid water content, and ground radar reflectivity factor.

[0033] Step 4.2: Based on the Doppler power spectrum, the atmospheric power spectrum, and the rain drop spectrum, perform inversion of air physical parameters to obtain air physical parameters, including air rain drop number concentration, air rainfall intensity, air liquid water content, air radar reflectivity factor, vertical atmospheric motion, and air rain drop spectrum.

[0034] Furthermore, the specific steps of Step 4.1 are as follows:

[0035] Step 4.11: Calculate the raindrop number concentration based on the ground raindrop falling velocity and the number of raindrops passing through the sampling area per unit sampling time. The formula is:

[0036]

[0037] Where: n ij Let A be the number of raindrops with the corrected droplet diameter located in the i-th scale channel and the falling velocity located in the j-th velocity channel, and Δt be the sampling area of ​​the instrument. i and ΔD i V represents the corrected center diameter of the ground raindrop in the i-th scale channel and the scale interval of that interval. j The center velocity of the j-th velocity channel;

[0038] Step 4.12: Calculate the ground rainfall intensity R1, ground liquid water content LWC1, and ground radar reflectivity factor Z1 based on the raindrop number concentration. The calculation formula is as follows:

[0039]

[0040]

[0041]

[0042] In the formula: ρ is the density of water;

[0043] Step 4.13: Fit the standardized gamma distribution parameters based on the raindrop spectrum using the step moment method, incorporating the step moment M of the raindrop spectrum during fitting. n The parameters N0, μ, and Λ of the standardized gamma distribution are estimated using the 2nd, 4th, and 6th moments of the raindrop spectrum, as shown in the following formula:

[0044]

[0045] Where n represents the nth moment;

[0046] Step 4.14, based on the step distance M n The mass-weighted average diameter D1 of raindrops on the ground was obtained. m The formula is:

[0047]

[0048] Step 4.15: Based on the mass-weighted average diameter D1 m The normalized concentration N1 was obtained. w The calculation formula is:

[0049]

[0050] Where w represents the vertical velocity of atmospheric motion.

[0051] Furthermore, the specific steps of step 4.2 are as follows:

[0052] Step 4.21: Based on the atmospheric power spectrum, use the Fourier deconvolution algorithm to eliminate atmospheric spectral broadening in the denoised Doppler power spectrum;

[0053] Step 4.22: Construct the initial altitude precipitation particle power spectrum based on the raindrop spectrum, that is, the precipitation particle Doppler power spectrum S under static and stable atmospheric conditions. dsd (v, r) is represented by the raindrop spectral distribution N dsd (D) and backscattering cross section Represented as:

[0054]

[0055] Among them, S dsd (v, r) represents the Doppler power spectrum of precipitation particles, i.e., the power spectrum of precipitation particles at initial height, where λ is the radar wavelength. 5 0.42cm, |K w | 2 Where is the dielectric constant. This represents the relationship between the final velocity of the falling droplet and the diameter of the raindrop, where D is the corrected raindrop diameter.

[0056] When the wavelength is 5.42 cm, precipitation particles undergo Rayleigh scattering. If these particles are considered spherical, the radar backscattering cross section is proportional to the sixth power of the particle diameter. It can be represented as:

[0057]

[0058]

[0059] Where, represents the Euler totient function, μ represents the shape factor, Λ represents the slope parameter, and the integral extends from 0 to infinity. During the inversion process, the raindrop spectrum is constrained by the minimum and maximum raindrop diameters. D m This represents the mass-weighted average diameter of raindrops on the ground.

[0060]

[0061]

[0062] Both the aerial rainfall intensity R and the atmospheric liquid water content LWC are the third moments of the aerial raindrop size distribution:

[0063]

[0064]

[0065]

[0066] Where ΔD represents the rate of change of the diameter of raindrops in the air, V(D) represents the relationship between the falling velocity of raindrops in the air and their diameter, p0 represents the atmospheric density at the ground, and p h The atmospheric density at ground level is represented by h, where h is the observation altitude.

[0067] Step 4.23: Based on the results obtained in Step 4.21, obtain the atmospheric motion at the initial altitude and remove the distribution differences between adjacent particles in the power spectrum of precipitation at the initial altitude.

[0068] Step 4.24: The airborne radar reflectivity factor Z is the zeroth moment of the raindrop spectrum, and the formula is:

[0069]

[0070] Substitute:

[0071]

[0072] N(D;N w D m ,μ)=N w f(D;D m ,μ)

[0073]

[0074] The reflectivity of pure precipitation particles under Rayleigh scattering, i.e., the airborne radar reflectivity factor Z, is obtained as follows:

[0075]

[0076] Where Δv represents the rate of change of the falling velocity of raindrops in the air;

[0077] Step 4.25: Based on the results obtained in Step 4.23, the raindrop spectrum of each distance library is normalized one by one, and the vertical atmospheric motion is obtained by minimizing the cost function.

