A climate prediction method based on linear inversion and correction of pattern error operators

Abstract

The present invention discloses a climate prediction method based on linear inversion and correction of pattern error operators, which includes, within the fitting period of model establishment, performing empirical orthogonal decomposition on the forecast error data of a dynamic model to extract the distribution spatial patterns of the first few leading modes of the monthly mean pattern errors in the forecast region and the corresponding principal component time series; using linear inversion technology as a tool for extracting the linear information of the pattern error operator, and realizing the correction of the forecast for the selected region through linear reconstruction of the error operator. The advantages of the present invention are that it combines the theoretical idea of "forecasting" the forecast errors of the dynamic model, uses linear inversion technology to extract the linear information of the pattern error operator, develops a correction technology based on linear inversion of the pattern error operator, and realizes the forecast correction of, such as precipitation in the East Asian region, by combining the historical pattern errors.

Description

Technical Field

[0001] The present invention relates to the technical field of atmospheric science, and particularly to the technical field of monthly-seasonal-yearly climate prediction, and specifically to a climate prediction method based on linear inversion and correction of a model error operator. Background Art

[0002] Numerical weather prediction has become the key to supporting modern climate prediction research and operations. However, due to the chaotic characteristics and complexity of the climate system itself and the limitations of imperfect climate models, relying solely on pure dynamic prediction still cannot meet the actual needs of short-term climate prediction. Given the large deviations still existing in current dynamic models, exploring how to further improve monthly-seasonal-yearly climate prediction skills including precipitation anomalies is very important for disaster prevention, mitigation and making the best use of favorable conditions and avoiding unfavorable ones.

[0003] In fact, the model error also changes continuously with the state of the climate system and can be regarded as a function of time and space for prediction. Therefore, based on the idea of "predicting" the prediction error of the dynamic model, the present invention establishes a climate prediction method based on linear inversion and correction of a model error operator, uses linear inversion technology as a tool to extract information of the linear error operator of the model, and further realizes prediction correction of climate elements such as precipitation in the East Asian region through linear reconstruction of the error operator. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] Aiming at the deficiencies of the prior art, the present invention provides a climate prediction method based on linear inversion and correction of a model error operator. Using linear inversion technology as a tool to extract information of the linear error operator of the model, and further realizing prediction correction of climate elements in the East Asian region through linear reconstruction of the error operator, the problems raised in the above background art can be effectively solved.

[0006] (2) Technical Solutions

[0007] To achieve the above object, the present invention provides the following technical solutions: A climate prediction method based on linear inversion and correction of a model error operator, comprising the following steps:

[0008] S1: Obtain historical observation data, dynamic model hindcasts, and forecast data;

[0009] S2: Preprocess the data in S1: First, perform interpolation processing to make the resolution of the model data consistent with that of the observation data; then calculate the difference between the historical observation data and the dynamic model hindcasts to obtain the historical data set of the forecast error E;

[0010] S3: For the dynamic mode prediction, the empirical orthogonal decomposition method is used to perform spatio-temporal decomposition on the model prediction error data set, obtaining the distribution spatial patterns of the first m leading modes of the monthly mean model error and the corresponding principal component time series. The error principal components are used as the prediction object X, which can be expressed as:

[0011] X(t + τ) = exp(Lτ)X(t) + ξ(t + τ) ≡ G(τ)X(t) + ξ(t + τ) (1)

[0012] S4: According to formula (1), model the first m principal component time series of the intercepted model error: Use the principal component time series of the model error within the model fitting period to inversely calculate the formal construction operator L of the model error;

[0013] S5: According to the formally constructed operator L of the inversely calculated model error, perform linear prediction on X to obtain the principal component time series of the model error based on the linear inversion technique for the prediction time period;

[0014] S6: Use the leading mode distribution spatial patterns of the model error within the modeling period and the principal component time series of the model error for the prediction time period obtained in S5 to obtain the target monthly model error result based on the linear inversion technique;

[0015] S7: Use the original prediction of the target prediction month of the dynamic mode and the target prediction month model error based on the linear inversion technique to obtain the prediction correction result of the target prediction month.

[0016] Preferably, according to the idea that the model error also changes continuously with the state of the climate system, the prediction error E of the dynamic model is regarded as a function of time and space for prediction, where

[0017]

[0018] Y M represents the model prediction result, and the left side of the equal sign represents the corrected model prediction result.

[0019] Preferably, assuming that there is also a linearly predictable part in the dynamic process that cannot be represented in the actual model, a linear prediction model for the model prediction error is then established using historical model error data, as shown in formula (1).

[0020] Preferably, in S3, X represents the object of m - dimensional prediction (the first m principal components intercepted by the EOF analysis of the X - field, so it is actually m - dimensional), L is an m×m - order deterministic coefficient matrix, G(τ) is the Green's function, which is determined by the sequence X itself, and the value of G(τ) can be calculated through the sequence X in the fitting period, and then L is inversely calculated, and ξ is an m - dimensional Gaussian white noise vector.

