CN107621637B - Shear region wind field inversion method based on single Doppler radar - Google Patents

Shear region wind field inversion method based on single Doppler radar Download PDF

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CN107621637B
CN107621637B CN201710793970.5A CN201710793970A CN107621637B CN 107621637 B CN107621637 B CN 107621637B CN 201710793970 A CN201710793970 A CN 201710793970A CN 107621637 B CN107621637 B CN 107621637B
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wind field
inversion
neighborhood
doppler radar
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吴晓锋
唐晓文
王元
沈文强
丁晓丽
徐昕
黄浩
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Nanjing University
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Abstract

The invention discloses a shear region wind field inversion method based on a single Doppler radar, which comprises the following steps: firstly, local constraint is used, the wind speeds of all points in a small enough neighborhood are assumed to be equal, and meanwhile, radial speed consistency constraint is added during neighborhood selection, so that the algorithm can be suitable for a shear region wind field; then, a preliminary inversion result is obtained by utilizing a least square method; then introducing a global constraint general function and assuming that the wind speed meets a certain condition in the whole inversion region; and finally, optimizing an inversion result by a method of solving the minimum value of the general function. According to the method, the actual wind field including the shear region can be inverted only by a radial velocity field observed by a single Doppler radar at a certain moment.

Description

Shear region wind field inversion method based on single Doppler radar
Technical Field
The invention relates to a wind field inversion method based on a single Doppler radar, in particular to a shear region wind field inversion method based on the single Doppler radar, and belongs to the field of atmospheric science remote sensing data analysis and research.
Background
Doppler radar is widely applied in the meteorological field at present, and can well observe and track small and medium-scale precipitation systems. Since the doppler radar can only observe the projection of the motion of the precipitation particles in the radar beam direction, which is usually called radial velocity, the actual wind field commonly used in meteorological analysis and forecasting needs to be obtained by means of inversion. Many meaningful works have been done by the predecessors in inverting the actual wind field using doppler radial velocity.
In 1970, Lhermitte et al proposed a coplanar inversion technique based on dual Doppler radars, which was improved and improved by Miller et al, but the current service radar has a small area covered by the dual Doppler radars, so the method has a small application range.
The current-stage service radar mainly uses a single Doppler radar as a main radar, has a wide coverage area, and is more beneficial to improving the analysis and forecast work in the actual service by researching a wind field inversion method based on the single Doppler radar.
As early as 1961, Lhermitte et al proposed a velocity and orientation display method (VAD) based on a single Doppler radar, and then by improvement and improvement of Brown et al, the parameters of divergence, deformation and the like of a wind field can be further obtained. The VAD method assumes that the actual wind field changes linearly, and has certain limitations in service use: firstly, the VAD method can only obtain the average horizontal wind field in the radar observation range, which is not beneficial to exerting the characteristic of high radar resolution; secondly, the assumption that the wind field varies linearly may not be well established in some cases, and the inverted wind field may deviate significantly from the actual wind field when there is a shear region in the wind field. In the 70 s of the 20 th century, under the assumption of a local linear wind field, Waldteufel et al proposed a velocity volume processing technique (VVP), which can invert the horizontal and vertical structures of a wind field at the same time, but due to the ill-conditioned problem of the coefficient matrix of the algorithm, errors are easily generated in inverting the wind field. There are studies attempting to alleviate the problems with the ill-conditioned matrix by reducing the number of inversion parameters, but the neglected parameters may become new sources of error in the inversion.
In order to improve the wind field inversion technology based on the Doppler radar, the former introduces an optical flow method which is widely applied in the field of computer vision. Scientists like Gibson and Wallach have proposed the basic principles of optical flow as early as the 50's of the 20 th century. Two scientists of horns and Schunck are really put forward an effective optical flow calculation method, creatively link a two-dimensional velocity field with image gray, and introduce an algorithm of an optical flow constraint equation to realize an optical flow method in the real sense. The application of the optical flow method in the inversion of the actual wind field by the Doppler radar is mainly to solve the problem of radar reflectivity, namely, the radar reflectivity at different moments is regarded as continuous multi-frame gray level images, and the average speed between the two moments can be obtained by using a standard algorithm. Although the optical flow method has certain advantages in terms of operation speed and inversion accuracy, model errors still exist when the radar reflectivity is applied to the optical flow method. The optical flow method requires that the image follows the assumption of gray scale invariance, and the actual radar reflectivity has generative evolution, so that an error caused by the change of the reflectivity intensity exists, and the error is more obvious in the process of rapidly changing strong convection weather.