[0078] The normalization formula is:

[0079] The cost function to be minimized is:

[0080] Step 4.26: Based on the results obtained in Steps 4.23 and 4.25, deconvolve to obtain the aerial raindrop spectrum.

[0081] Compared with the prior art, the beneficial effects of this invention are as follows:

[0082] This invention, based on corrected raindrop spectral data, uses a standardized gamma raindrop spectral distribution to establish a real-time raindrop spectral distribution model, providing initial values ​​for the inversion of atmospheric precipitation microphysical parameters. Under this premise, it utilizes vertical pointing radar data after spectral broadening, extracting the corresponding differences in radar power spectrum caused by the evolution of atmospheric raindrop spectral velocity through reflectivity factor decomposition. Then, it obtains atmospheric vertical velocity (i.e., vertical atmospheric velocity) based on the normalized power spectrum. Based on the precipitation power spectrum after removing atmospheric vertical velocity, it uses the relationship between particle diameter and velocity to obtain the atmospheric raindrop spectral distribution. This invention can accurately obtain inversion parameters for ground and atmospheric microphysical parameters, enabling effective understanding of the formation, development, and variation mechanisms of atmospheric cloud precipitation, thereby accurately predicting and interpreting atmospheric processes and meteorological disasters. Attached Figure Description

[0083] Figure 1 This is the process for inverting microphysical parameters in the air in this invention;

[0084] Figure 2 This is a schematic diagram illustrating an example of layered cloud inversion in this invention;

[0085] Figure 3 This is an example of the inversion of a layered hybrid cloud in this invention;

[0086] Figure 4 This is an example of the inversion of a convective cloud in this invention;

[0087] Figure 5 This is a scatter plot for comparison and verification in this invention. Detailed Implementation

[0088] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.

[0089] Observation equipment:

[0090] C-band frequency-modulated continuous wave radar (C-band FMCW) differs from other weather radars in that it uses a continuous wave system to modulate the frequency of its transmitted signal. It transmits electromagnetic waves by gradually increasing the transmission frequency from low to high, a process achieved by injecting a linearly frequency-modulated signal into the frequency source. When the electromagnetic wave signal encounters a target and is reflected back, the difference between the received signal frequency and the transmitted frequency is the Doppler shift corresponding to the target's relative velocity. By measuring this Doppler shift, the target's velocity can be determined. Simultaneously, the FMCW radar can also use changes in the received Doppler shift to determine the target's position. Specifically, when the radar transmits a signal to the target, it records the time of transmission. When it receives the signal reflected back from the target, it also records the time of reception. By calculating the time difference between the transmitted and received signals, the signal propagation time can be determined, thereby determining the distance between the target and the radar. In summary, FMCW radar can achieve high-precision target detection. Its advantages include excellent ranging and velocity measurement performance, the ability to detect targets at long distances and in weak signal environments, and the ability to acquire target position, velocity, and azimuth information in real time. It also offers high resolution for detecting meteorological phenomena such as tropospheric and strong convection phenomena. Furthermore, the C-band's narrow frequency range and short wavelength allow it to penetrate clouds effectively in the atmosphere, enabling the detection of internal cloud physical processes with good results. This makes it possible to detect complex microphysical processes within real clouds.

[0091] The radar used in this study has high temporal and spatial resolutions of 3s and 30m, respectively, and a detection altitude range of 0.03–15km, essentially covering the entire formation and development of precipitation processes in South China with no blind spots, sufficient to ensure continuous observation of precipitation processes at all altitudes. Furthermore, the radar's minimum detectable signal power is -166dBm, significantly better than the -115dBm of conventional weather radars, enabling it to better reflect detailed information during precipitation processes.

[0092] A wind profiler radar is an instrument that uses radar technology to measure meteorological and climatic elements. It can monitor and measure horizontal and vertical wind speeds in real time across different altitude ranges, and can also retrieve atmospheric parameters such as temperature, humidity, and vorticity. Compared to traditional weather balloons, it provides more comprehensive information for various time periods. The principle of wind profiler radar is based on the Doppler effect to measure wind speed in the atmosphere. When the radar emits a stable frequency electromagnetic wave into the upper atmosphere, the frequency of the echo undergoes a Doppler shift due to the wind field, thus reflecting the wind speed in the atmosphere. Similarly, wind profiler radar can use the Doppler effect to retrieve other atmospheric parameters.

[0093] The wind profiler radar has an altitude resolution of 60 meters and 120 meters in different detection modes. It also has a temporal resolution of 6 minutes and a detection range covering 0.1 to 2.86 kilometers and 0.99 to 5.55 kilometers, respectively. In addition, the radar can provide several basic observational data products, including horizontal wind, vertical wind, radial wind, and refractive index structure constant. This data can be used to monitor weather changes over a large area in real time and provide detailed atmospheric parameter information with high horizontal and vertical resolution.

