JP2013205151A - Device for computing phase difference between specific polarized waves, rainfall observation system employing the same and method for computing phase difference between specific polarized waves - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a device for computing a phase difference between specific polarized waves during a rainfall from a phase difference between specific polarized waves observed by a radar, and a rainfall observation system.SOLUTION: A phase difference computing device 3 comprises phase difference return correcting means 31 which corrects discontinuity of a phase difference and restores an original continuous phase difference, means 32 which manages data of an observation point having a correlation coefficient less than or equal to a threshold so as not to use the data, outlier removing means 33 which calculates a moving average and a standard deviation for distances of the phase difference and, when a difference between the phase difference and a moving average of each of the distances exceeds a threshold, substitutes the data of that distance with the moving average, discrimination means 35 which discriminates a rainfall layer and an area including waterfall particles other than rain and discriminating data other than the rainfall layer from an analysis object, means 36 which determines a boundary condition of the phase difference in the vicinity of and away from the range, and means 37 which determines a phase difference to minimize a cost function constituted by computing a difference between the observed phase difference and a phase difference that should be calculated.

Description

  The present invention relates to a phase difference calculation device between specific polarizations at the time of rainfall observation by a dual polarization weather radar, a rain observation system using the same, and a phase difference calculation method between specific polarizations.

  Conventionally, the weather radar emits radio waves from the antenna to the atmosphere, and the emitted radio waves hit the rain and return to the antenna, thereby measuring the strength of the radio waves and estimating the rainfall position, rainfall intensity, and rainfall. There was a rain observation device.

In addition, phase difference between polarized waves, reflection factor difference, reflection factor obtained by multi-parameter radar The temperature around the ground using the formula for estimating the rainfall intensity and the formula for estimating the amount of rainwater The temperature profile in the range direction is calculated from the observed elevation angle and the temperature decrease rate of the standard atmosphere, and the three-dimensional distribution of the rainfall intensity and the amount of rainwater is calculated using the coefficient and power index of the estimation formula considering the temperature dependency and elevation angle dependency. The thing which raised the estimation precision of the three-dimensional distribution of rainfall intensity and the amount of rainwater by estimating is disclosed (patent document 1).

  In the technique described in Patent Document 1, more accurate rainfall intensity can be estimated by using a multi-parameter radar. However, in areas such as the rear surface of a very strong rainfall area, a large amount of rain attenuation occurs. Sometimes it was not possible. In this case, the area where rain data cannot be obtained is determined by another radar and the rain data is obtained.

  However, for areas that cannot be covered by other radars, it is not possible to distinguish between areas where rainfall data cannot be acquired due to rain attenuation and areas where precipitation is not possible, and it is impossible to make judgments. Data synthesis and data assimilation into numerical models In some cases, an error may occur.

  Therefore, in the technique described in Patent Document 2, it is possible to easily distinguish and determine a region where rainfall data cannot be acquired due to rain attenuation and a region where no precipitation occurs.

JP 2006-208195 A JP 2009-98001 A

Fubbert, J. and V. N. Bringi, 1995: An iterative filtering technique for the analysis of copolar differential phase and dual-frequency radar measurements, J. Atmos. Oceanic Technol., 12, 643-648.

  As described in Patent Documents 1 and 2, when a raindrop with a large particle size falls, the raindrop has a flat shape in which the vertical particle size is smaller than the horizontal particle size due to air resistance. For this reason, it is known that in the rain, the phase delay of horizontal polarization is greater than that of vertical polarization.

This phase difference Φ _DP between the polarized waves is a physical quantity that can be observed by a multi-parameter radar, and since the phase delay is integrated as the distance increases, it is an amount that increases as the distance r from the radar increases in the rain. . The distance differentiation of the phase difference Φ _DP between the polarizations is called the specific polarization phase difference K _DP and is expressed by the following equation (1).

The ratio polarization retardation K _DP against rain becomes a large value the larger the flat large water droplets in the horizontal direction at that point, precipitation intensity larger the water droplet is large since it also increases, and the ratio polarization retardation K _DP rain A relationship called K _DP -R exists between precipitation intensities R.

In quantitative rainfall estimation using K _DP -R relationship, it is important to observe the phase difference [Phi _DP of polarization precisely, several error factors with respect to the observation of the phase difference [Phi _DP polarizations Are known.

FIG. 11 is a diagram illustrating an example of a phase difference due to backscattering. FIG. 12 is a diagram showing a range profile of the actually observed phase difference Φ _DP between the polarizations and the phase difference K _DP between the specific polarizations. 12A is a diagram illustrating a range profile of the phase difference Φ _DP between actually observed polarizations, and FIG. 12B is a diagram illustrating a range profile of the phase difference K _DP between the actually observed polarizations. is there.

In FIG. 11, the solid line indicates the range profile of the equation (2) observed by the radar, the broken line indicates the range profile of the phase difference Φ _DP between the polarizations to be restored, the horizontal axis indicates the distance, and the vertical axis indicates the phase difference.

FIG. 12 shows the range profile and relative deviation of the phase difference Φ _DP between the polarizations at an azimuth angle of 232 ° and an elevation angle of 2.6 ° observed by a multi-parameter radar installed in Ebina City, Kanagawa Prefecture on July 9, 2005. The range profile of wave phase difference K _DP is shown. The phase difference K _DP between specific polarizations was calculated by linear regression of the phase difference Φ _DP between polarizations using data with a range width of 1 km.

