CN114219143B - Global spectrum mode initial field vertical layering arbitrary interval smooth encryption method - Google Patents
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Abstract
The invention discloses a global spectrum mode initial field vertical layering random interval smooth encryption technology, which relates to the field of numerical weather forecast, and adopts an exponential stretching algorithm to determine a mixed coordinate coefficient of a newly added vertical layer according to a given air pressure interval needing encryption and the newly added vertical layer number; smoothing at the boundary end through a second-order function to ensure the smoothness between the newly added vertical layer interval and the port; after determining the vertical coordinates of the newly added layers, adopting cubic spline interpolation to the global spectrum-lattice point data from the original layers to the new layers, and accelerating the interpolation speed by using a catch-up method rapid algorithm in the process of cubic spline interpolation. The invention finally provides a new initial field for vertically and uniformly encrypting the appointed area, and the field can be suitable for a global spectrum mode and can be used for stabilizing integration; the vertical layer is added above the top of the mode troposphere, so that analysis of upward propagation of gravitational waves can be promoted, and the problem of stratospheric refrigeration is relieved.
Description
Technical Field
The invention belongs to the technical field of numerical weather forecast, and particularly relates to a global spectrum mode initial field vertical layering random interval smooth encryption method.
Background
The current stage global spectrum mode vertical stratification generally employs 137 layers, which are close to the surface area at the bottom of the mode, dense layers because human activity is substantially concentrated in this area, and sparse layers at and above the top stratosphere of the mode. Scientific researches show that excessive sparseness of stratosphere layering can lead to insufficient resolution of upward propagation of gravitational waves, so that the temperature of the lower part of the stratosphere is warm, and the top of the stratosphere is cold. The problem of partial cooling at the top of the stratosphere can be effectively relieved by locally encrypting the stratosphere with the mode of vertical layering.
The global spectrum mode initial field is divided into a spherical harmonic spectrum data initial field and a lattice point data initial field, the spherical harmonic spectrum data initial field and the lattice point data initial field are positioned on a gas pressure surface based on mixed coordinates, local encryption is difficult for a given gas pressure interval, especially a new layering after local encryption needs to be given in the form of mixed coordinates A and B, and the new layering needs to be ensured to be smooth and uniform, so that the initial field can keep stability during mode integration. Therefore, developing a smooth encryption technology aiming at a local air pressure interval has relatively complex and important significance.
After the new vertical layering determination, if linear interpolation is adopted for data interpolation, the calculation speed is higher but the accuracy is not high, if cubic spline interpolation is adopted, the calculation accuracy is improved but the calculation cost is increased, and particularly for the global spectrum mode and mass data, a quick algorithm is necessary to be developed in order to ensure the calculation instantaneity.
Disclosure of Invention
The invention aims to provide a global spectrum mode quality mixed coordinate initial field vertical layering random interval smooth encryption technology, which can carry out local encryption on vertical layering aiming at a global spectrum mode initial field, spectrum coefficient data and lattice point field data, and the new encrypted initial field layering change is smooth, and integral stabilization is an excellent encryption technology.
In order to solve the technical problems, the invention firstly adopts an exponential stretching algorithm to calculate the newly added layering air pressure coordinates of a given interval and layer number, and simultaneously performs quadratic polynomial smoothing on layering intervals at two ends of the interval to ensure the mode integration stability. After layering is determined, the original layering data is interpolated to new layering data to serve as a new initial field by utilizing a cubic spline, and a catch-up method is adopted in the cubic spline interpolation to keep the calculation accuracy and greatly increase the calculation speed.
The invention provides a global spectrum mode initial field vertical layering arbitrary interval smooth encryption method, which comprises the following specific steps:
acquiring global spectrum-grid point data;
determining the air pressure position of a newly added layer in a given area by adopting an index catch-up method;
Determining a mixed coordinate coefficient and a layered coordinate of the newly added vertical layer by using an index stretching algorithm according to the given air pressure interval needing to be encrypted and the newly added vertical layer number;
at the boundary end, the smoothness between the newly added vertical layer interval and the port is ensured by second-order polynomial smoothing, and the initial field is ensured to be stable during mode integration;
After determining the layering coordinates of the newly added vertical layering, interpolating the original layering data to the new layering data by adopting a cubic spline, and accelerating the interpolation speed by utilizing a catch-up method in the cubic spline interpolation process;
And outputting the encrypted initial field data.