[0021] Preferably, in S2, sea surface temperature, precipitation, wind field, etc. are used as factor variables in the climate prediction process, and correlation tests are performed based on the characteristics of the forecast object and historical model forecasts and climate factors to screen out a set of key factors that have physical meaning for the forecast object.

[0022] Preferably, in S3, the empirical orthogonal decomposition method is used to screen and decompose a set of key factors having physical meanings for the forecast object to obtain the principal mode distribution space type of the factors and the corresponding principal component time series.

[0023] Preferably, in S4, the truncated factor principal component time series and the pattern error principal component time series are used as input data for modeling.

[0024] Preferably, in S3, the specific method flow and formula of the empirical orthogonal decomposition method are:

[0025] The empirical orthogonal function (EOF) method can identify the main spatial type and its temporal evolution law from a meteorological data field, perform anomaly or standardization on any meteorological variable field Y (l is the number of stations or grid points, n is the sample length), and then calculate its covariance matrix:

[0026] S=YY T , (3)

[0027] Use the Jacobi method to find the eigenvalues ​​(λ) and eigenvectors (V) of the covariance matrix S, and arrange the eigenvalues ​​in order of size:

[0028] λ 1 ≥λ 2 ≥…≥λ l ≥0, (4)

[0029] And find the corresponding time coefficient:

[0030] T=V T Y, (5)

[0031] Then calculate the variance contribution of each eigenvector separately:

[0032]

[0033] (k=1,2,3,…,p <l),及前p个特征向量的累积方差贡献:

[0034]

[0035] EOF analysis is widely used in meteorological statistical analysis. It can decompose a physical quantity field into spatial eigenvectors and time series, and concentrate the information of variables on several modes. According to the magnitude of the explained variance, the modes can be divided into main and secondary modes.

[0036] (III) Beneficial effects

[0037] Compared with the prior art, the present invention provides a climate prediction method based on linear inversion and correction of a pattern error operator, having the following beneficial effects:

[0038] 1. The present invention combines the theoretical idea of "forecasting" the prediction error of a dynamic model, extracts the linear information of the pattern error operator by using the linear inversion technology idea, develops a correction technology based on the pattern error operator, realizes the forecasting of the monthly mean pattern error, and further improves the forecasting skill of the dynamic model prediction result.

[0039] 2. The climate prediction method based on linear inversion and correction of a pattern error operator has strong practicability, can provide better, more stable and more accurate forecasting information for the climate elements in the East Asian region, and thus can provide effective early warning information for national climate disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0041] Figure 1 is a flow diagram of the prediction method of the present invention;

[0042] Figure 2 is the spatial distribution of the temporal correlation coefficient (TCC) between the summer precipitation forecast and the observation in the Chinese region of the model before (left) and after (middle) correction during the verification sample time period in the embodiment of the present invention, and the spatial distribution of the improvement of TCC (right). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0044] Embodiment 1

[0045] As Figure 1 shown, the present invention provides a climate prediction method based on linear inversion and correction of a pattern error operator, including the following steps:

[0046] S1: Obtain historical observation data, dynamic model hindcasts, and forecast data;

[0047] S2: Preprocess the data in S1: First, perform interpolation to make the resolution of the model data consistent with that of the observed data; then calculate the difference between the historical observed data and the dynamical model hindcast to obtain the historical data set of the forecast error E.

[0048] S3: For the dynamical model forecast, use the empirical orthogonal decomposition method to perform spatio-temporal decomposition on the model forecast error data set, obtain the spatial patterns of the first m leading modes of the monthly mean model error and the corresponding principal component time series, and take the error principal components as the forecast object X, which can be expressed as:

[0049] X(t + τ) = exp(Lτ)X(t) + ξ(t + τ) ≡ G(τ)X(t) + ξ(t + τ) (1)

[0050] S4: Model the first m principal component time series of the model error intercepted according to formula (1): Use the principal component time series of the model error during the modeling fitting period to invert the formal construction operator L of the model error.

[0051] S5: According to the formally inverted construction operator L of the model error, perform a linear forecast on X to obtain the principal component time series of the model error based on the linear inversion technique for the prediction time period.

[0052] S6: Use the spatial patterns of the leading modes of the model error during the modeling period and the principal component time series of the model error for the prediction time period obtained in S5 to obtain the target monthly model error result based on the linear inversion technique.

[0053] S7: Use the original forecast for the target forecast month of the dynamical model and the target forecast month model error based on the linear inversion technique to obtain the forecast correction result for the target forecast month.

[0054] Preferably, according to the idea that the model error also changes continuously with the state of the climate system, regard the forecast error E of the dynamical model as a function of time and space for forecasting, where

[0055]

[0056] Y M represents the model forecast result, and the left side of the equal sign represents the corrected model forecast result.