For example, the phase difference δ due to backscattering may become prominent in the case of very heavy rain or when the rain includes huge particles such as soot. Then, as in the vicinity of the distance of 17 km in FIG. 12, the phase difference Φ _DP between the polarizations is excessively observed at that location. That is, the polarization phase difference Ψ observed by the radar is expressed by the following equation (2).

Then, if the phase difference Φ _DP between polarizations at a certain location is observed excessively, as shown in FIG. 12, the phase difference K _DP between specific polarizations is excessively calculated on the side closer to the radar at that location, and the opposite side Then, the negative specific polarization phase difference K _DP is calculated.

Another error factor is noise. FIG. 12 (a) shows an example of a range profile of the observed phase difference Φ _DP between the polarized waves. As shown in FIG. 12 (a), strong rainfall occurs when the range from the radar is between 14km and 16km. And the phase difference Φ _DP between the polarizations greatly changes at that location. However, the observed phase difference Φ _DP between the polarizations includes noise that fluctuates for each range bin. For example, a distance of 18 km at which the signal is considered to be weak due to attenuation of radio waves behind a heavy rain region. Where the signal S / N ratio is small, such as in a far region, the noise fluctuation tends to increase.

FIG. 12 (b) shows the result of linear regression in the range of 1 km range with respect to the phase difference Φ _DP between the polarizations in FIG. 12 (a), and the phase difference K _DP between the specific polarizations calculated from the obtained slope. It is. A large inter-polarization phase difference K _DP is calculated in the heavy rain area, but the profile of the inter-polarization phase difference K _DP fluctuates around a value of 0 in the light rain area.

Originally, during rainfall, the phase difference Φ _DP between the polarizations should increase monotonously with respect to the distance, and the phase difference K _DP between the specific polarizations should always be a positive value. However, due to the noise included in the observed phase difference Φ _DP between the polarizations, a negative specific polarization phase difference K _DP that does not appear originally is calculated. The full width at half maximum of the variation of the phase difference K _DP between specific polarizations due to the noise is about 1 ° km ^-1 to 2 ° km ^-1 , which is 20mm hour ^-1 to 35mm hour ^-1 in terms of rainfall intensity. Variation in the phase difference K _DP between specific polarizations is not negligible.

In the present invention, an inter-polarization phase difference calculating device that corrects a variation due to an error factor and calculates an accurate inter-polarization phase difference K _DP , a rain observation system using the same, and a inter-polarization phase difference calculating method are provided. The purpose is to provide.

  In order to solve the above-described problem, the rain attenuation determination apparatus of the present invention corrects the discontinuous situation of the phase difference between the polarizations of the observation data changing with respect to the distance, and the original continuous observed phase difference between the polarizations is corrected. Interpolated polarization phase difference aliasing correction means, quality control means for managing observation point data having a correlation coefficient between polarizations equal to or less than a predetermined threshold so as not to be used for analysis, and observed polarization phase difference An outlier that calculates the moving average and standard deviation for the distance and replaces the distance data with the moving average if the difference between the observed polarization phase difference and the moving average exceeds the threshold at each distance. The removal means, the rain layer and the region that seems to contain precipitation particles other than rain, and the rain layer discrimination means that excludes the data other than the rain layer from the analysis target, and the boundary of the phase difference between the polarizations near and far from the range Minimizing the cost function consisting of the sum of the square of the difference between the observed phase difference between the polarization and the phase difference to be obtained and the square of the second derivative with respect to the distance acting as a low-pass filter And a means for determining a phase difference between specific polarizations for determining a phase difference between specific polarizations.

  And removing means for removing a phase difference caused by backscattering of the observation data.

前記コストファンクションＪは、以下の式（Ｇ）〜（Ｊ）で定義されることを特徴とする。

Also, J _obs and J ′ _obs are the sum of squares of the difference between the observed polarization phase difference Ψ and the polarization phase difference to be obtained Φ _DP, and J _lpf is the sum of squares of the second derivative with respect to the distance of k functioning as a low-pass filter. , K is the square root of K _DP multiplied by the width of the range bin and 2, C _lpf is the adjustment parameter of the low-pass filter, Φ _near and Φ _far are the boundary conditions of the phase difference between the polarization near and _far , respectively, When formulas (A) to (F) are used,

The cost function J is defined by the following formulas (G) to (J).

  Furthermore, the rain observation system using the phase difference calculation device between specific polarizations was observed by a dual-polarization weather radar using radio waves of two types of polarization, horizontal and vertical, and the dual-polarization weather radar. A phase difference calculation device between specific polarizations that calculates a phase difference between specific polarizations based on data, observation data acquired by the dual polarization weather radar, and a phase difference between specific polarizations calculated by the phase difference calculation device between specific polarizations The rainfall intensity estimating means for estimating the rainfall intensity distribution from the rain, and estimating the undetectable region from the observation data acquired by the dual polarization weather radar and the phase difference between the specific polarizations calculated by the phase difference calculation unit between the specific polarizations It comprises attenuation determination means, and output means for outputting a rainfall intensity distribution from the observation result of the rainfall intensity estimation means and the observation result of the rain attenuation determination means.

