KR101244544B1 - Method for calculating quality index of sampling error for single and dual-polarization radar parameters - Google Patents

Abstract

PURPOSE: A method for calculating quality index of sampling errors for single and dual-polarization radar parameters is provided to reduce uncertainty of the parameter. CONSTITUTION: A method for calculating quality index of sampling errors for single and dual-polarization radar parameters comprises: a step of selecting a rain fall area using vertical profile data and information on maximum and minimum height of the rain fall area(S210); a step of calculating uncertainty of parameters including reflectance, spectrum width, differential reflectivity, and cross-coefficient of correlation according to the number of radar samples(S220); and a step of calculating the quality index using the calculated uncertainty(S230). [Reference numerals] (AA) Start; (BB) End; (S210) Selecting a rain fall area; (S220,S242) Calculating the uncertainty of each observation parameter; (S221) Adjusting the sample number of each observation parameter; (S222) Calculating the deviation of each observation parameter by altitude; (S223) Drawing the frequency distribution function of each observation parameter; (S230,S232) Calculating the sampling error quality index of each observation parameter; (S231) Drawing an uncertainty estimation equation

Description

Method for calculating quality index of sampling error for single and dual-polarization radar parameters}

The present invention relates to a quality control technique of radar observation data, and more particularly, by calculating the statistical uncertainty of observation variables using vertically oriented observation data of single and double polarized radar. The present invention relates to a method for calculating the sampling error quality index of an observation variable that can quantitatively quantify the actual observation error of the radar observation variable.

Weather radar provides high temporal and spatial resolution data and is used in a wide range of areas such as ground precipitation and three-dimensional wind field estimation. In addition, the accuracy of the observed variables of weather radar is directly related to the reliability (accuracy) of ground precipitation estimation and three-dimensional wind field estimation.

The weather radar concentrates and transmits energy to a narrow area (usually around 1 °) using an antenna and processes the energy returned from the target in that direction. You must move it. The number of radar transmissions and receptions is limited to hundreds to thousands of hardware per second, so in order to observe a large area of atmosphere in three dimensions within a given time (usually within 10 minutes), the number of times of energy transmission and reception in a specific direction (or Number of samples) is limited.

In the observation using the weather radar, the larger the number of observation samples, the more accurate the statistically accurate observation value can be obtained. The error reduction effect of radar observation variable with increasing number of samples in monopolar and bipolar is theoretically demonstrated (Bringi and Chandrasekar, 2001). In actual radar observations, the error of the observation variable according to the number of samples may affect the radar observation strategy. For example, a decrease in the number of samples causes a decrease in the accuracy of the radar observation variable. Therefore, in order to improve the accuracy of the observation variable, the number of samples should be increased. .

Also, reflectivity and differential reflectivity are used directly in quantitative rainfall estimation, and their accuracy directly affects the accuracy of rainfall estimation. For example, a 1dB reflectance error can cause an error of about 18% in estimating ground rainfall using reflectance, and an 0.2dB error in differential reflectance can cause an error of about 18% in rainfall estimation.

As the error of the observation variable according to the number of samples can be transferred to the error of rainfall estimation, it is necessary to accurately grasp the error of the observation variable according to the number of samples and use it as a quantitative quality index.

In order to solve the above-described needs, the present invention provides a method of calculating a sampling error quality index of an observation variable that can quantitatively quantify an error according to the number of samples of an observation variable using vertically oriented observation data of a single or double polarized radar. The purpose is to provide.

One embodiment of the present invention for achieving the above object, the step of selecting the rainfall region using the vertical profile data of the observation variable generated from the vertical-oriented observation data, and the information about the maximum height and the minimum height of the rainfall area; Calculating uncertainty according to the number of radar samples of each of the observation variables including reflectance, line speed, spectral width, differential reflectance, and cross-correlation coefficient in the selected rainfall region; And calculating a sampling error quality index of each observation variable by using the calculated uncertainty of each observation variable.

In this case, the uncertainty calculation step may include adjusting the number of samples by calculating an average value in the azimuth direction and the visual direction with respect to the observation variable; Calculating a deviation for each altitude based on a difference between the calculated average value of each observation variable and the corresponding observation value; And calculating an uncertainty of each observation variable by using the calculated deviation of each observation variable for each altitude.

