CN114219143A - Global spectrum mode initial field vertical layering arbitrary interval smooth encryption method - Google Patents

Abstract

The invention discloses a global spectrum mode initial field vertical layering arbitrary 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 to be encrypted and the newly-added vertical layer number; smoothing at the boundary end by a second order function to ensure smoothness between the newly added vertical layer spacing and the ports; after the vertical coordinate of the newly added layer is determined, cubic spline interpolation is adopted for global spectrum-lattice point data from the original layer to the new layer, and the interpolation speed is accelerated by utilizing a catch-up method fast algorithm in the cubic spline interpolation process. The invention finally provides a new initial field which is vertically and uniformly encrypted for the designated area, and the field can be suitable for a global spectrum mode and can stabilize the integral; and a vertical layer is added above the top of the mode convection layer, so that the analysis of upward propagation of gravity waves can be promoted, and the problem of partial cooling of a stratosphere is solved.

Description

Global spectrum mode initial field vertical layering arbitrary interval smooth encryption method

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 arbitrary interval smooth encryption method.

Background

The current global spectral pattern vertical stratification generally employs 137 layers, which are close to the surface region at the bottom of the pattern, dense in layers due to human activity being substantially concentrated in this region, and sparse at the top stratosphere of the pattern and above. Scientific research shows that the gravity wave upward propagation analysis degree is not enough due to the fact that stratosphere layering is too sparse, and therefore the problems that the temperature of the lower portion of the stratosphere is warm and the top of the stratosphere is cold are caused. The problem of partial cold at the top of the stratosphere can be effectively solved by partially encrypting the stratosphere in the mode vertical layering process.

The global spectrum mode initial field is divided into a spherical harmonic spectrum data initial field and a lattice point data initial field, is positioned on an air pressure surface based on a mixed coordinate, is difficult to perform local encryption aiming at a given air pressure interval, and particularly, a new layer after local encryption needs to be given in the form of mixed coordinates A and B, and the new layer needs to be ensured to be smooth and uniform, so that the initial field can keep stability during mode integration. Therefore, the development of a smooth encryption technology for the local air pressure interval has more complexity and important significance.

After the new vertical hierarchy is determined, if linear interpolation is adopted for data interpolation, the calculation speed is high but the accuracy is not high, if cubic spline interpolation is adopted, the calculation accuracy is improved but the calculation overhead is increased, and particularly for global spectrum modes and mass data, a rapid algorithm needs to be developed for ensuring the calculation real-time performance.

Disclosure of Invention

The invention aims to provide a global spectrum mode quality mixed coordinate initial field vertical layering arbitrary interval smooth encryption technology, which can be used for locally encrypting vertical layering aiming at global spectrum mode initial fields, spectral coefficient data and lattice point field data, and the encrypted new initial field layering is smooth in change and stable in integral, so that the global spectrum mode quality mixed coordinate initial field vertical layering arbitrary interval smooth encryption technology is an excellent encryption technology.

In order to solve the technical problem, the invention firstly adopts an exponential stretching algorithm to calculate the newly added layered air pressure coordinate of a given interval and the number of layers, and simultaneously carries out quadratic polynomial smoothing on the layered intervals at the two ends of the interval so as to ensure the stability of mode integration. After the layering is determined, the original layered data is interpolated into new layered data as a new initial field by utilizing a cubic spline, and the cubic spline interpolation adopts a catch-up method to keep the calculation precision and simultaneously 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-lattice 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 a newly-added vertical layer by using an exponential stretching algorithm according to a given air pressure interval needing to be encrypted and the newly-added vertical layer number;

at the boundary end, smoothness between the newly added vertical layer interval and the port is ensured through second-order polynomial smoothing, and the initial field is ensured to be stable during mode integration;

after the layered coordinates of the newly added vertical layers are determined, interpolating the original layered data to new layered data by adopting a cubic spline, and accelerating the interpolation speed by utilizing a catch-up method in the process of cubic spline interpolation;

and outputting the encrypted initial field data.