  Furthermore, the method for calculating the phase difference between specific polarizations corrects the discontinuous state of the phase difference between the polarizations of the observation data changing with respect to the distance, and restores the original continuous observed phase difference between the polarizations; The management of the observation point data having the correlation coefficient between the polarizations below the threshold value of not to be used for the analysis, the moving average and the standard deviation for the distance of the observed phase difference between the polarizations are obtained, and each distance is obtained. When the difference between the observed polarization phase difference and its moving average value exceeds the threshold, it is assumed that the data of the distance is replaced with the moving average value, and the precipitation layer and precipitation particles other than rain are included. The step of discriminating the region and excluding the data other than the rain layer from the analysis target, the step of determining the boundary condition of the phase difference between the polarizations near and far from the range, and the observed phase difference between the polarizations should be obtained. And having the steps of: determining the ratio polarizations phase difference that minimizes a cost function comprising a sum of the squares of the second order derivative with respect to distance that serves as the square and the low-pass filter of the difference between the polarizations phase difference, the.

  Further, the step of determining the boundary condition of the phase difference between polarizations near and far from the range includes obtaining a linear regression line using a predetermined number of normal observation data from near and far from the range, and near the range and Determining whether the slope of the linear regression line obtained at a distance is positive or negative, and if the slope of the linear regression line near the range is positive, setting a value corresponding to the nearest point as a boundary condition in the vicinity And if the slope of the linear regression line near the range is negative, the average value of a predetermined number of normal observation data from the vicinity of the range from which the linear regression line was determined is used as a boundary condition of the neighborhood, When the slope of the linear regression line far from the range is positive, the step corresponding to the farthest point is a far boundary condition, and the slope of the linear regression line far from the range is negative. If, and having the steps of: a remote boundary conditions the mean value of normal observation data of the linear regression line the predetermined number from the range far obtained.

With such a specific polarization phase difference calculation device, a rain observation system using the same, and a specific polarization phase difference estimation method, the fluctuation due to the error factor is corrected and the accurate specific polarization phase difference K _DP is calculated. It becomes possible.

It is a figure which shows the main structures of the rainfall observation system of embodiment of this invention. It is a flowchart of the return correction | amendment process of the phase difference (PSI) between polarization | polarized-lights observed with the dual polarization weather radar. It is a figure which shows before and after the correction | amendment correction | amendment of the phase difference (PSI) between polarization | polarized-lights observed with the dual polarization weather radar. It is a flowchart of the removal process of the phase difference by backscattering. It is a conceptual diagram of a rainfall layer and a melting layer. It is a flowchart of the boundary condition determination process of the phase difference between polarized waves. It is a conceptual diagram of the range profile and variable of phase difference Φ _DP between polarizations. It is a flowchart of the determination process of the phase difference between specific polarizations which minimizes a cost function. It is a figure which shows the result of using the method of this embodiment with respect to phase difference (PHI) _DP between the observed polarized waves of FIG. The dependence of the adjustment parameter _Clpf in this embodiment is examined. It is a figure which shows the example of the phase difference by backscattering. It is a figure which shows the range profile of the phase difference between polarized waves, and the phase difference between specific polarizations.

  Embodiments of the present invention will be described with reference to the drawings.

  FIG. 1 is a diagram showing a main configuration of a rainfall observation system according to an embodiment of the present invention.

  In the figure, 1 is a rain observation system, 2 is a dual-polarization weather radar, 3 is a phase difference calculation device between specific polarizations, 31 is a phase difference folding correction means between polarizations, and 32 is a phase difference between polarizations based on a correlation coefficient between polarizations. Quality control means, 33 is an out-of-polarization phase outlier removal means, 34 is a phase difference removal means due to backscattering, 35 is a precipitation layer discrimination means, 36 is an inter-polarization phase difference boundary condition determination means, 37 Specific polarization phase difference determining means for minimizing the cost function, 4 is rainfall intensity estimating means, 5 is rain attenuation determining means, and 6 is output means.

The rain observation system 1 calculates the inter-polarization phase difference K _DP by the inter-polarization phase difference calculation device 3 based on the data observed by the dual-polarization weather radar 2, and the rainfall intensity estimation means 4 and the rain attenuation The determination means 5 obtains the rain condition and outputs it from the output means 6.

  In the present embodiment, an X-band multi-parameter radar is applied as the dual polarization weather radar 2. The dual-polarization weather radar 2 uses two types of radio waves of horizontal and vertical polarization. This is because the principle that the shape of raindrops changes depending on the intensity of rain is used. Raindrops change from spherical to flat as the particle size increases. The dual-polarization weather radar 2 can observe the change in the shape with radio waves of two types of polarization, horizontal and vertical. In this embodiment, the X-band multi-parameter radar is applied. However, the present invention is not limited to this, and any dual-polarization radar may be used. The dual-polarization weather radar 2 transmits radio waves of two types of polarization, horizontal and vertical, from an antenna. These radio waves are scattered by raindrops and received by the antenna. Various parameters are acquired as observation data from the received radio wave and output to the phase difference calculation device 3 between specific polarizations.

The inter-polarization phase difference calculation device 3 uses the observation data output by the dual-polarization weather radar 2 to correct fluctuation due to an error factor and estimate the inter-polarization phase difference K _DP with high accuracy. . A detailed configuration will be described later.