Disclosure of Invention
Aiming at the defects of the existing wind field inversion technology based on the Doppler radar, the invention provides a novel wind field inversion method based on the single Doppler radar and suitable for a shear region. The main technical innovation is that the actual wind field including a shear region can be inverted only by a radial velocity field observed by a single Doppler radar at a certain moment.
In order to solve the technical problem, the shear zone wind field inversion method based on the single doppler radar comprises the following steps: introducing a local constraint equation Urx+Vry＝VrWherein
Figure BSA0000150180960000021
Is an actual wind field, rx、ryIs the component of the unit vector of the radar beam direction in the x, y directions, VrIs the Doppler radial velocity; taking any point as a reference point, selecting a neighborhood of a 5 × 5 or 7 × 7 grid near the point and assuming that wind speeds of all points in the neighborhood are equal; comparing the radial velocity difference between each point and the reference point in the neighborhood to ensure that the absolute value of the difference between the selected point and the reference point is less than a critical value Vth(ii) a Obtaining preliminary inversion result by least square method
Figure BSA0000150180960000022
A is an Nx 2 matrix formed by components of unit vectors of each point in the neighborhood in the radial direction in the x direction and the y direction, B is an Nx 1 matrix formed by the radial speed of each point in the neighborhood, and N is the number of points in the neighborhood; introducing a global constraint general function, and optimizing an inversion result by a method of solving a minimum value of the general function.
In the above scheme, the critical value VthBy inverting error EOSTo determine, said
Figure BSA0000150180960000023
Wherein
Figure BSA0000150180960000024
For a given actual wind field it is desirable to,
Figure BSA0000150180960000025
v is not less than 4.0 for the inverted wind fieldth≤6.0。
In the above technical solution, the global constraint general function is:
Figure BSA0000150180960000026
wherein
Figure BSA0000150180960000027
Is an actual wind field, VrFor doppler radial velocity, the subscripts x, y denote the components of the variable in the x, y direction,
Figure BSA0000150180960000028
the method comprises the steps of calculating to obtain a preliminary inversion wind field by using a least square method under local constraint; the first term of the general function is a motion constraint term, the second term is a smoothing term, the third term is a least square method wind speed consistency constraint term, alpha and beta are Lagrange coefficients, alpha is 5.0, and beta is 1.0.
In the above scheme, the global constraint general function may be converted into an euler-lagrange equation, and then the minimum value is solved by using a gaussian-seidel iterative equation, and the iterative formula may be written as follows:
Figure BSA0000150180960000031
when the n +1 th iteration result Vn+1Result of iteration with nth time VnWhen the difference is less than a threshold value, Vn+1The critical value is 0.001 as the result.
Compared with the wind field inversion method based on the Doppler radar, the wind field inversion method has the following advantages:
1. compared with a double-Doppler radar inversion method, the method can invert the actual wind field only by observation data of a single Doppler radar, and has the characteristic of wide application range;
2. compared with VAD and VVP methods, the method can invert a linear wind field and can invert a wind field with a shear zone;
3. compared with the traditional optical flow method, the method can invert the actual wind field only by the radial velocity field observed by the Doppler radar at a certain moment, and avoids errors caused by the change of the reflectivity intensity in the traditional optical flow method.
Drawings
FIG. 1 is a flow chart of a wind field inversion;
FIG. 2 is EOSDistance following VthVariation diagram of (E)OSFor inversion of errors, VthThe maximum value which can be reached by the absolute value of the radial velocity difference value of each point in the neighborhood and the reference point (the center point of the neighborhood);
FIG. 3 is a graph of the superposition of wind field inversion results and reflectivity factors (shaded areas) of the present invention at 1 st 13:09 (world time) 6/2015;
FIG. 4 is a graph showing the superposition of wind field inversion results and reflectivity factors (shaded areas) for dual Doppler radars (Jingzhou radar and Yueyang radar) at 13:09 (world time) at 6.1.2015;
Detailed Description
Hereinafter, specific embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The wind field inversion algorithm mainly comprises the following four steps (figure 1): firstly, local constraint (formula 1) is used, and assuming that the wind speeds of all points in a sufficiently small neighborhood are equal, the neighborhood is usually a 5 × 5 or 7 × 7 grid, after a plurality of tests, the 5 × 5 grid is selected in the embodiment, and meanwhile, radial speed consistency constraint is added when the neighborhood is selected, so that the algorithm can be suitable for a shear region wind field; then, a preliminary inversion result is obtained by utilizing a least square method; then introducing a global constraint general function (formula 5), and assuming that the wind speed meets a certain condition in the whole inversion region; and finally, optimizing an inversion result by a method of solving the minimum value of the general function.
The method comprises the following specific steps:
1. local constraint
First, a local constraint equation is introduced:
Urx+Vry＝Vr(1)
wherein
Figure BSA0000150180960000041