Further, the layered interval between the air pressures of 10hPa and 20hPa is smoothly changed by a second-order polynomial.

Furthermore, the original hierarchical data comprises spectrum data and lattice point data, the format of the original hierarchical data and the format of the new hierarchical data are GRIB, and the spectrum lattice attribute is kept unchanged.

Further, the step of determining the air pressure position of the newly added layer in the given region by using an index catch-up method includes: the stretch parameter z is obtained by solving the following equation_e

Wherein p is_tN is the total number of layers newly added for the upper boundary of the given pressure interval.

Further, the stretch coefficient s (l) of the l-th layer of the incremental delamination is calculated as follows:

wherein p is_tFor the upper boundary of a given pressure interval, n is the number of newly added layers, z_eIs a drawing parameter.

Further, a newly added vertical layer is arranged on the top of the convection layer.

The invention has the following beneficial effects:

the method can quickly interpolate the global spectrum mode initial field to generate a new initial field with higher vertical resolution, the generation format is a GRIB format, and the data content comprises spectrum data and lattice point data;

the invention can smoothly and newly increase the grid spacing between the vertical layers, provide a new initial field for vertically and uniformly encrypting the designated area, and the field can be suitable for a global spectrum mode and can stabilize mode integration;

the vertical layer is added above the top of the mode convection layer, so that the upward propagation analysis of gravity waves can be promoted, the problem of partial cooling of the top of the stratosphere can be remarkably solved, and the integral precision of the top of the mode layer is increased, so that the method has higher practical value in the aspect of encryption of the specified interval of the initial field of the numerical prediction mode.

Drawings

FIG. 1 is a general flow chart of the present invention;

FIG. 2 is a vertical interlayer spacing distribution diagram of the present invention assuming that the encryption position is 10-270hPa, the number of original layers is 137, and 20 to 157 additional layers are added;

FIG. 3 is a schematic view of the positions of two end points of the pneumatic layer;

FIG. 4 is a vertical cross-sectional view of the averaged latitudinal average temperature;

FIG. 5 is a statistical test result of the root mean square error of the 157-layer data after interpolation by the invention;

FIG. 6 is a graph of the integrated one-month temperature field statistical test results of 157 layer data interpolated using the present invention.

Detailed Description

The invention is further described with reference to the accompanying drawings, but the invention is not limited in any way, and any alterations or substitutions based on the teaching of the invention are within the scope of the invention.

The invention uses an exponential stretching algorithm, calculates new layered air pressure coordinates for a given interpolation interval and added layered numbers, and smoothes two ends.

As shown in fig. 1, the technique for smoothly encrypting any interval in a vertical hierarchy of an initial field in a global spectrum mode of the present invention includes 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 pressure interval p_t,p_bAnd the newly added total number of layers n (including the upper and lower boundaries), each layer being represented by l epsilon (0, n), the tensile coefficient s (l) of the l-th layer

Wherein, 0 < z_e< 1 is the stretching parameter to be determined and the air pressure value of each layer is

p_l＝s(l)p_b (2)

The upper and lower boundary conditions are

p_t＝p₀， (3)

p_b＝p_n (4)

It is clear that the condition (4) is satisfied, and in order for the upper boundary condition (3) to be satisfied, there is

Obtaining z by solving for (5)_e. The solution of the above formula is difficult to obtain an analytic form, and Newton iteration can be adopted to obtain an approximate solution with given precision.

And S2, determining the newly added layered coordinates by using an index stretching algorithm.

For a given interval and number of newly added layers, the air pressure coordinates of the newly added layers located within the interval are determined. For example, 10-270hPa, 20 layers of newly added layers, and the newly added uniform layer is about 298m by using an exponential stretching algorithm. FIG. 2 is a vertical interlayer spacing distribution diagram of the present invention assuming that the encryption position is 10-270hPa, the number of original layers is 137 layers, and 20 to 157 layers are added.