[0094] The working principle of a ground-based raindrop spectrometer is to use two laser beams to strike raindrop particles. The light reflected back from the raindrop particles is received, and the mass and velocity of the raindrop particles are analyzed using time-resolved techniques and echo intensity. Therefore, the PARSIVEL laser raindrop spectrometer can not only monitor the size, velocity, and quantity of raindrops in real time, but also obtain accurate raindrop spectra. By simultaneously monitoring the size, velocity, and quantity of raindrops, it can obtain a more refined raindrop spectral distribution, which has significant application value in weather forecasting and climate research. The sampling object is the diameter and velocity information of all particles within a region (18cm × 3cm), with a time resolution of 1 minute. The instrument's signal processor divides the particle diameter and velocity into 32 channels, retrieving rainfall amount, rainfall intensity, reflectivity intensity, and mass-weighted average diameter (mass / volume-weighted average diameter). m Normalized intercept parameter N w Parameters such as these.

[0095] Data quality control:

[0096] Data quality control for C-band frequency-modulated continuous wave radar primarily focuses on the quality control of Doppler power spectrum data. Doppler power spectrum data is obtained by processing the Doppler frequency shift of the radar echo signal (i.e., the frequency change caused by the velocity of the meteorological target). In radar Doppler mode, the radar transmits a continuous series of pulses that scan the meteorological target. After obtaining the echo signal, Doppler processing is used to extract the velocity and power spectrum information of the meteorological target. Therefore, meteorological radar Doppler power spectrum data is the most fundamental data for radar; specific parameters such as echo intensity, radial velocity, and velocity spectral width can all be calculated from Doppler power spectrum data. Data quality control for the Doppler power spectrum mainly involves two aspects: noise level removal and power spectrum broadening correction.

[0097] Noise level is the main component that needs to be removed from the Doppler power spectrum. Commonly used denoising methods include segmentation, wavelet denoising, and local time-frequency noise filtering. Segmentation assumes that C-band frequency-modulated continuous wave radar noise follows a central χ distribution with 2N / k degrees of freedom. The observed power spectrum is divided into k segments, and the average power spectrum of each segment is calculated. The minimum value is taken as the noise level and removed. Wavelet denoising removes wavelet coefficients from the observed power spectrum that exceed a given noise level through wavelet decomposition and filtering. The obtained coefficients are then recombined into a time-domain signal to obtain the denoised observed power spectrum. Local time-frequency noise processing combines time-domain, frequency-domain, and local area information, resulting in a better reduction of noise level. Local time-frequency analysis analyzes the characteristic histogram and cumulative distribution function of the LT region in the observed power spectrum. Noise filtering is performed on small time-frequency regions that clearly distinguish noise from signal, yielding the denoised observed power spectrum. Here, LT refers to local time-frequency. Among the three methods, segmentation is preferred due to its high stability, accuracy, and fast processing efficiency. This method removes noise while retaining all information.

[0098] To obtain a more accurate raindrop spectral distribution, eliminating the influence of atmospheric spectral broadening on the shape of the Doppler power spectrum is essential. Atmospheric turbulence power spectrum convolves with precipitation power spectrum, increasing the variance of the observed Doppler power spectrum and consequently causing spectral broadening. A direct deconvolution algorithm was employed for spectral broadening correction. Based on quality-controlled wind profiler radar observations of horizontal wind data, we established the atmospheric power spectrum and used a Fourier deconvolution algorithm to eliminate the influence of atmospheric spectral broadening in the C-band frequency-modulated continuous wave radar observations of the Doppler power spectrum. This method successfully eliminated the influence of atmospheric turbulence power spectrum on spectral broadening, thus enabling the acquisition of a more accurate raindrop spectral distribution.

[0099] Wind profiler radar data can be used to acquire atmospheric horizontal wind data with high resolution, but this data can be affected by environmental noise, interference, and problems with the radar itself. Especially during precipitation periods, the data quality of wind profiler radar is affected by many factors, including atmospheric turbulence, precipitation, and turbulent shear, thus requiring more stringent data quality control. The wind profiler radar used in this study employs a common 5-beam detection mode, which has advantages in both spatial and temporal resolution. Specifically, the 5-beam detection mode includes the following five beams: the vertical beam obtains wind speed and direction information perpendicular to the ground, serving as the basis for the other beams; the north, east, south, and west beams (each with a tilt angle of 15°) obtain the wind speed and direction components in their respective directions. By simultaneously collecting data from these five beams and performing appropriate processing and analysis, more comprehensive and accurate wind field information can be obtained.

[0100] The quality control of wind profiler radar data employs a consistent averaging method. Its basic idea is to use the average value of sample data as a reference, comparing wind speed and direction data at adjacent times or altitudes. Data with differences exceeding a predetermined threshold are considered outliers, and these outliers are then replaced with the average value. Specifically, this involves judging whether the vertical velocity difference between the vertical beam and the four tilting beams, and the difference between the two corresponding sets of horizontal winds, exceed a given threshold. If the difference exceeds the preset threshold, outlier data is restricted or excluded; otherwise, it is retained. This process is repeated until all data has passed quality control.