Is an actual wind field, rx、ryIs the component of the unit vector of the radar beam direction in the x, y directions, VrIs the doppler radial velocity. To obtain the actual wind field at a point, a sufficiently small neighborhood is selected around the point and wind speeds are assumed to be equal for all points in the neighborhood. For a neighborhood containing N points (the neighborhood is defined as a 5 × 5 grid in the present invention, so N — 25), a linear system of equations containing N equations can be obtained:
Figure BSA0000150180960000042
equation (2) can also be written as:
Figure BSA0000150180960000043
wherein A is an Nx 2 matrix formed by components of unit vectors of each point in the neighborhood in the radial direction in the x direction and the y direction, V comprises the actual wind speed of each point in the neighborhood in the x direction and the y direction, and B is an Nx 1 matrix formed by the radial speed of each point in the neighborhood. If and only if ATIn the case of reversible A, the least square method can be used to obtain the final inversion result (A)
Figure BSA0000150180960000044
Represents the result calculated by the least squares method):
Figure BSA0000150180960000045
2. radial velocity uniformity constraint
We add radial velocity when selecting neighborhoodsConsistency constraints, before which, a specific definition of consistency is required. Here we define that the absolute value of the difference between the radial velocities of each point in the neighborhood and the reference point (the center point of the neighborhood) is less than a certain threshold value VthThe radial velocity is uniform. And when the neighborhood is selected, the point with larger radial speed difference with the reference point in the neighborhood can be effectively eliminated by adding the radial speed consistency constraint. To determine this optimum threshold value VthWe designed an ideal data experiment: firstly, a group of assumed wind fields are given as actual wind fields, then corresponding radial velocity fields are calculated, then inversion is carried out by utilizing the algorithm in the invention to obtain inversion wind fields, and finally the inversion wind fields are compared with the assumed actual wind fields. At the same time we define EOSTo reflect the inversion error, the calculation formula is as follows:
Figure BSA0000150180960000051
wherein
Figure BSA0000150180960000052
For a given actual wind field it is desirable to,
Figure BSA0000150180960000053
and inverting the obtained wind field. FIG. 2 is EOSDistance following VthWhen V is changed, as can be seen from the figurethBelow 2.0, the inversion error is large because of VthThe smaller the number of points in the neighborhood that satisfy the condition, the larger the calculation error, and even the case where the points in the neighborhood cannot satisfy the calculation requirement. When V isthWhen V is more than or equal to 4.0, the error tends to be smooth, and when V is larger than or equal to 4.0thWhen the inversion error is larger, the inversion error of the wind field in the shear region is larger, and after a plurality of tests, V is more than or equal to 4.0th≤6.0。
3. Global constraints
In order to make the inversion result smoother and closer to the real wind field, a global constraint general function is introduced:
Figure BSA0000150180960000054
wherein
Figure BSA0000150180960000055
Is an actual wind field, VrFor radar radial velocity, the indices x, y denote the components of the variables in the x, y direction,
Figure BSA0000150180960000056
the method is an inversion wind field calculated by a least square method under local constraint. The first term of the general function is a motion constraint term which requires that the projection of the inversion wind field in the radar beam direction is consistent with the radar radial velocity; the second term is a smoothing term which can ensure that the wind field obtained by inversion is as smooth as possible; the third term is a least square method wind speed consistency constraint term which requires that the calculation result is as close as possible to the inversion result of the least square method. α and β are lagrange coefficients and represent the relative importance of the second term and the third term, respectively (α and β may take any value, and through a plurality of experiments, α is 5.0, and β is 1.0).
Due to the fact that
Figure BSA0000150180960000057
Figure BSA0000150180960000058
Can be unfolded into Ur1+Vr2We can convert to the euler-lagrange equation and take its minimum:
Figure BSA0000150180960000059
Figure BSA00001501809600000510
get approximate
Figure BSA00001501809600000511
The Euler-Lagrange equation can be written as a matrix as followsForm (a):
Figure BSA00001501809600000512
wherein the content of the first and second substances,
Figure BSA0000150180960000061
the final gaussian-seidel iteration equation can be written as follows:
Figure BSA0000150180960000062
when the n +1 th iteration result Vn+1Result of iteration with nth time VnWhen the difference is less than a threshold value, Vn+1As the result, we take the critical value to be 0.001 in the present invention.
4. Demonstration of effectiveness
In order to verify the validity of the content of the invention, the observation data of the Yueyang radar in the event of sinking the ship by the east star at 6 and 1 days 2015 is selected for wind field inversion, and the inversion results of the dual-Doppler radar, namely the Jingzhou radar and the Yueyang radar, are used for comparison. Fig. 3 and 4 are an inversion effect graph and a dual doppler radar inversion effect graph of the present invention at one time, respectively, and it can be seen that the process is a squall line process, the inversion result of the present invention can well reflect the front side inflow and the rear side inflow of the squall line, a wind field shear area in a strong echo center area can be well reproduced, and the inversion result is substantially consistent with the dual doppler radar inversion result (the same conclusion is also provided at other times).