And S3, performing quadratic polynomial interpolation smoothing on two ends of the newly added layer.

After the vertical layering is calculated by using an exponential stretching algorithm, the interval of each layer is basically uniform, but the interval can cause sudden change at two ends, so that integration error or unstable integration is caused, and the layering at the end points needs to be adjusted once, so that the interval at the end points of the scoring layer keeps smoothly changing. As shown in fig. 2, the layering interval varies smoothly in a second order polynomial between pressures of 10hPa and 20 hPa.

Assume two port positions P₀ P₁And P_(N)P_N+1As shown in fig. 3.

The interval of each air pressure layer is d_n＝p_n+1-p_nKnown as d₀,d_NAnd is and

in order that the physical distance between the layered intervals is a smooth function, the interval distance is set to satisfy the following function

d_l＝a+bl+cl²

Knowledge of conditions for two endpoints

d₀＝a

d_N＝a+bN+cN²

Can be pushed out

a＝d₀

According to the sum formula

Order to

Is provided with

a＝d₀

b+cN＝δd

Push out

b+cN＝δd

Is provided with

a＝d₀

b＝δd-cN

The spacing of the layering at the port is therefore found, and the specific location of the layering at the port is obtained.

And S4, carrying out cubic spline data interpolation based on a catch-up method.

After the layered coordinates are determined through the steps, the original data are interpolated into new layered data.

And interpolating the original hierarchical data including the spectrum data and the lattice point data to new hierarchical data by utilizing a pursuit method cubic spline interpolation. The original data is in a GRIB format, the original data is also in the GRIB format after the interpolation is finished, and the spectrum lattice attribute of the original data is kept unchanged, so that new encrypted initial field data is generated.

The original initial field is assumed to be interpolated from the original 137 layers to 157 layers by cubic spline interpolation. The cubic spline interpolation function can be expressed as:

wherein,

h_j＝x_j-x_j-1

s (x) at node x_jIs subject to the following conditions²Continuous, cubic polynomials in each interval. M in formula (6)_jIs node x_jThe second derivative of (d) is unknown and can be solved by the following matrix equation:

wherein,

d_j＝6f[x_j-1,x_j,x_j+1]

solving equation (7) can directly adopt a matrix inversion method, but the calculation overhead is somewhat high. A more efficient algorithm is catch-up.

For a system of tri-diagonal equations with diagonal dominance as follows

Can be described as Ax ═ f, when | i-j | > 1, a_i,j0 and satisfies the following conditions

|b₁|＞|c₁|＞0；

|b_i|≥|a_i|+|c_i|,a_ic_i≠0,i＝2,3,…n-1；

|b_n|＞|a_n|＞0；

A catch-up method may be employed. A can be decomposed into

The notation a ═ LU, so solving Ax ═ f is equivalent to solving two sets of trigonometric equations:

the solving steps are as follows:

(1) calculating beta_iThe recurrence formula of (c):

(2) solution of Ly ═ f

(3) Solving Ux ═ y

Under the condition of not losing any calculation precision by a catch-up method, the calculation expense brought by the multiplication operation of the original matrix is reduced.

The present invention will be described in further detail with reference to the following examples and drawings, but the present invention is not limited thereto.

Specific examples are as follows:

in order to understand the technical content of the invention, the statistical test result of one month is particularly operated from 2017, month 2 to 2017, month 8 and month 2.

The monthly average latitudinal average temperature vertical profile of fig. 4. It can be seen that the interpolated high resolution 157 layer can correct the cooling deviation in the stratosphere (100-25hPa) and can also better correct the top (more than 5hPa) warming deviation, which is caused by the fact that the vertical resolution in the stratosphere is improved and the upward propagating gravitational wave elements can be better analyzed, and thus the correctness and stability of the invention are verified.

Figure 5 shows a northern hemisphere statistical test scorecard after one month integration of 157 layer data interpolated using the present invention. The new layer 157 of northern hemisphere compares with the old layer 137, and it can be seen that the high resolution mode has better performance of root mean square error at 30-70hPa after vertical encryption.