[0101] Ground precipitation measurements use the OTTT Parsivel to measure raindrop size and falling velocity. However, raindrops are affected by deformation during their fall. An isolated, relatively large raindrop will exhibit significant flattening as it falls with its final velocity, becoming an ellipsoid rather than a streamlined conical shape, often described as a "teardrop" shape. This leads to an overestimation of the raindrop size. Therefore, deformation correction is required, and the formula is as follows:

[0102]

[0103] In the formula: D is the corrected equivalent diameter (mm); D par The measured diameter (mm) is given. Raindrops with a diameter of 6-8 mm are generally considered unstable in nature (depending on turbulence intensity), so this data will also be discarded.

[0104] Ground microphysical parameter inversion

[0105] Ground microphysical parameter inversion is based on Parsivel's observational data. The observational data represents the number of raindrops passing through the sampled area per unit sampling time. Therefore, the raindrop number concentration N(m²) is calculated. -3 ·mm -1 The calculation is as follows:

[0106]

[0107] Where: n ij Let A be the number of raindrops whose diameter is located in the i-th scale channel and whose falling velocity is located in the j-th velocity channel; A is the instrument sampling area, 54 cm. 2 ; Δt is the sampling time interval, 60s; D i and ΔD i V represents the center diameter (mm) of the i-th scale channel and the scale interval (mm) of that interval; j The center velocity (m·s) of the j-th velocity channel -1 ).

[0108] Surface rainfall intensity R1 (mm·h) -1), Ground liquid water content LWC1 (mg·m -3 The ground radar reflectivity factor Z1 can be calculated using the following formula:

[0109]

[0110]

[0111]

[0112] In the formula: ρ is the density of water (g·cm³) -1 ).

[0113] Currently, the gamma distribution is widely used to describe the spectrum of raindrops on the ground and in the air. Based on raindrop spectrum data, the formula can be expressed as:

[0114] N(D) = N0D μ exp(-ΛD) (3-5)

[0115] N0 is the intercept parameter (m -3 ·mm -μ-1 μ is the shape factor; is the slope parameter (mm). -1 The gamma distribution parameters were fitted using the step-moment method, with the raindrop spectral step M introduced during the fitting process. n Its subscript represents the nth moment. The parameters (N0, μ, A) of the gamma distribution can be estimated using the 2nd, 4th, and 6th moments of the observations, and the calculation formula is as follows:

[0116]

[0117] Therefore, the mass-weighted average diameter D m (mm) can be represented as:

[0118]

[0119] Normalized concentration N W (mm -1 ·m -3 )for

[0120]

[0121] Inversion of microphysical parameters in the air

[0122] The returned signals obtained by various precipitation detection devices in practical applications are actually caused by the combined effects of the scattered signals from precipitation particles and the scattered signals from atmospheric turbulence. The measured power spectrum obtained using C-FMCW radar technology is essentially the Doppler power spectrum of precipitation particles and atmospheric turbulence after convolution. The corresponding mathematical formulas are as follows.

[37] :

[0123] S obs (v, r) = S dsd (vw, r)*S air (v, r) + S noise (v, r) (3-9)

[0124] In the formula: S obs (v, r)[(mm) 6 m -3 (ms) -1 ) -1 ]、S air (v, r), S dsd (vw, r) and S noise (v, r) represent the measured Doppler power spectrum, the atmospheric turbulence motion Doppler power spectrum, the precipitation particle Doppler power spectrum, and the measured Doppler power spectrum noise, respectively. Variables v, r, and w represent the radial velocity and the vertical atmospheric motion velocity, respectively. We employed a preprocessing method for the DC component and noise level of the observed Doppler power spectrum. The noise level refers to the average power of all radar noise in the Doppler power spectrum, and this value varies with each range of the radar. Furthermore, due to the influence of atmospheric turbulence and vertical atmospheric motion, the Doppler power spectrum tends to shift laterally, which may lead to an underestimation or overestimation of the retrieved raindrop spectrum. For example, detailed error statistical analysis shows that when the vertical velocity deviation of the turbulence is 1 ms... -1 In raindrop spectrum inversion, the error in rainfall rate can be as high as 50%. Therefore, we cannot directly obtain the distribution of raindrop spectrum and perform quantitative analysis.

[0125] This paper presents an algorithm for inverting atmospheric vertical motion. In this process, we need to consider the influence of precipitation, as strong atmospheric vertical motion promotes various evolutionary processes of precipitation particles, thus affecting the distribution of the precipitation particle power spectrum along the Doppler velocity axis. This can lead to an underestimation or overestimation of the obtained raindrop spectrum. Therefore, we employ a novel principle to extract atmospheric vertical velocity—analyzing the changes in the precipitation particle power spectrum by comparing the differences between the power spectra of precipitation particles in two adjacent distance databases. This difference is caused by the evolution of atmospheric vertical velocity and the raindrop spectrum during descent. By extracting atmospheric vertical velocity, we can mitigate this influence and improve the accuracy of raindrop spectrum inversion.