The calculating of the deviation for each altitude may include calculating an average value for each altitude by averaging in the azimuth direction with respect to the observation variable; And deriving a frequency distribution function by using the calculated altitude difference value and the deviation of each observation variable.

In addition, the uncertainty of each of the reflectivity and the differential reflectance among the observation variables may be calculated by the following equation using the calculated respective deviation.

는 고도별 평균값을 각각 나타낸다.)Where σ _X is the uncertainty, H is the number of altitudes, N is the number of observations at each altitude, X _{n , h} is the observation,

Indicates the average value for each altitude.)

In addition, the uncertainty of the gaze velocity, the spectral width, and the cross-correlation coefficient among the observation variables may be calculated by the following equation using each calculated deviation.

는 고도별 평균값을 각각 나타낸다.)Where σ _X is the uncertainty, H is the number of altitudes, N is the number of observations at each altitude, X _{n , h} is the observation,

Indicates the average value for each altitude.)

The calculating of the sampling error quality index of each observation variable may include deriving an uncertainty estimation equation through an uncertainty analysis result of each observation variable according to the number of samples; And calculating a sampling error quality index of each observation variable by using the derived uncertainty estimation equation.

In addition, the uncertainty estimation equation may be derived from the following equation through a least-squares method using the number of samples obtained by calculating an average value in the azimuth direction and the line direction for each observation variable.

(Where n is the number of samples, x is the observation variable for which you want to estimate uncertainty, and a and b are constants that represent values that vary with observation variable x.)

In addition, the quality index of reflectivity and differential reflectivity among the observation variables may be calculated by the following equation using the derived uncertainty estimation equation.

Also, the quality index of the gaze velocity, the spectral width, and the cross-correlation coefficient among the observation variables may be calculated by the following equation using the derived uncertainty estimation equation.

In addition, the sampling error quality index may have a range of 0 to 1.

According to the present invention, accuracy can be provided for single and double polarized variables, thereby reducing the uncertainty when using single and double polarized variables.

1 is a block diagram schematically illustrating an entire system for implementing a method for calculating a sampling error quality index of an observation variable according to an exemplary embodiment of the present invention.
2 is a flowchart illustrating a method for calculating a sampling error quality index of observation variables according to an embodiment of the present invention.
FIG. 3 is a two-dimensional frequency distribution graph of deviations according to a range and azimuth in the uncertainty calculation process of each observation variable of FIG. 2.
FIG. 4 is a graph showing the uncertainty according to the number of samples for each observation variable calculated according to the uncertainty calculation process of each observation variable of FIG. 2.
FIG. 5 is a graph showing an uncertainty estimation equation approximated by an exponential function using the least square method in the uncertainty graph according to the number of samples for each observation variable.
FIG. 6 is an exemplary diagram illustrating an example of actually applying a sampling error quality index calculation process of each observation variable of FIG. 2.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, which will be readily apparent to those skilled in the art to which the present invention pertains. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Further, in order to clearly illustrate the present invention in the drawings, portions not related to the description are omitted. In addition, the same code | symbol is attached | subjected about the similar part throughout the specification. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.

In the method for calculating the sampling error quality index of single and double polarization variables according to the present invention, the statistical uncertainty (sampling error) of the observation variable can be calculated by calculating the variation of the observation value from the mean value at each altitude, and the calculated statistical uncertainty Can be quantitatively exponential. This invention will be described with reference to the drawings.

1 is a block diagram schematically illustrating an entire system for implementing a method for calculating a sampling error quality index of an observation variable according to an exemplary embodiment of the present invention.

Referring to FIG. 1, the sampling error quality index calculation method of an observation variable according to the present invention may be implemented through a system consisting of a vertical-oriented observation system 10 and a sampling error quality index calculation system 20.

Here, the sampling error quality index calculation system 20 includes a data collection unit 201, an uncertainty calculation unit 202, and a sampling error quality index calculation unit 203, which are single and double of the vertical-oriented observation system 10. Collect the vertical-oriented observation data observed by the polarization radar, calculate the statistical uncertainty according to the increase in the number of samples of the observation variable using the vertical-oriented observation data collected, and use the result to calculate the uncertainty estimation equation. Calculate the sampling error quality index.