  The rainfall intensity estimating means 4 estimates the rainfall intensity distribution from the corrected data obtained by correcting the observation data acquired by the dual polarization weather radar 2 by the relative polarization phase difference calculation device 3. The rain attenuation determination means 5 estimates the undetectable region from the correction data obtained by correcting the observation data acquired by the dual-polarization weather radar 2 by the inter-polarization phase difference calculation device 3. Then, the output means 6 outputs display data and numerical data of observation results corrected in consideration of the result.

  Note that the techniques described in Patent Documents 1 and 2 may be used for the dual polarization weather radar 2, the rainfall intensity estimating means 4, and the rain attenuation determining means 5.

Hereinafter, the method of estimating the specific polarization phase difference computation unit 3 according to the specific polarization retardation K _DP is described.

In addition to the phase difference between polarized waves Φ _DP generated when radio waves propagate in rain, i) local phase difference due to backscattering phase difference δ Peak of phase difference Φ _DP between various polarizations, and ii) noise. These error factors appear locally as shown in FIG. 11, and are considered to have almost no correlation with respect to distance. Therefore, in the present embodiment, the profile of the entire range is close to the phase difference Ψ between the polarizations observed by the dual-polarization weather radar 2 and monotonically increasing the phase difference Φ _DP between the polarizations, thereby obtaining the ratio between the specific polarizations. The phase difference K _DP is estimated.

  FIG. 2 is a flowchart of the aliasing correction processing of the polarization phase difference Ψ observed by the dual polarization weather radar 2. FIG. 3 is a diagram showing before and after the correction of the phase difference Ψ between polarizations observed by the dual polarization weather radar 2.

  The phase difference between the polarizations is a parameter that changes continuously with respect to the distance, but the phase is generally measured in the range of 0 ° to 360 °. Therefore, when the observed inter-polarization phase difference Ψ changes from 350 ° to 370 °, the measured value changes from 350 ° to 360 ° and then changes from 0 ° to 10 °. Occurs. This situation is called turnaround. Therefore, prior to all the processing, the inter-polarization phase difference folding correction means 31 shown in FIG. 1 corrects this folding and restores the original continuously observed inter-polarization phase difference Ψ.

As shown in FIG. 2, the return correction processing of the inter-polarization phase difference ψ observed by the dual-polarization weather radar 2 is first performed at step 1 with sin (ψ _i ) for the observed inter-polarization phase difference ψ _i. And cos (Ψ _i ) are calculated, and a moving average profile represented by the following expression (3) is obtained for each distance (ST1). The average number of data when calculating the moving average is about 30 to 50, and is about 3 to 5 km in terms of distance. Note that i is a subscript related to distance.

Next, in step 2, the following equation (4) is obtained for the distance (i = 0) closest to the dual polarization weather radar 2 (ST2).

Next, in step 3, loop processing is performed for i = 1, 2, 3,..., And Ψ _i is obtained by the following procedure (ST3).

First, the following formula (5) is calculated.

Subsequently, an integer n satisfying the following expression (6) is determined and is defined as the following expression (7).

Next, in step 4, for all i, an integer m _i that satisfies the following equation (8) is determined (ST4).

Next, in step 5, a correction amount 360 × m _i is added to the observed inter-polarization phase difference Ψ _i at the distance i (ST5).

  In this way, when the return correction processing of the polarization phase difference Ψ observed by the dual-polarization weather radar 2 is performed, the data in FIG. 3A is continuously converted into the data in FIG. 3B. It can be restored.

  Next, the quality management process is executed by the quality management means 32 for the phase difference between the polarizations based on the correlation coefficient between the polarizations.

The correlation coefficient ρ _HV between the polarizations is a parameter that can be measured by the dual polarization weather radar 2. For the complex received signal time series output by the receiver of the dual-polarization weather radar 2, the autocorrelation functions for horizontal and vertical polarization are R _H and R _V , respectively, and the cross-correlation function between the polarizations is R _HV Then, the following formulas (9) and (10) hold. Where arg is the complex argument.

When the correlation coefficient ρ _HV between the polarizations becomes small, the response of the phase difference Φ _DP between the polarizations to the received signal noise (observed phase difference Ψ between the polarizations) becomes large. In other words, when the correlation coefficient ρ _HV between polarizations is small, noise fluctuations appear in the observed phase difference Ψ between polarizations, and the phase difference Φ _DP between polarizations (specific phase difference K _DP between polarizations) is determined with high accuracy. It becomes difficult to do.

During normal rainfall, the correlation coefficient ρ _HV between polarizations is close to 1, but it is less than 1 when the S / N ratio is small or in the case of non-precipitation echoes. Therefore, in order to prevent the data of the region where the S / N ratio is small and the non-precipitation echo from adversely affecting the derivation of the phase difference Φ _DP (specific polarization phase difference K _DP ) between the polarizations, The data of the observation point having the relation number ρ _HV is not used for analysis by substituting undefined values and invalid values. The threshold value of the correlation coefficient ρ _HV between polarizations is preferably about 0.5 to 0.7.

  Next, outlier removal processing is executed by the outlier removal means 33 for the phase difference between the polarizations.

  In the outlier removal processing, a moving average and a standard deviation with respect to the observed distance between the polarization phase differences Ψ are obtained. If the difference between the observed polarization phase difference Ψ and its moving average value exceeds the threshold value at each distance, the data of the distance is replaced with the moving average value. The threshold is about twice the moving standard deviation. The average number of data when calculating the moving average and the standard deviation is about 30 to 50, and is about 3 to 5 km in terms of distance.