[0126] Under stable atmospheric conditions, the Doppler power spectrum of precipitation particles S dsd (v, r) can be represented by the raindrop spectral distribution N dsd (D) and backscattering cross section Represented as:

[0127]

[0128] In the formula: λ is the radar wavelength, 5.42 cm; |K w | 2 The dielectric constant is 0.93; This indicates the relationship between the final velocity of the falling droplet and the diameter of the raindrop.

[0129] At a wavelength of 5.42 cm, precipitation particles undergo Rayleigh scattering, assuming they are spherical. In this case, the radar backscattering cross section is proportional to the sixth power of the particle diameter. It can be represented as:

[0130]

[0131] If the raindrop spectrum is represented by a three-parameter gamma distribution:

[0132] N(D) = N0D μ exp(-ΛD) (3-12)

[0133] Where, μ(mm) -1 ), Λ(mm) -1 ) and N0 (mm -1-μ m -3 ) represent the shape, slope, and intercept parameters of the gamma distribution, respectively.

[0134] Willis (1984) gave another expression for the DSD, used to compare raindrop spectra with different liquid water contents, called the normalized gamma raindrop spectral distribution, expressed as:

[0135]

[0136] In the formula, N is w Normalized number concentration parameter, D m (mm) is the mass-weighted average diameter, and μ is the gamma shape factor. " represents the Euler totient function. Its integral extends from 0 to infinity. In fact, the raindrop spectrum is subject to a minimum (D) during the inversion process. min ) and maximum (D max Limitations on raindrop diameter.

[0137] Precipitation parameters can be calculated using the size distribution of raindrops. Aerial rainfall rate R (mm·h) -1 ) and atmospheric liquid water content LWC (g·m -3 All of these are the third moments of the droplet size distribution:

[0138]

[0139]

[0140]

[0141]

[0142] Under ideal Rayleigh backscattering conditions, different parameters exhibit varying sensitivities to raindrop size distribution. For instance, reflectivity is more easily affected by large raindrops, but their contribution to LWC is smaller compared to small raindrops under the same reflectivity conditions; meanwhile, cloud droplets also significantly contribute to LWC.

[39] .

[0143] At this point, the raindrop spectrum can also be modeled using a normalized gamma distribution, and the raindrop spectrum distribution can also be written as follows:

[0144] N(D;N w D m ,μ)=N w f(D;D m ,μ) (3-18)

[0145] in

[0146]

[0147] The precipitation particle power spectrum is calculated using formula (3-18) based on the raindrop size distribution:

[0148]

[0149] In the formula, D 6 Let denot be the backscattering cross section of a raindrop under assumed Rayleigh scattering, and ΔD and Δv represent the rates of change of the raindrop diameter and falling velocity, respectively.

[0150] At this point, the relationship between the falling speed of raindrops and their diameter can be expressed as:

[0151]

[0152] In the formula, at an observation height of h, the atmospheric density at the ground is ρ. h ρ0 represents the atmospheric density at the ground surface. The ratio of the two is... It is influenced by many factors, including ground temperature, the rate of change of atmospheric temperature with altitude, and the observation altitude. Under low-altitude conditions, this ratio can be simplified into a function that depends only on altitude.

[0153] At this moment, the falling velocity of the raindrops in the air is the first moment of the pure raindrop spectrum, which can be expressed as:

[0154]

[0155] Meanwhile, the reflectivity Z is the zeroth moment of the raindrop spectrum, which can be expressed as:

[0156]

[0157] Substituting into formulas (3-18), (3-19), and (3-20), we can transform them into:

[0158]

[0159] The above formula represents the reflectivity of pure precipitation particles during Rayleigh scattering.

[0160] Because the reflectance factor Z(r)(mm -6 m -3 ) and D m (mm) is measured using different units. Take the logarithm of both sides of formula (3-25), Z dB (r)(dBZ) can be decomposed into the number concentration function Nw dB (dB) and particle spectral shape number That is, in the following form:

[0161]

[0162]

[0163]

[0164]

[0165] The reflectivity shape factor is equivalent to the normalized backscattered reflectivity, i.e., N. w Reflectivity = 1. Because N w These are canceled out in equation (3-29), therefore the shape function and the raindrop descent velocity depend only on the shape factor μ and the average mass-weighted diameter D. m .

[0166] It can also be expressed in the following form:

[0167]

[0168] Where f is the radar operating frequency.