Specifically, the vertically oriented observation system 10 includes single and double polarized radars, and rotates while shooting the radar beam toward the ceiling with the elevation angle of the radar antenna set at 90 ° from the ground. At this time, the radar beam is directed to the same place while rotating 360 °. Through this, the vertically oriented observation system 10 may obtain a vertical profile of each radar observation variable at a specific point (radar position).

For reference, since the radar looks at the same place during the vertical orientation observation, the observed variables observed by the radar will have the same value unless there is a large change in the rainfall system. Thus, the statistical uncertainty of the observation variable can be obtained by calculating the variation of the observed observation variable from the mean value at each altitude. In other words, the observed observations should have the same value at the same location in a homogeneous rainfall system. However, actual observations are subject to variation due to undersampling, and the uncertainty of statistical undersampling can be quantitatively calculated. This can be done through vertically oriented observation that continues to observe the same location. In other words, by removing the average and regular variation from vertical-oriented observations, the remaining values can be used as an approximation of statistical uncertainty. Therefore, in this embodiment, the uncertainty can be obtained through the standard deviation of the observation variable.

The data collection unit 201 of the sampling error quality index calculation system 20 collects the observation data from the vertically oriented observation system 10. Here, observation data are vertical-oriented observation data, single and double polarized data.

The uncertainty calculator 202 of the sampling error quality index system 20 obtains observation variables from the collected observation data and generates a vertical profile of each observation variable. Here, the observation variables include reflectivity, doppler velocity, spectral width, differential reflectivity, and cross-correlation coefficient, which are single polarization variables. do.

Then, the uncertainty calculator 202 selects the rainfall region using the vertical profile of each observation variable, the highest height and the lowest height of the rainfall region, obtains the standard deviation of each observation variable in the selected rainfall region, The uncertainty of each observed variable is then calculated from the standard deviation obtained.

In detail, the uncertainty calculator 202 selects the rainfall region using the vertical profile of the reflectivity, the differential reflectivity, and the cross correlation coefficient. The rainfall area can be determined by inputting the minimum and highest altitude of the rainfall area by the user or by using the characteristics of the vertical profile of each observation variable. For example, if the minimum and maximum altitudes of the input rainfall region are 0.5km and 3.0km, respectively, only the observation data from 0.5km to 3km above ground are used to calculate the sampling error quality index.

Then, the uncertainty calculator 202 averages each observation variable in the azimuth and line of sight only for the rainfall region, thereby increasing the number of samples. Subsequently, the uncertainty calculator 202 calculates an altitude deviation between the observation variables averaged in the azimuth angle and the visual direction and the observed observation variables within the increased number of samples. The uncertainty calculator 202 calculates the uncertainty of each observation variable by using the deviation value obtained at each point.

In the present embodiment, the reason why the rainfall region is used is that the shapes of the particles are different in the bright bands or the snow regions, not the rainfall regions, and include various variations such as the degree of tilting the particles and the size of the particles. It is difficult to distinguish whether the variation is caused by the variation of snow or melted particles or by observation errors. Therefore, in the present invention, only the rainfall region under the bright band is selected using the vertical profile data of the reflectivity, the differential reflectivity, and the cross-correlation coefficient obtained by the vertically oriented observation.

The sampling error quality index calculation unit 203 of the radar quality management system 20 quantifies the uncertainty of each observation variable obtained by the uncertainty calculation unit 202 to calculate the sampling error quality index Q _SE . That is, the sampling error quality index calculation unit 203 derives an uncertainty estimation equation using the uncertainty of each observation variable, and calculates the sampling error quality index using the uncertainty estimation equation for each observation variable.

2 is a flowchart illustrating a method for calculating a sampling error quality index of observation variables according to an embodiment of the present invention.

2, the sampling error quality index calculation method of the observation variable according to the present invention, first, the vertical profile data of the reflectivity, differential reflectance, cross-correlation coefficients generated from the vertical-oriented observation data obtained by the vertical-oriented observation, and rainfall The rainfall region below the bright strip (melting layer) is selected using the highest height and the lowest height of the region (S210).