  Next, a phase difference removal process due to backscattering is executed by the phase difference δ removal means 34 due to backscattering. In this embodiment, an iterative filter method (see Non-Patent Document 1) is applied to remove the phase difference δ due to backscattering. Note that the phase difference removal processing due to backscattering may be omitted because the same effect can be obtained when the control coefficient of the low-pass filter is set to a relatively large value.

  FIG. 4 is a flowchart of the processing for removing the phase difference due to backscattering.

  As shown in FIG. 4, the phase difference removal processing by backscattering first creates a profile in which an FIR filter having a cutoff period of about 4 km is applied to the observed inter-polarization phase difference Ψ in step 11. And output as Ψ ′ (ST11).

Next, in step 12, it is determined whether or not the difference | Ψ _i −Ψ ′ _i | between before and after applying the FIR filter is larger than a predetermined threshold (ST12).

If the difference | Ψ _i −Ψ ′ _i | before and after the application of the FIR filter is larger than a predetermined threshold in step 12, Ψ ′ _i is substituted into Ψ _i in step 13 (ST13).

In step 12, when the difference | Ψ _i −Ψ ′ _i | before and after the application of the FIR filter is smaller than a predetermined threshold value, the process proceeds to step 14.

  Next, in step 14, it is determined whether or not the value has been replaced in all range bins (ST14).

  If it is determined in step 14 that all the range bins have not been replaced, the process returns to step 11.

  In step 14, when the value is not replaced in all the range bins, the phase difference removal processing due to backscattering is terminated.

  Next, the rain layer discrimination processing is executed by the rain layer discrimination means 35.

  FIG. 5 is a conceptual diagram of the rain layer and the melted layer.

In this embodiment, since it is assumed that the phase difference Φ _DP between polarized waves is monotonically increased, the present invention can be applied only to the rain layer. Therefore, by substituting undefined values and invalid values into the data beyond the distance corresponding to the bottom of the melting layer, the data of the snow layer and melting layer shown in Fig. 5 that seems to contain precipitation particles other than rain can be analyzed. Don't use it.

  The precipitation layer can be identified by using the result of precipitation particle identification using the observation result of the dual-polarization weather radar 2, but the temperature can be determined from the vertical profile of temperature and GPV (Grid Point Value) data separately prepared. It can also be determined by examining the altitude at which is 0 ° C. and assuming the thickness of the molten layer.

Next, boundary condition determination processing for the phase difference between polarizations is executed by the boundary condition determination means 36 for the phase difference between polarizations. In the boundary condition determination processing for the phase difference between the polarizations, the boundary condition (Φ _near · Φ _far ) of the phase difference Φ _DP between the polarizations in the vicinity of the range and in the distance is determined.

FIG. 6 is a flowchart of boundary condition determination processing for the phase difference between polarizations. FIG. 7 is a conceptual diagram of the range profile and variables of the phase difference Φ _DP between the polarizations.

In FIG. 7, the horizontal axis represents the distance, and the vertical axis represents the phase difference Φ _DP between the polarized waves. The point is the observed polarization phase difference Ψ. r _near is the distance from the radar at the nearest point where valid data exists, and r _far is the distance from the radar at the farthest point where valid data exists. Neighboring region observed values used to determine the neighborhood boundary conditions [Phi _near the points of the phase difference [Phi _DP of polarization near the boundary region BD in _near, the phase difference [Phi _DP of the points distant boundary region BD in _{far-polarization} This is a far field observation value used to determine the far boundary condition Φ _far of. The solid line in the near boundary region BD _near is the neighborhood regression line A1 used to determine the boundary value, and the solid line in the _far boundary region BD _far is the far regression line B1 used to determine the boundary value. A broken line Ln is a boundary condition Φ _near near the determined range, and a broken line Lf is a boundary condition Φ _{far near the} determined range.

  As shown in FIG. 6, in the boundary condition determination process between the polarization phase differences, first, in step 21, the number of normal observation data designated from the vicinity of the range is used to determine a section for calculating the boundary condition. Then, the neighborhood regression line A1 is obtained within the section (ST21).

In the present embodiment, as shown in FIG. 7, the data in the neighborhood area BD _near is used as the neighborhood boundary data, and the neighborhood regression line A1 is obtained in the neighborhood area BD _near . The number of data is preferably about 30 to 50.

  Next, in step 22, it is determined whether the slope of the neighborhood regression line A1 is positive or negative (ST22).

In step 22, if the slope of the neighborhood regression line A1 is positive, in step 23, the value corresponding to the nearest point of the neighborhood regression line A1 is set as the neighborhood boundary condition Φ _near in the vicinity of the range (ST23).

If the slope of the neighborhood regression line A1 is negative in step 22, the average value of the data in the neighborhood region BD _near is set as the neighborhood boundary condition Φ _near in the neighborhood of the range (ST24).

In the present embodiment, as shown in FIG. 7, since the slope of the neighborhood regression line A1 is positive, the value corresponding to the nearest point of the neighborhood regression line A1 is set as the neighborhood boundary condition Φ _near in the vicinity of the range.

  Next, in step 25, a section for calculating the far boundary condition is determined using the number of normal observation data designated from the far side of the range, and the far regression line B1 is obtained within the section (ST25).