FIG. 6 is a east Asian statistical test scorecard after one month integration of 157 layer data interpolated using the present invention. Compared with the old layering (137), the east Asian new layering (157) can show that after vertical encryption, the high-resolution mode has better performance in the root mean square error at 30-70hPa, the gravity potential height root mean square error at 50hPa is reduced, and the mode integration precision is improved and has better performance in the autocorrelation coefficient of 100 hPa.

The invention has the following beneficial effects:

the method can quickly interpolate the global spectrum mode initial field to generate a new initial field with higher vertical resolution, the generation format is a GRIB format, and the data content comprises spectrum data and lattice point data;

the invention can smoothly and newly increase the grid spacing between the vertical layers, provide a new initial field for vertically and uniformly encrypting the designated area, and the field can be suitable for a global spectrum mode and can stabilize mode integration;

the vertical layer is added above the top of the mode convection layer, so that the upward propagation analysis of gravity waves can be promoted, the problem of partial cooling of the top of the stratosphere can be remarkably solved, and the integral precision of the top of the mode layer is increased, so that the method has higher practical value in the aspect of encryption of the specified interval of the initial field of the numerical prediction 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 application is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless specified otherwise or clear from context, "X employs A or B" is intended to include either of the permutations as a matter of course. That is, if X employs A; b is used as X; or X employs both A and B, then "X employs A or B" is satisfied in any of the foregoing examples.

Also, although the disclosure has been shown and described with respect to one or an implementation, 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 appended 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. In addition, 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. Furthermore, 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.

Each functional unit in the embodiments of the present invention may be integrated into one processing module, or each unit may exist alone physically, or a plurality of or more than one unit are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium. The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Each apparatus or system described above may execute the storage method in the corresponding method embodiment.

In summary, the above-mentioned embodiment is an implementation manner of the present invention, but the implementation manner of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be regarded as equivalent replacements within the protection scope of the present invention.

Claims (6)

1. A global spectral mode initial field vertical layering arbitrary interval smooth encryption method is characterized by comprising the following steps:

acquiring global spectrum-lattice 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 a newly-added vertical layer by using an exponential stretching algorithm according to a given air pressure interval needing to be encrypted and the newly-added vertical layer number;

at the boundary end, smoothness between the newly added vertical layer interval and the port is ensured through second-order polynomial smoothing, and the initial field is ensured to be stable during mode integration;

after the layered coordinates of the newly added vertical layers are determined, interpolating the original layered data to new layered data by adopting a cubic spline, and accelerating the interpolation speed by utilizing a catch-up method in the process of cubic spline interpolation;

and outputting the encrypted initial field data.

2. The global spectral pattern initial field vertical stratification arbitrary interval smoothing encryption method of claim 1, wherein the stratification interval between barometric pressures 10hPa-20hPa is smoothly changed with a second order polynomial.

3. The global spectral pattern initial field vertical layering arbitrary interval smooth encryption method of claim 1, wherein the original layered data comprises spectral data and lattice point data, the format of the original layered data and the new layered data is GRIB, and the spectral lattice property is kept unchanged.

4. The method for smoothly encrypting any interval of the vertical hierarchies of the initial field of the global spectral mode according to claim 1, wherein said determining the barometric pressure position of the newly added hierarchy of the given region by using an exponential catch-up method comprises: the stretch parameter z is obtained by solving the following equation_e

Wherein p is_tN is the total number of layers newly added for the upper boundary of the given pressure interval.

5. The global spectral mode initial field vertical layering arbitrary interval smooth encryption method according to claim 4, wherein the stretch coefficient s (l) of the added layer I is calculated as follows:

wherein p is_tFor the upper boundary of a given pressure interval, n is the number of newly added layers, z_eIs a drawing parameter.

6. The global spectral mode initial field vertical layering arbitrary interval smooth encryption method of claim 1, wherein the added vertical layering is on top of the convection layer.

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