[0169] Since the difference in Doppler velocity spectra between adjacent distances is mainly affected by turbulence and raindrop spectral variations during descent, this principle can be used to extract the vertical atmospheric velocity. After normalizing the two Doppler power spectra, calculating their difference yields the position of the spectrum on the Doppler velocity axis. This position reflects the sum of the vertical atmospheric motion and the difference in raindrop velocity.

[0170] The raindrop spectrum for each distance reservoir was normalized one by one.

[0171]

[0172] After confirming the difference in raindrop velocity, Know The difference should depend on the vertical atmospheric motion. The vertical atmospheric motion can be obtained by minimizing the cost function (CF).

[0173]

[0174] When the CF value reaches its minimum, vertical atmospheric motion can be considered completely eliminated. The absolute value of vertical atmospheric motion can be calculated by multiplying the number of movements by the velocity resolution. By shifting the power spectrum to the right to obtain the minimum CF, the airflow can be determined to be rising or descending.

[0175] To more intuitively illustrate the inversion results, we selected stratus, stratocumulus-mixed clouds, and convective clouds from typical precipitation clouds in a four-day cumulative precipitation event in South China in June 2020, and chose one radial inversion example for each. In this process, we used downward as the positive direction to describe atmospheric motion, such as... Figure 2 As shown.

[0176] The case study of stratocumulus clouds was selected from the Doppler power spectrum of the LCT at 14:00:14 on June 8, 2020. For example... Figure 2 As shown in Figure 2a, the area with significantly increased reflectivity at an altitude of 5 km marks the height of the bright band. Below this height, reflectivity is low, exhibiting clear stratiform cloud characteristics. Figure 2b shows the precipitation power spectrum after removing vertical atmospheric motion, with black and red lines indicating the mean vertical atmospheric motion and mean particle descent velocity, respectively. Overall, the mean vertical atmospheric motion is relatively stable, showing weak downward movement, consistent with the understanding that stratiform clouds appear during the dissipation phase of a precipitation system and exhibit weak downward movement. The raindrop spectrum distribution with altitude is shown below. Figure 2 As shown in 'c', the overall situation is relatively stable.

[0177] The case study of stratified mixed clouds was selected from the Doppler power spectrum of the LCT at 07:00:21 on June 9, 2020. (Example:...) Figure 3 As shown in a, the area with significantly increased reflectivity at an altitude of 5km marks the height of the bright band. Below the height of the bright band, the reflectivity remains strong, indicating both convective and stratiform cloud characteristics. Figure 3 In the figure, 'b' represents the precipitation power spectrum after removing vertical atmospheric motion. Overall, the average vertical atmospheric motion is relatively stable and shows strong downward movement. The distribution of raindrop spectra with altitude is as follows: Figure 3As shown in c, the overall relative number concentration is greater than that of stratocumulus.

[0178] The convection case was selected from the Doppler power spectrum of the LCT at 06:05:07 on June 9, 2020. For example... Figure 4 As shown in a, there is no obvious bright band structure overall. Compared with other cases, the reflectivity is not significantly reduced at the height of the bright band, which shows obvious convection characteristics. Figure 4 In the figure, 'b' represents the precipitation power spectrum after removing vertical atmospheric motion. Overall, the average vertical atmospheric motion shows an upward trend in the upper layer and a downward trend in the lower layer, combined with the overall tilt of the system, demonstrating the alternating characteristics of rising and sinking airflows in convection, consistent with previous understanding. The distribution of raindrop spectra with height is shown below. Figure 4 As shown in c, the overall high concentration of large raindrops is consistent with Raut's conclusion.

[0179] This study employs an inversion algorithm that leverages the vertical continuity of the radar spectrum to eliminate the influence of vertical atmospheric motion on the results. Ground-based raindrop spectrometers can measure the distribution of precipitation particles of different sizes on the ground, while the inversion of airborne microphysical parameters obtains microphysical parameters at different altitudes through the vertical continuity of the radar spectrum. To verify the conclusions, we compared and analyzed ground-based raindrop spectrometer data and airborne data at a height of 150 meters, selecting reflectivity factor and N... w A comparison was made to verify the rationality of the inversion method in the microphysical parameter inversion process and the availability of radar data. The formula derivation shows that N w This will be canceled out in formula (3-29), therefore N is chosen. w Making comparisons is reasonable. Figure 3-5 Display reflectivity factor and logN w The comparison results of the two parameters show that the correlation of the reflectivity factor is 0.95, the root mean square error is 2.12, and logN... w The correlation was 0.92, and the root mean square error was 0.073. Overall, these results are in line with expectations, indicating that the previous data correction and inversion algorithms used are reasonable and verifying their reliability.

[0180] Furthermore, logN was observed w The inversion results underestimated the concentration at fractional concentrations and overestimated it at high fractional concentrations, possibly due to an inappropriate range of raindrop diameters (0.25 mm–6 mm). However, since raindrops larger than 6–8 mm in diameter are unstable in nature, the specific critical value depends on the level of turbulence in the airflow.