Then, in the selected rainfall region, the vertically-oriented observations are used to reflect the single polarization variables Reflectivity, Doppler velocity, Spectrum width, and the dual polarization variables Differential reflectivity, and cross-correlation. The uncertainty of each observation variable according to the number of radar samples of the cross-correlation coefficient is calculated (S220).

Uncertainty calculation process (S220) for each observation variable, averaging each observation variable in the azimuth direction or a visual direction to adjust the number of samples (S221), deviation calculation process by altitude (S222), frequency distribution function calculation Process (S223) and uncertainty calculation process (S224).

Specifically, first, the sample number adjustment process S221 is performed by calculating an average value in the azimuth angle and the radar line of sight for each observation variable for each altitude in the selected rainfall region. That is, the number of samples can be increased by averaging the observation variables selected in the rainfall region in the azimuth direction and the radar line of sight, respectively. To account for the reduction of statistical uncertainty with increasing number of samples, the observed observations are averaged in the azimuth and radar line of sight. When the number of samples increases in the azimuth direction, the observation area is constant regardless of the 360-degree rotation of the radar, so the pulse dwell time can be increased, and the average in the eye direction increases the sampling volume of the radar. Can be obtained.

Subsequently, the altitude deviation calculation process (S222) calculates the altitude deviation of each observation variable using the calculated average value by the difference between the observation value and the average value at the same altitude, as shown in Equation (1).

At this time, the average value of the observation variable is obtained for each PPI (Plane Position Indication) in the vertical-oriented observation. This average value calculation is performed to eliminate variations in single and double polarization variables due to variations in precipitation system. By using different average values calculated according to the altitude, the variation of the variable with the altitude is also eliminated.

은 특정 고도 h에서의 평균값을 각각 나타낸다.Where ΔX is the deviation and X _{n , h} are the nth observation at a specific altitude h,

Represents the mean value at a specific altitude h, respectively.

Then, the frequency distribution function calculation process (S223) is performed by calculating the frequency distribution function of the deviation for each elevation of each observation variable.

Subsequently, the uncertainty calculation process S224 is performed by obtaining the uncertainty σ _X for each observation variable as in Equation 2 and Equation 3 using the frequency distribution function of the deviation for each elevation.

First, the uncertainty of the reflectivity and the differential reflectivity among the observation variables is obtained through Equation 2.

는 고도별 평균값을 각각 나타낸다.Where σ _X is the uncertainty, H is the number of altitudes, N is the number of observations at each altitude, X _{n , h} is the observations,

Represents the average value for each altitude.

Uncertainty about the line speed, the spectral width, and the cross-correlation coefficient among the observation variables is obtained through Equation 3.

는 고도별 평균값을 각각 나타낸다.Where σ _X is the uncertainty, H is the number of altitudes, N is the number of observations at each altitude, X _{n , h} is the observations,

Represents the average value for each altitude.

Next, the sampling error quality index is calculated using the calculated uncertainty of each observation variable (S230).

Sampling error quality index (Sampling error index, Q _SE ) calculation process (S230) is a process of indexing the error due to the limited sampling, in the present embodiment uses the results of the analysis of the variability of statistical uncertainty according to the number of samples. 4 and 5, as a result of the uncertainty according to the number of samples in the distribution of variation of the mean of each observation variable, it can be seen that the uncertainty decreases as the number of samples increases.

Specifically, first, a process of deriving an uncertainty estimation equation in the form of an exponential function, such as Equation 4, is performed by approximating the least squares method using an uncertainty analysis result according to the number of samples acquired in the vertical-oriented observation (S231). .

Where n denotes the number of samples, x denotes an observation variable to estimate uncertainty, and a and b denote constants that vary depending on the observation variable x.

According to Equation 4, since a and b are constants, uncertainty can be calculated from the sample number n, and the sample number n can be obtained from the header information of the radar data.