In the present embodiment, as shown in FIG. 7, data in the far region BD _far is used as the far boundary data, and the far regression line B1 is obtained in the far region BD _far . The number of data is preferably about 30 to 50.

  Next, in step 26, it is determined whether the slope of the far regression line B1 is positive or negative (ST26).

If the slope of the far regression line B1 is positive in step 26, in step 27, the value corresponding to the farthest point of the far regression line B1 is set as the far boundary condition Φ _far in the far range (ST27).

If the slope of the far regression line B1 is negative in step 26, in step 28, the average value of the data in the far region BD _far is set as the far boundary condition Φ _far in the far range (ST28).

In the present embodiment, as shown in FIG. 7, since the slope of the far regression line B1 is negative, the average value of the data in the far region BD _far is set to the far boundary condition Φ _far in the far range.

Then, to execute the process of determining the ratio polarizations retardation K _DP that minimizes a cost function by the ratio polarization retardation K _DP determining means 37 that minimizes a cost function.

  FIG. 8 is a flowchart of the process for determining the phase difference between specific polarizations that minimizes the cost function.

As shown in FIG. 8, in the determination process of the relative polarization phase difference K _DP that minimizes the cost function, first, in step 31, an average value of all the slopes of the polarization phase difference profile is obtained, and k is calculated from that value. calculate the _a, which is the initial value of k _m. Here, m is a subscript related to distance, and m = 0, 1, 2,..., N (ST31).

In this method, it is assumed that K _DP always takes a positive value. Therefore, k _i that satisfies the following expression (11) is defined. However, i is a subscript relating to the distance as with m, and i = 0, 1, 2,..., N.

Prior to all processing, setting the initial profile of k _m. As this initial profile, providing a k _a corresponding to the average value of the ratio polarizations retardation K _DP in all range bins to all range bins.

In the profile of the phase difference Φ _DP between the polarizations in FIG. 7, the average value of the slope of the profile is expressed by the following formula (12). From formula (1), formula (11), and formula (12), k _a is the initial value of k _m is expressed by the equation (13).

Next, at step 32, for the current k _m, it calculates a differential value related to the cost function and k _m (ST32).

The range profile of the phase difference Φ _DP between the polarizations obtained by approximating the observed range profile ψ _i of the phase difference Ψ between the polarizations is defined as (Φ _DP ) _i . Here, i is a subscript relating to distance, i = 0, 1, 2,..., N. With respect to the phase difference range profile (Φ _DP ) _i between the polarized waves, φ _i as shown in FIG. 7 where the following equation (14) is established is defined.

ただし、Δｒはレンジビンの幅、（Ｋ_DP）_iは比偏波間位相差のレンジプロファイルである。 From the equation (1), when φ _i is expressed in discrete form, it is expressed by the following equations (15) and (16).

Where Δr is the width of the range bin, and (K _DP ) _i is the range profile of the phase difference between the specific polarizations.

When Expression (11) is used, Expression (16) is replaced as Expression (17).

On the other hand, when φ ′ _i as shown in FIG. 7 is defined as in the following equation (18), the following equations (19) and (20) hold as in φ _i .

Similarly for the range profile ψ _i of the observed phase difference Ψ between polarizations, ψ _i and ψ ′ _i are defined as the following equations (21) and (22).

Here, the cost function J to be minimized is defined as in the following Expression (23), Expression (24), Expression (25), and Expression (26).

J _obs and J ′ _obs are the sum of squares of the difference between the observed polarization phase difference Ψ and the polarization difference Φ _DP to be obtained, and J _lpf is the second derivative of the k-distance that functions as a low-pass filter. The sum of squares. C _lpf is an adjustment parameter for the low-pass filter. The larger the adjustment parameter C _lpf for the low-pass filter, the smoother the result.

Here, the characteristics of the low-pass filter adjusted by the adjustment parameter C _lpf will be considered. The cost function J includes J _obs + J ′ _obs for fitting to observation data and J _lpf having a low-pass filter function. When J _lpf is larger than J _obs + J ′ _obs , the contribution of J _{lpf to} the entire cost function increases, and the smoothing effect increases. On the contrary, when J _lpf becomes a value smaller than J _obs + J ′ _obs , the smoothing effect becomes small.

Assuming that k changes periodically in the distance direction with the wavelength L, if k is placed as in the following equation (27) and substituted into equation (11), the following equation (28) is obtained. .

The wavelength of the periodic change of K _DP corresponding to Equation (27) is L / 2, and the fluctuation range is 0 to a ² / 2Δr. The square of the second derivative with respect to r of k is as shown in the following equation (29).

The average value of this value in all range bins is the following equation (30).

Therefore, the following equation (31) is obtained from the equation (26).

On the other hand, J _obs and J ′ _obs are quantities corresponding to the mean square of the observation error of the phase difference between the polarizations. If the value is σ _obs ² , J _lpf and J _obs + J ′ _obs are approximately equal to each other. In this case, the following equation (32) is satisfied, and when transformed, equation (33) is obtained.

That is, when L is a value smaller than the right side of Expression (33), J _lpf is a value larger than J _obs + J ′ _obs , so that the smoothing effect is increased. In setting the adjustment parameter C _lpf , it is preferable to set a value such that the expression (33) is several hundred meters to several kilometers.