[44] Therefore, it is difficult to give an accurate boundary.

[0181] This paper focuses on the algorithm for inverting microphysical parameters from the ground and air, emphasizing the algorithm based on the joint inversion of atmospheric dynamic parameters and microphysical parameters using ground raindrop spectrum data, wind profiler radar, and C-band frequency-modulated continuous wave radar. The inclusion of ground raindrop spectrum data allows the algorithm to move away from the assumption that the near-surface atmospheric vertical velocity is zero, further improving data reliability. Simultaneously, horizontal wind data from the wind profiler radar is used to simulate the atmospheric turbulence power spectrum, and deconvolution is applied to the precipitation power spectrum observed by the C-band radar to eliminate the influence of atmospheric spectral broadening. Comparative validation data comes from a four-day continuous precipitation event in South China in June 2020. The results show that real-time inversion of the airborne raindrop spectrum based on radar data and ground raindrop spectrometer data is feasible. This undoubtedly promotes research on radar-based precipitation estimation and model parameterization.

[0182] The above are merely representative embodiments among the many specific applications of this invention, and do not constitute any limitation on the scope of protection of this invention. All technical solutions formed by transformation or equivalent substitution fall within the scope of protection of this invention.

Claims

1. A method for inverting the particle spectrum of atmospheric precipitation, characterized in that, Includes the following steps: Step 1: Obtain the observed power spectrum based on C-band frequency modulated continuous wave radar, and use a denoising method to remove noise levels. The observed power spectrum refers to the Doppler power spectrum. Step 2: Construct the atmospheric power spectrum based on horizontal wind data obtained from wind profiler radar; Step 3: Construct raindrop spectra based on ground raindrop data acquired by a ground raindrop spectrometer and standardized gamma distribution; Step 4: Based on the results obtained in Steps 1-3, perform ground microphysical parameter inversion and airborne microphysical parameter inversion; the airborne microphysical parameter inversion includes the following steps: Step 4.2: Based on the Doppler power spectrum, atmospheric power spectrum and raindrop spectrum, perform airborne microphysical parameter inversion to obtain airborne microphysical parameters, including airborne raindrop number concentration, airborne rainfall intensity, airborne liquid water content, airborne radar reflectivity factor, vertical atmospheric motion and airborne raindrop spectrum; The specific steps of step 4.2 are as follows: Step 4.21: Based on the atmospheric power spectrum, use the Fourier deconvolution algorithm to eliminate atmospheric spectral broadening in the denoised Doppler power spectrum; Step 4.22: Construct the initial altitude precipitation particle power spectrum based on the raindrop spectrum, i.e., the precipitation particle Doppler power spectrum under static and stable atmospheric conditions. Raindrop spectral distribution and backscattering cross section Represented as: in, This represents the Doppler power spectrum of precipitation particles, specifically the power spectrum of precipitation particles at initial altitude. The radar wavelength is 5.42 cm. Where is the dielectric constant. This indicates the relationship between the final velocity of the falling droplet and the diameter of the raindrop. The corrected raindrops; When the wavelength is 5.42 cm, precipitation particles undergo Rayleigh scattering. If these particles are considered spherical, the radar backscattering cross section is proportional to the sixth power of the particle diameter. It can be represented as: Where Γ represents the Euler totient function and μ represents the shape factor. The slope parameter is represented by the integral extending from 0 to infinity. During the inversion process, the raindrop spectrum is limited by the minimum and maximum raindrop diameters. This represents the mass-weighted average diameter of raindrops on the ground. Rainfall intensity and the water content of liquid water in the air These are all third moments representing the size distribution of raindrops in the air: in, This represents the rate of change of the diameter of raindrops in the air. This indicates the relationship between the falling speed and diameter of raindrops. The density of the atmosphere representing the ground. This represents the atmospheric density at the ground level at an observation height of h, where h is the observation height. Step 4.23: Based on the results obtained in Step 4.21, obtain the atmospheric motion at the initial altitude and remove the distribution differences between adjacent particles in the power spectrum of precipitation at the initial altitude. Step 4.24: The airborne radar reflectivity factor Z is the zeroth moment of the raindrop spectrum, and the formula is: Substitute: The reflectivity of pure precipitation particles under Rayleigh scattering, i.e., the airborne radar reflectivity factor Z, is obtained as follows: in, These represent the rates of change of the falling velocity of raindrops in the air; Step 4.25: Based on the results obtained in Step 4.23, the raindrop spectrum of each distance library is normalized one by one, and the vertical atmospheric motion is obtained by minimizing the cost function. The normalization formula is: ; The cost function to be minimized is: Step 4.26: Based on the results obtained in Steps 4.23 and 4.25, deconvolve to obtain the aerial raindrop spectrum.