Further, the layering interval between the pressures 10hPa and 20hPa is smoothly changed by a second order polynomial.
Further, the original hierarchical data comprises spectrum data and lattice point data, the formats of the original hierarchical data and the new hierarchical data are GRIB, and the spectrum lattice attribute is kept unchanged.
Further, the determining the air pressure position of the newly added layer in the given area by adopting the index catch-up method comprises the following steps: obtaining the stretching parameter z by solving e
Where p t is the upper boundary of a given pressure interval and n is the total number of layers newly added.
Further, the tensile coefficient s (l) of the first layer of the added delamination is calculated as follows:
Where p t is the upper boundary of a given pressure interval, n is the total number of layers newly added, and z e is the stretching parameter.
Further, the newly added vertical stratification is above the troposphere top.
The beneficial effects of the invention are as follows:
the invention can quickly interpolate the initial field of the global spectrum mode to generate a new initial field with higher vertical resolution, the generated format is GRIB format, and the data content comprises spectrum data and lattice point data;
The invention can smoothly and newly increase the grid spacing between vertical layering, provide a new initial field for vertically and uniformly encrypting the appointed area, and the field can be suitable for a global spectrum mode and can stabilize mode integration;
According to the invention, the vertical layer is added above the top of the mode troposphere, so that analysis of upward propagation of gravitational waves can be promoted, the problem of partial cold at the top of the stratosphere is remarkably relieved, and the integration precision at the top of the mode layer is increased, so that the method has higher practical value in the encryption of the appointed section of the initial field of the numerical forecasting mode.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a graph showing the vertical inter-layer distance distribution of the present invention assuming that the encryption position is 10-270hPa, the number of original layers is 137, and the number of layers is newly increased by 20 to 157;
FIG. 3 is a schematic diagram of two end positions of a pneumatic layer;
FIG. 4 is a vertical cross-section of the average weft average temperature;
FIG. 5 is a graph showing the result of a one month gravity potential height root mean square error statistical test of the interpolated 157 layer data of the present invention;
Fig. 6 shows the interpolated 157-layer data integrated one month temperature field statistical test result.
Detailed Description
The invention is further described below with reference to the accompanying drawings, without limiting the invention in any way, and any alterations or substitutions based on the teachings of the invention are intended to fall within the scope of the invention.
According to the method, an index stretching algorithm is used, for a given interpolation interval and an increased layering number, a newly increased layering air pressure coordinate is calculated, and then two ends are smoothed.
As shown in FIG. 1, the global spectrum model initial field vertical layering arbitrary interval smooth encryption technology of the invention comprises the following steps:
s1, determining the air pressure position of a newly added layer in a given area by adopting an index catch-up method.
Given the pressure interval p t,pb, and the newly added total number of layers n (including upper and lower boundaries), each layer is denoted by l E (0, n), then the stretch coefficient of the first layer s (l)
Wherein z e < 1 is the stretching parameter to be determined, and the air pressure value of each layer is
pl＝s(l)pb (2)
The upper and lower boundary conditions are
pt＝p0， (3)
pb＝pn (4)
Obviously, the condition (4) is satisfied, in order to satisfy the upper boundary condition (3), there is
Z e is obtained by solving (5). The solution of the formula is difficult to obtain an analytic form, and Newton iteration can be adopted to obtain an approximate solution with given precision.
S2, determining a newly added layered coordinate by using an index stretching algorithm.
And for a given interval and the number of newly added layers, determining the air pressure coordinates of the newly added layers in the interval. For example, 10-270hPa, 20 layers are added, and the newly added uniform layers are about 298m by using an index stretching algorithm. FIG. 2 is a graph showing the vertical inter-layer distance distribution assuming that the encryption position is 10-270hPa, the original layer number is 137 layers, and 20 layers to 157 layers are added.
S3, performing quadratic polynomial interpolation smoothing on two ends of the newly added layer.
After the vertical layering is calculated by using the exponential stretching algorithm, the interval of each layer is basically uniform, but the interval at each end is suddenly changed, so that the integral error or the integral instability is caused, and layering adjustment at the end points is needed once, so that the interval at the end points of the layering keeps smooth change. As shown in FIG. 2, the layering interval smoothly varies with a second order polynomial between pressures 10hPa and 20 hPa.
Assume two port locations P 0 P1, and P (N)PN+1, as shown in fig. 3.