Further, as can be seen from the equation (33), the wavelength L is proportional to the 1/4 power of the adjustment parameter C _lpf . That is, even if the value of the adjustment parameter C _lpf is increased ten times, the amount of change in the wavelength L is only about 1.78 times, so there is little meaning to the _minute fluctuation of the adjustment parameter C _lpf . The adjustment of the adjustment parameter C _lpf is preferably performed with a change width of about 10 ⁻³ times to 10 ³ times.

To determine the k _m that minimizes J using variational method, the following equation (34), equation (35), and as shown in equation (36), determine the partial differential of k _m of J.

Next, at step 33, obtains the k _m to reduce the cost function than the current k _m (ST33).

Since the partial differential related to k _m of the defined cost function J is known, in the present embodiment, by using the BFGS (Broyden-Fletcher-Goldfarb- shanno) method which is a kind of quasi-Newton method to deal with non-linear programming problem cost Find km _m that minimizes function J. In addition, you may use not only the BFGS method but another method.

In the Newton method, the function F (v) of a certain vector v = (v ₁ , v ₂ ,..., V _n ) is used using the Hessian matrix A (v) defined by the following equation (37): V that minimizes the function F (v) is obtained by the following equation (38). However, the subscript k is a subscript representing the number of iterations, and α is a step size separately determined by a one-dimensional search.

However, this recurrence formula includes an inverse matrix of the Hessian matrix, and its calculation cost is very high. In a method called the quasi-Newton method, instead of the inverse matrix of the Hessian matrix, H obtained by successive approximation is used, and the final v is obtained by the following recurrence formula (39).

ただし、以下の式（４１）〜式（４３）とする。

In the BFGS method, H is obtained by the following recurrence formula (40).

However, it is set as the following formulas (41) to (43).

  Since the matrix H has a size of n × n, when a problem with a large n is handled by the BFGS method, the computer memory capacity for H becomes a problem. In the case of radar data, since the number of range bins is about several hundreds, the amount of memory used for H on the computer is only about several megabytes, so the BFGS method can be used without any problem.

Next, at step 34, k _m is determined whether the convergence (ST34).

In step 34, if k _m has not converged, the process returns to step 32.

In step 34, if k _m converges, in step 35, the ratio polarizations retardation K _DP corresponding to the final k _m obtained from equation (11) (ST35).

FIG. 9 is a diagram showing a result of using the method of this embodiment with respect to the observed phase difference Φ _DP between the polarizations in FIG. A smooth line is the result of this method.

The range bin width Δr of this range profile is 100 m, and 1.0 × 10 ¹¹ is used as the adjustment parameter _Clpf . In the present embodiment, the iterative filter method is not used.

As shown in FIG. 9A, the observed phase difference Φ _DP between the polarized waves includes a large δ near the distance of 17 km, but δ is removed in the result of the present embodiment.

Further, as shown in FIG. 9B, a negative value is obtained in the specific polarization phase difference K _DP obtained by linear regression having a width of 1 km with respect to the observed phase difference Φ _DP between the observed polarizations. Although many are calculated, the negative specific polarization phase difference K _DP is not calculated in the result of the present embodiment. Furthermore, the ratio polarization near the phase difference peak value of K _DP near distance 15km, profile by both methods is almost identical.

FIG. 10 shows the dependency of the adjustment parameter _Clpf in this embodiment.

The result of FIG. 10C is the same as that of FIG. 9B, and the adjustment parameter C _lpf was scaled with the result as a reference, and the result was examined.

FIG. 10A shows a case where the adjustment parameter C _lpf in FIG. 10C is multiplied by 10 ⁻² so that the adjustment parameter C _lpf = 1.0 × 10 ⁹ . adjustment parameter C _lpf by fold 10 ^-1 of, when the adjustment parameter C _lpf = 1.0 × 10 ^10, FIG. 10 (d) is by 10 ¹ times the adjustment parameter C _lpf shown in FIG. 10 (c) , when the adjustment parameter C _lpf = 1.0 × 10 ^11, and FIG. 10 (e) is ^doubled 10 adjustment parameter C _lpf in FIG. 10 (c), the adjustment parameter C _lpf = 1.0 × 10 FIG. ¹³ is a diagram showing each of the cases.

It can be seen that as the adjustment parameter _Clpf increases, the variation of the specific polarization phase difference K _DP becomes smoother and the peak value becomes smaller. Further, when the adjustment parameter _Clpf is small, it can be seen that the drop of the relative polarization phase difference K _DP on the peak rear side becomes sharper than the relative polarization phase difference K _DP on the near peak side. This is because when the phase difference Φ _DP between the polarizations is fitted to the observation site while the specific phase difference K _DP between the specific polarizations is constrained to a positive value, the phase difference Φ _DP between the polarizations is biased upward. This is because the change in the phase difference Φ _DP between the waves is suppressed, and the effect of causing the phase difference K _DP between the specific polarizations to be zero appears even on the convex portion of the smaller spatial scale.

Further, in the observed phase difference Φ _DP between the polarized waves, the influence of the phase difference δ due to backscattering also appears as a similar convexity. It is preferable to apply a double, iterative filter using a small adjustment parameter C _lpf .

  In addition, this invention is not limited by this embodiment. That is, in the description of the embodiments, many specific details are included for illustration, but those skilled in the art can add various variations and modifications to these details without departing from the scope of the present invention. It will be understood that this is not exceeded. Accordingly, the exemplary embodiments of the present invention have been described without loss of generality or limitation to the claimed invention.