In addition, the values of a and b can be derived from an uncertainty estimation equation in the form of an exponential function derived through the approximation using the least square method. An example of the least square approximation of the uncertainty is indicated by the solid line in FIG. The uncertainty estimation equations derived from the equations are presented. Constants a and b for each observation variable are shown in Table 1.

      Table 1.Coefficients (a) and exponents (b) of the uncertainty estimation equation for each observed variable a b Reflectivity (Z _H ) 0.9756 -0.3138 Line speed (V _R ) 0.4424 -0.3389 Spectral Width (SW) 0.0698 -0.2920 Differential Reflector (Z _DR ) 0.6367 -0.5011 Cross correlation coefficient (ρ _HV ) -1.0772 -0.3880

Next, the sampling error quality index of each observation variable is calculated using the uncertainty estimation equation according to Equation 4 (S232).

That is, the reflectivity and differential reflectance of which uncertainty (σ _X ) is calculated in decibels (dB) among the observation variables are calculated by Equation 5, and the uncertainty (σ _X ) is calculated in units of linear ratio. The estimated line speed, spectral width, and cross correlation coefficient are used to calculate the sampling error quality index through Equation 6.

The sampling error quality index (Q _SE ) ranges from 0 to 1, with 1 representing good quality and 0 representing poor quality.

FIG. 3 is a two-dimensional frequency distribution graph of deviations according to a range and azimuth in the process of calculating the uncertainty of each observation variable of FIG. 2. In this embodiment, the case of September 11, 2010 was used, the deviation from the average value of the observed variables was obtained through Equation 1, the upper portion shows the deviation distribution with respect to the visual direction, the lower portion with respect to the azimuth direction Indicates the distribution of the deviations.

Referring to Figure 3, the + shape is the average value in the azimuth direction at each altitude, the horizontal bar represents the standard deviation, the deviation of the other observation variables except the deviation of the cross-correlation coefficient in the visual distribution of the upper end is near zero The wide spread distribution of the cross-correlation deviation can be assumed to be due to weak precipitation. In addition, the differential reflection shows a wave shape in the azimuth direction, which can be estimated to be caused by the terrain effect.

FIG. 4 is an exemplary diagram illustrating a variation of uncertainty according to the number of samples of each observation variable calculated according to the uncertainty calculation process of each observation variable of FIG. 2. In this embodiment, the number of samples of the original observation data was applied to 42 samples on June 28, 2010, September 11, 2010, and May 11, 2011, respectively. By averaging.

Referring to FIG. 4, the + shape represents an uncertainty value averaged in the azimuth direction, and the shape represents an uncertainty averaged in the viewing distance (line of sight) direction, with red being June 28, 2010 and green being 2010. September 11, blue indicates May 11, 2011. In addition, it can be seen that there is no significant change in uncertainty by averaging in the azimuth angle and the visual direction except for the cross correlation coefficient among the observation variables. In the case of cross-correlation coefficients, the uncertainty decreases more clearly when averaged in the visual direction.

For example, in the case of September 11, 2010, the cross-correlation coefficient of uncertainty was large, but the uncertainty reduction effect of the increase in the number of samples was more significant.

Statistical uncertainty according to the number of samples of the spectral width, the differential reflectance, and the cross-correlation coefficients converges to a specific value as the number of samples increases.

The statistical uncertainty of the reflectivity and the differential reflectivity has values of 1.2 dBZ and 0.2 dBZ, respectively, when the number of samples is about 500, and errors of 1 dBZ and 0.2 dBZ, respectively, cause an error of 18% when estimating rainfall. Therefore, it can be seen that in order to reduce the sampling error to the maximum, it is necessary to average the observation variables to have at least 500 samples.

FIG. 5 is a graph showing an uncertainty estimation equation approximated by an exponential function using the least square method in the uncertainty graph according to the number of samples for each observation variable. FIG. 5 shows the distribution of variation in the mean of the observation variables as the uncertainty according to the number of samples. will be. Here, in this embodiment, in order to quantify the uncertainty of the observation data according to the number of samples to calculate the quality index, the variation of the variation according to the increase in the number of samples was obtained by moving and averaging the observation data in the azimuth and visual directions.

Referring to FIG. 5, it can be seen that the uncertainty of the observation variable decreases as the number of samples increases.