The spacing of each air pressure layer is d n＝pn+1-pn, d 0,dN, andIn order that the physical spacing of the layering intervals is a smooth function, the interval distance is set to satisfy the following function
dl＝a+bl+cl2
Conditions known for two endpoints
d0＝a
dN＝a+bN+cN2
Can be pushed out
a＝d0
According to the sum formula
Order theHas the following components
a＝d0
b+cN＝δd
Pushing out
b+cN＝δd
Has the following components
a＝d0
b＝δd-cN
Therefore, the layering interval at the port is obtained, and the layering specific position at the port is obtained.
S4, interpolating cubic spline data based on a catch-up method.
After the layered coordinates are determined through the steps, the original data are interpolated to the new layered data.
And interpolating the original layered data comprising the spectrum data and the lattice point data to new layered data by utilizing a chase method cubic spline interpolation. The original data is in GRIB format, and after interpolation is completed, the original data is also in GRIB format, and the spectrum lattice attribute is kept unchanged, so that new encrypted initial field data is generated.
Assuming that the original initial field is interpolated from the original 137 layers to 157 layers, this is achieved by cubic spline interpolation. The cubic spline interpolation function can be expressed as:
Wherein,
hj＝xj-xj-1
S (x) satisfies C 2 succession at node x j, a cubic polynomial in each interval. M j in equation (6) is the second derivative at node x j, which is unknown, and can be solved by the following matrix equation:
Wherein,
dj＝6f[xj-1,xj,xj+1]
The solution formula (7) can directly adopt a matrix inversion method, but the calculation cost is somewhat high. A more efficient algorithm is the catch-up method.
For a system of tri-diagonal equations with dominant diagonal shape
Can be noted as ax=f, when i-j > 1, a i,j =0 and the following condition is satisfied
|b1|＞|c1|＞0；
|bi|≥|ai|+|ci|,aici≠0,i＝2,3,…n-1；
|bn|＞|an|＞0；
A catch-up method may be employed. A can be decomposed into
Let a=lu, so solving ax=f is equivalent to solving two sets of trigonometric equations:
The solving steps are as follows:
(1) A recursive formula for calculating beta i:
(2) Solution ly=f
(3) Solution ux=y
Under the condition that no calculation accuracy is lost by the catch-up method, the calculation cost brought by the original matrix multiplication operation is reduced.
The present application will be described in further detail with reference to specific examples and drawings, but is not limited thereto.
Specific examples are:
To better understand the technical content of the invention, the statistical test results of one month are run from 7 months, 2 days, 2017 to 8 months, 2 days, 2017 are specifically mentioned.
Fig. 4 is a vertical cross-section of a month average weft average temperature. It can be seen that the interpolated high resolution 157 layer can correct the chill bias at the stratosphere (100-25 hPa) and better correct the top (above 5 hPa) chill bias, which is caused by the improved vertical resolution at the stratosphere, better resolving the upwardly propagating gravitational wave elements, which also verifies the correctness and stability of the invention.
Fig. 5 shows a northern hemisphere statistical test scoring card after one month of interpolation using the present invention. The northern hemisphere new hierarchy (157) shows a better performance of the root mean square error at 30-70hPa for the high resolution mode after vertical encryption compared to the old hierarchy (137).
Figure 6 is an east asia statistical test scoring card after one month of interpolation using the present invention for 157 layers. The east Asia new hierarchy (157) compares with the old hierarchy (137), and it can be seen that after vertical encryption, the high resolution mode has better performance in terms of root mean square error at 30-70hPa, and the high root mean square error in terms of gravity potential at 50hPa is reduced, and the mode integration accuracy is improved to have better performance in terms of 100hPa autocorrelation coefficient.
The beneficial effects of the invention are as follows:
the invention can quickly interpolate the initial field of the global spectrum mode to generate a new initial field with higher vertical resolution, the generated format is GRIB format, and the data content comprises spectrum data and lattice point data;
The invention can smoothly and newly increase the grid spacing between vertical layering, provide a new initial field for vertically and uniformly encrypting the appointed area, and the field can be suitable for a global spectrum mode and can stabilize mode integration;
According to the invention, the vertical layer is added above the top of the mode troposphere, so that analysis of upward propagation of gravitational waves can be promoted, the problem of partial cold at the top of the stratosphere is remarkably relieved, and the integration precision at the top of the mode layer is increased, so that the method has higher practical value in the encryption of the appointed section of the initial field of the numerical forecasting mode.