Claims (7)

1. The shear zone wind field inversion method based on the single Doppler radar is characterized by comprising the following steps: introducing a local constraint equation Urx+Vry＝VrWherein
Figure FSA0000150180950000011
Is an actual wind field, rx、ryFor radar beam directionComponent of the bit vector in the x, y direction, VrIs the Doppler radial velocity; taking any point as a reference point, selecting a neighborhood of a 5 × 5 or 7 × 7 grid near the point and assuming that wind speeds of all points in the neighborhood are equal; comparing the radial velocity difference between each point and the reference point in the neighborhood to ensure that the absolute value of the difference between the selected point and the reference point is less than a critical value Vth(ii) a Obtaining preliminary inversion result by least square method
Figure FSA0000150180950000012
A is an Nx 2 matrix formed by components of unit vectors of each point in the neighborhood in the radial direction in the x direction and the y direction, B is an Nx 1 matrix formed by the radial speed of each point in the neighborhood, and N is the number of points in the neighborhood; introducing a global constraint general function, and optimizing an inversion result by a method of solving a minimum value of the general function.
2. The single doppler radar based shear zone wind field inversion method of claim 1, wherein: the critical value VthBy inverting error EOSTo determine, said
Figure FSA0000150180950000013
Wherein
Figure FSA0000150180950000014
For a given actual wind field it is desirable to,
Figure FSA0000150180950000015
and inverting the obtained wind field.
3. The single doppler radar based shear zone wind field inversion method of claim 1 or 2, wherein: v is not less than 4.0th≤6.0。
4. The single doppler radar based shear zone wind field inversion method of claim 1 or 2, characterized in thatIn the following steps: the global constraint general function is
Figure FSA0000150180950000016
Wherein
Figure FSA0000150180950000017
Is an actual wind field, VrFor doppler radial velocity, the subscripts x, y denote the components of the variable in the x, y direction,
Figure FSA0000150180950000018
the method comprises the steps of calculating to obtain a preliminary inversion wind field by using a least square method under local constraint; the first term of the general function is a motion constraint term, the second term is a smoothing term, the third term is a least square method wind speed consistency constraint term, and alpha and beta are Lagrange coefficients.
5. The single doppler radar based shear zone wind field inversion method of claim 4, wherein: α is 5.0 and β is 1.0.
6. The single doppler radar based shear zone wind field inversion method of claim 5, wherein: the global constraint general function can be converted into an Euler-Lagrange equation, and then the minimum value of the Euler-Lagrange equation is solved through a Gauss-Seidel iteration equation, and the iteration formula can be written into the following form:
Figure FSA0000150180950000021
when the n +1 th iteration result Vn+1Result of iteration with nth time VnWhen the difference is less than a threshold value, Vn+1I.e. as the result of the finding.
7. The single doppler radar based shear zone wind field inversion method of claim 6, wherein: the critical value is 0.001.
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