6 is an exemplary view showing an example of actually applying the sampling error quality index calculation process of each observation variable of Figure 2, (a) is the reflectivity, (b) the line speed, (c) the spectral width, (d) (E) shows the cross-correlation coefficient, respectively. Here, in the present embodiment, the sampling error quality information for each observation variable is calculated for the number of samples (n = 64) for each azimuth of the bismuth radar data on September 22, 2010 at 11:22.

Referring to (a) to (e) of FIG. 6, the sampling error quality information is 0.5542 for the reflectance, 0.8899 for the viewing speed, 0.6447 for the spectral width, 0.8833 for the differential reflectivity, and 0.9831 for the cross correlation coefficient. have.

So far I looked at the center of the preferred embodiment for the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Accordingly, the disclosed embodiments are to be considered in an illustrative rather than a restrictive sense, and all differences within the scope of equivalents thereof should be construed as being included in the present invention.

Further, the apparatus and method according to the present invention can be embodied as computer readable codes on a computer-readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. Examples of the recording medium include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like, and also include a carrier wave (for example, transmission through the Internet). The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.

10. Vertical Orientation Observation System 20. Sampling Error Quality Index Calculation System

Claims (11)

Selecting a rainfall region using vertical profile data of observation variables generated from vertical-oriented observation data and information on the highest and lowest heights of the rainfall region;
Calculating uncertainty according to the number of radar samples of each of the observation variables including reflectance, line speed, spectral width, differential reflectance, and cross-correlation coefficient in the selected rainfall region; And
Calculating a sampling error quality index of each observation variable using the calculated uncertainty of each observation variable. The method of claim 1,
The uncertainty calculating step may include: adjusting an average number of samples by calculating an average value in the azimuth direction and the visual direction with respect to the observation variable;
Calculating a deviation for each altitude based on a difference between the calculated average value of each observation variable and the corresponding observation value; And
And calculating an uncertainty of each observation variable by using the calculated deviation of each observation variable for each altitude. The method of claim 2,
The calculating of the deviation for each altitude may include calculating an average value for each altitude by averaging in the azimuth direction with respect to the observation variable; And
And deriving a frequency distribution function using the calculated average value for each altitude and the deviation of each observation variable. The method of claim 3,
The uncertainty of each of the reflectivity and the differential reflectivity among the observation variables is calculated by the following equation using the calculated deviations.

Where σ _X is the uncertainty, H is the number of altitudes, N is the number of observations at each altitude, X _{n , h} is the observation,

Indicates the average value for each altitude.) The method of claim 3,
The uncertainty of each of the observation variables, the gaze velocity, the spectral width, and the cross-correlation coefficient, is calculated by the following equation using the calculated deviations.

Where σ _X is the uncertainty, H is the number of altitudes, N is the number of observations at each altitude, X _{n , h} is the observation,

Indicates the average value for each altitude.) The method of claim 1,
The calculating of the sampling error quality index of each observation variable may include deriving an uncertainty estimation equation through an uncertainty analysis result of each observation variable according to the number of samples; And
Calculating a sampling error quality index of each observation variable using the derived uncertainty estimation equation. The method according to claim 6,
The uncertainty estimation equation is a sampling error quality index calculation method, characterized in that derived by the following equation through the least-squares method using the number of samples obtained by calculating the average value in the azimuth direction and the visual direction for each observation variable .

(Where n is the number of samples, x is the observation variable for which you want to estimate uncertainty, and a and b are constants that represent values that vary with observation variable x.) The method of claim 7, wherein
The method of calculating the quality of sampling error, characterized in that the quality index of reflectivity and differential reflectivity among the observation variables is calculated by the following equation using the derived uncertainty estimation equation.

9. The method of claim 8,
The quality index of the gaze velocity, the spectral width, and the cross-correlation coefficient among the observation variables are calculated by the following equation using the derived uncertainty estimation equation.

10. The method of claim 9,
The sampling error quality index is a sampling error quality index calculation method characterized in that it has a range of 0 to 1. A recording medium having recorded thereon a program which can be read and executed by a digital signal processing apparatus for performing the method of any one of claims 1 to 10.

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