DESCRIPTION OF SYMBOLS 1 ... Rainfall observation system 2 ... Dual polarization weather radar 3 ... Specific polarization phase difference calculating device 31 ... Interpolarization phase difference folding correction means 32 ... Interpolarization phase difference quality control means 33 by polarization correlation coefficient 33 ... Interphase phase outlier removal means 34 ... Phase difference removal means 35 caused by backscattering ... Rain layer discrimination means 36 ... Interpolarization phase difference boundary condition determination means 37 ... Specific polarization phase difference that minimizes cost function Determining means 4 ... Precipitation intensity estimating means 5 ... Rain attenuation determining means 6 ... Output means

Claims (6)

Correcting the discontinuous state of the phase difference between the polarizations of the observation data that changes with respect to the distance, and restoring the phase difference between the polarizations of the original continuous observation to restore the phase difference between the polarizations observed continuously,
Quality control means for managing observation point data having a correlation coefficient between polarizations below a predetermined threshold so as not to be used for analysis;
Obtain the moving average and standard deviation for the distance between the observed polarization phase differences, and if the difference between the observed polarization phase difference and the moving average value exceeds the threshold value at each distance, the distance data Outlier removal means that replaces with a moving average;
A method for determining a rain layer and a region that is considered to contain precipitation particles other than rain, and for determining a rain layer that excludes data other than the rain layer from the analysis target,
Boundary condition determining means for determining the boundary condition of the phase difference between the polarizations near and far from the range;
A ratio that determines the phase difference between the polarizations that minimizes the cost function consisting of the square of the difference between the observed phase difference between the polarizations and the phase difference between the polarizations to be determined and the square of the second derivative with respect to the distance that functions as a low-pass filter. Means for determining the phase difference between the polarizations;
An apparatus for calculating the phase difference between specific polarizations. Removing means for removing a phase difference due to backscattering of the observation data;
The phase difference calculation apparatus between specific polarizations according to claim 1, comprising: Sum of squares of the differences between the polarizations retardation [Phi _DP to be obtained with the polarization phase difference Ψ observed the J _obs and J _'obs,
The sum of squares of the second derivative with respect to the distance of k, where J _lpf functions as a low-pass filter,
k is the square root of K _DP multiplied by the width of the range bin and 2; C _lpf is the adjustment parameter of the low-pass filter;
Φ _near and Φ _far are the boundary conditions of the phase difference between polarizations near and _far from the range,
age,
When the following formulas (A) to (F) are used,

3. The phase difference calculation device between specific polarizations according to claim 1, wherein the cost function J is defined by the following equations (G) to (J). 4.

A dual-polarization weather radar that uses radio waves of two types of polarization, horizontal and vertical,
A phase difference calculation device between specific polarizations that calculates a phase difference between specific polarizations based on data observed by the dual polarization weather radar; and
A rainfall intensity estimating means for estimating a rainfall intensity distribution from the observation data acquired by the dual-polarization weather radar and the phase difference between specific polarizations calculated by the phase difference calculation unit between specific polarizations;
Rain attenuation determination means for estimating an undetectable region from the observation data acquired by the dual-polarization weather radar and the phase difference between specific polarizations calculated by the phase difference calculation unit between specific polarizations;
Output means for outputting a rainfall intensity distribution from the observation result of the rainfall intensity estimating means and the observation result of the rain attenuation determining means;
The rain observation system using the phase difference calculation apparatus between specific polarizations of any one of Claims 1 thru | or 3 characterized by the above-mentioned. Correcting the discontinuity of the phase difference between the polarizations of the observation data that varies with distance, and restoring the original continuous observed phase difference between the polarizations;
Managing data of observation points having a correlation coefficient between polarizations equal to or lower than a predetermined threshold so as not to be used for analysis;
Obtain the moving average and standard deviation for the distance between the observed polarization phase differences, and if the difference between the observed polarization phase difference and the moving average value exceeds the threshold value at each distance, the distance data Replacing with a moving average,
Discriminating regions that are likely to contain precipitation and non-rain precipitation particles, and removing non-rainfall data from the analysis;
Determining boundary conditions for the phase difference between polarizations near and far from the range;
Determining a specific interpolarization phase difference that minimizes the cost function consisting of the square of the difference between the observed interpolarization phase difference and the interpolarization phase difference to be determined, and the square of the second derivative with respect to the distance acting as a low-pass filter. When,
A method for calculating the phase difference between specific polarizations, comprising: Determining the boundary condition of the phase difference between polarizations near and far from the range,
Obtaining a linear regression line using a predetermined number of normal observation data from near and far from the range;
Determining whether the slope of the linear regression line determined near and far from the range is positive or negative;
When the slope of the linear regression line near the range is positive, a value corresponding to the closest point is set as a boundary condition in the vicinity;
When the slope of the linear regression line in the vicinity of the range is negative, a step of setting an average value of a predetermined number of normal observation data from the vicinity of the range from which the linear regression line has been obtained as a boundary condition of the neighborhood;
When the slope of the linear regression line far from the range is positive, a value corresponding to the farthest point is set as a far boundary condition;
When the slope of the linear regression line far from the range is negative, the average value of a predetermined number of normal observation data from the far range to obtain the linear regression line as a far boundary condition;
The method of calculating a phase difference between specific polarizations according to claim 5.

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