The word "preferred" is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as advantageous over other aspects or designs. Rather, use of the word "preferred" is intended to present concepts in a concrete fashion. The term "or" as used in this disclosure is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless specified otherwise or clear from the context, "X uses a or B" is intended to naturally include any of the permutations. That is, if X uses A; x is B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.
Moreover, although the disclosure has been shown and described with respect to one or more implementations, equivalent alterations and modifications will occur to others skilled in the art based upon a reading and understanding of this specification and the annexed drawings. The present disclosure includes all such modifications and alterations and is limited only by the scope of the following claims. In particular regard to the various functions performed by the above described components (e.g., elements, etc.), the terms used to describe such components are intended to correspond, unless otherwise indicated, to any component which performs the specified function of the described component (e.g., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary implementations of the disclosure. Furthermore, while a particular feature of the disclosure may have been disclosed with respect to only one of several implementations, such feature may be combined with one or other features of the other implementations as may be desired and advantageous for a given or particular application. Moreover, to the extent that the terms "includes," has, "" contains, "or variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term" comprising.
The functional units in the embodiment of the invention can be integrated in one processing module, or each unit can exist alone physically, or a plurality of or more than one unit can be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product. The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like. The above-mentioned devices or systems may perform the storage methods in the corresponding method embodiments.
In summary, the foregoing embodiment is an implementation of the present invention, but the implementation of the present invention is not limited to the embodiment, and any other changes, modifications, substitutions, combinations, and simplifications made by the spirit and principles of the present invention should be equivalent to the substitution manner, and all the changes, modifications, substitutions, combinations, and simplifications are included in the protection scope of the present invention.
Claims (6)
1. The method for smoothly encrypting the global spectrum mode initial field vertical layering arbitrary interval is characterized by comprising the following steps of:
acquiring global spectrum-grid point data;
determining the air pressure position of a newly added layer in a given area by adopting an index catch-up method;
Determining a mixed coordinate coefficient and a layered coordinate of the newly added vertical layer by using an index stretching algorithm according to the given air pressure interval needing to be encrypted and the newly added vertical layer number;
at the boundary end, the smoothness between the newly added vertical layer interval and the port is ensured by second-order polynomial smoothing, and the initial field is ensured to be stable during mode integration;
After determining the layering coordinates of the newly added vertical layering, interpolating the original layering data to the new layering data by adopting a cubic spline, and accelerating the interpolation speed by utilizing a catch-up method in the cubic spline interpolation process;
And outputting the encrypted initial field data.
2. The global spectrum model initial field vertical layering arbitrary interval smoothing encryption method according to claim 1, wherein layering intervals between 10hPa and 20hPa are smoothly changed by a second order polynomial.
3. The global spectrum pattern initial field vertical layering arbitrary interval smooth encryption method according to claim 1, wherein the original layering data comprises spectrum data and lattice point data, the formats of the original layering data and the new layering data are GRIB, and the spectrum lattice attribute is kept unchanged.
4. The global spectrum pattern initial field vertical layering arbitrary interval smoothing encryption method according to claim 1, wherein said determining the barometric pressure position of a new layering of a given area by using an exponential catch-up method comprises: obtaining the stretching parameter z by solving e
Where p t is the upper boundary of a given pressure interval and n is the total number of layers newly added.
5. The global spectrum mode initial field vertical layered arbitrary interval smooth encryption method according to claim 4, wherein the stretch coefficient s (l) of the first layer of the added layer is calculated as follows:
Where p t is the upper boundary of a given pressure interval, n is the total number of layers newly added, and z e is the stretching parameter.
6. The global spectrum mode initial field vertical layering arbitrary interval smoothing encryption method of claim 1, wherein the newly added vertical layering is above the troposphere top.
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| CN110703357A (en) * | 2019-04-30 | 2020-01-17 | 国家气象中心 | Global medium term numerical forecast (GRAPES _ GFS) |
| CN110941790A (en) * | 2019-09-27 | 2020-03-31 | 成都信息工程大学 | High-resolution numerical value-based low-altitude flight meteorological information processing method for unmanned aerial vehicle |
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| CN110941790A (en) * | 2019-09-27 | 2020-03-31 | 成都信息工程大学 | High-resolution numerical value-based low-altitude flight meteorological information processing method for unmanned aerial vehicle |
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