2. The method according to claim 1, characterized in that, The specific steps of step 1 are as follows: Step 1.1: Obtain the observed power spectrum based on C-band frequency-modulated continuous wave radar, which is the Doppler power spectrum of precipitation particles and atmospheric turbulence after convolution operation. The formula for the Doppler power spectrum is: in, , , and These are the measured Doppler power spectrum, the atmospheric turbulent motion Doppler power spectrum, the precipitation particle Doppler power spectrum, and the noise level of the measured Doppler power spectrum, respectively. , , These represent radial velocity, Coulomb number, and atmospheric vertical velocity, respectively. Step 1.2: Use denoising methods to remove noise levels from the observed power spectrum. Denoising methods include segmentation, wavelet denoising, and local time-frequency analysis. The segmentation method assumes that the noise of the C-band frequency-modulated continuous wave radar follows a central χ distribution with 2N / k degrees of freedom. The observed power spectrum is divided into k segments, the average power spectrum of each segment is calculated, the minimum value is taken as the noise level and removed, thus obtaining the denoised observed power spectrum. Wavelet denoising removes wavelet coefficients from the observed power spectrum that contain more than a given amount of noise by wavelet decomposition and filtering, and then recombines the obtained coefficients into a time domain signal to obtain the denoised observed power spectrum. Local time-frequency analysis involves analyzing the characteristic histogram and cumulative distribution function of the LT region in the observed power spectrum, and filtering noise in small time-frequency regions that clearly distinguish noise from signal to obtain the denoised observed power spectrum. Here, LT refers to local time-frequency.

3. The method according to claim 1, characterized in that, The specific steps of step 2 are as follows: Step 2.1: The wind profiler radar uses a 5-beam detection mode to obtain vertical beams, with beams in the north, east, south, and west directions, all tilted at 15°. The vertical beams include wind speed and wind direction components perpendicular to the ground, and the beams in the north, east, south, and west directions respectively obtain the wind speed and wind direction components in the corresponding directions. Step 2.2: Based on the average value of the acquired sample data, and the horizontal wind obtained in Step 2.1, compare the wind speed and direction components at adjacent times or adjacent heights. Data with differences exceeding a predetermined threshold are considered outliers and then replaced with the average value. That is, by judging whether the difference in vertical velocity between the vertical beam and the four tilt beams and the difference in the two sets of corresponding horizontal winds exceeds a given threshold, if the difference exceeds the preset threshold, the outlier data is restricted or excluded; otherwise, it is retained. Step 2.3: Construct the atmospheric power spectrum based on the quality-controlled horizontal wind obtained in Step 2.

2.

4. The method according to claim 3, characterized in that, The specific steps of step 3 are as follows: Step 3.1: The ground raindrop spectrometer acquires raindrop data, including the size of ground raindrops, falling velocity, and the number of raindrops passing through the sampling area per unit sampling time; Step 3.2: Correct the obtained ground raindrop size using the following formula: In the formula: D is the corrected diameter of the raindrop on the ground. This represents the measured diameter of raindrops on the ground. Step 3.3: After removing raindrops with a corrected diameter of 6-8 mm, construct the raindrop spectrum based on the normalized gamma distribution, using the following formula: in, The intercept parameter is represented by μ, and the shape factor is represented by μ. This represents the slope parameter.

5. The method according to claim 4, characterized in that, The specific steps for inverting ground microphysical parameters in step 4 are as follows: Step 4.1: Based on raindrop data and raindrop spectrum, perform ground microphysical parameter inversion to obtain ground microphysical parameters, including ground raindrop number concentration, ground rainfall intensity, ground liquid water content, and ground radar reflectivity factor.

6. The method according to claim 5, characterized in that, The specific steps of step 4.1 are as follows: Step 4.11: Calculate the raindrop number concentration based on the ground raindrop falling velocity and the number of raindrops passing through the sampling area per unit sampling time. The formula is: In the formula: The corrected number of raindrops with a diameter in the i-th scale channel and a falling velocity in the j-th velocity channel is given by A, where A is the instrument sampling area and ∆t is the sampling time interval. and Let be the corrected center diameter of the ground raindrop in the i-th scale channel and the scale interval of that scale channel. The center velocity of the j-th velocity channel; Step 4.12: Calculate the surface rainfall intensity based on raindrop number concentration. Ground liquid water content and ground radar reflectivity factor The calculation formula is: In the formula: ρ is the density of water; Step 4.13: Fit the standardized gamma distribution parameters based on the raindrop spectrum using the step moment method, incorporating the step moment of the raindrop spectrum during the fitting process. Among them, the parameters of the standardized gamma distribution μ、 The estimation was obtained using the 2nd, 4th, and 6th order moments of the raindrop spectrum, and the formula is as follows: Where n represents the nth moment; Step 4.14, based on the step distance Obtain the mass-weighted average diameter of raindrops on the ground. The formula is: ； Step 4.15: Based on the mass-weighted average diameter The normalized concentration was obtained. The calculation formula is: in, This indicates the vertical velocity of atmospheric motion.

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