[0057] Preferably, assume that there is also a linearly predictable part in the dynamical processes not represented in the actual model, and then use the historical model error data to establish a linear forecast model for the model forecast error, as shown in formula (1).

[0058] Preferably, in S3, X represents the object of m-dimensional prediction (the first m principal components intercepted by the EOF analysis of the X field, so it is actually m-dimensional), L is an m×m-order deterministic coefficient matrix, G(τ) is a Green's function, which is determined by the sequence X itself. The value of G(τ) can be calculated by fitting the sequence X of the time period, and then L is obtained by inversion, and ξ is an m-dimensional Gaussian white noise vector.

[0059] Preferably, in S2, sea surface temperature, precipitation, wind field, etc. are used as factor variables in the climate prediction process, and correlation tests are performed based on the characteristics of the forecast object and historical model forecasts and climate factors to screen out a set of key factors that have physical meaning for the forecast object.

[0060] Preferably, in S3, the empirical orthogonal decomposition method is used to screen and decompose a set of key factors having physical meanings for the forecast object to obtain the principal mode distribution space type of the factors and the corresponding principal component time series.

[0061] Preferably, in S4, the truncated factor principal component time series and the pattern error principal component time series are used as input data for modeling.

[0062] Preferably, in S3, the specific method flow and formula of the empirical orthogonal decomposition method are:

[0063] The empirical orthogonal function (EOF) method can identify the main spatial type and its temporal evolution law from a meteorological data field, perform anomaly or standardization on any meteorological variable field Y (l is the number of stations or grid points, n is the sample length), and then calculate its covariance matrix:

[0064] S=YY T , (3)

[0065] Use the Jacobi method to find the eigenvalues ​​(λ) and eigenvectors (V) of the covariance matrix S, and arrange the eigenvalues ​​in order of size:

[0066] λ 1 ≥λ 2 ≥……≥λ l ≥0, (4)

[0067] And find the corresponding time coefficient:

[0068] T=V T Y, (5)

[0069] Then calculate the variance contribution of each eigenvector separately:

[0070]

[0071] (k = 1, 2, 3, …, p < l), and the cumulative variance contribution of the first p eigenvectors:

[0072]

[0073] EOF analysis is widely used in meteorological statistical analysis. It can decompose a physical quantity field into spatial eigenvectors and time series, and concentrate the information of variables on several modes. According to the magnitude of the explained variance, the modes can be divided into main and secondary modes.

[0074] Example 2

[0075] As Figure 2 shown, based on Example 1, the present invention provides a technical solution: This example is based on the precipitation reforecast data of the BCC_CSM1.1M model from 1991 to 2015, and uses the prediction method provided by the present invention to conduct a corrected prediction application for the global precipitation forecast from 1991 to 2015. The figure shows the summer precipitation skills and skill improvements in the Chinese region before and after correction during the rolling independent sample test period from 2002 to 2015. It can be seen from the distribution map of the increase in the time correlation coefficient (TCC) that the precipitation forecast skills after correction have improved in most regions of the country. And as the number of months of the lead forecast increases, the range of skill improvement also increases.

[0076] By adopting the above technical solution disclosed by the present invention, the following beneficial effects are obtained:

[0077] The present invention provides a climate prediction method based on the linear inversion and correction of the model error operator, which can be used for climate forecasting of elements such as East Asian precipitation. The method is as follows: It includes, within the fitting period of model building, performing empirical orthogonal decomposition on the forecast error data of the dynamic model, extracting the distribution spatial patterns of the first few main modes of the monthly average model error in the forecast area and the corresponding principal component time series; using the linear inversion technique as a tool to extract the linear information of the model error operator, and realizing the correction of the forecast for the selected area through the linear reconstruction of the error operator. The advantages of the present invention are that it combines the theoretical idea of "forecasting" the forecast error of the dynamic model, uses the linear inversion technique idea to extract the linear information of the model error operator, develops a correction technology based on the model error operator, realizes the forecasting of the model error, and thus improves the climate forecasting skills of elements such as East Asian precipitation. The present invention significantly improves the accuracy of climate prediction, can better serve the social economy, meet the needs of national disaster prevention and reduction, and better provide guarantee for government decision-making.

[0078] It should be noted that in this article, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process or method including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or also includes elements inherent in such a process or method. Without further limitation, an element defined by the statement "including a reference structure" does not exclude the existence of additional identical elements in the process or method including the said element.

Claims

1. A climate prediction method based on linear inversion and correction of pattern error operators, characterized in that, it includes the following steps: S1: Obtain historical observation data, dynamical model reforecasts, and forecast data; S2: Preprocess the data in S1: First, perform interpolation to make the resolutions of the model data and the observation data consistent; then calculate the difference between the historical observation data and the dynamical model reforecasts to obtain the historical data set of the forecast error E; S3: For dynamical model forecasts, use empirical orthogonal decomposition method to perform spatio-temporal decomposition on the model forecast error data set, obtain the distribution spatial patterns of the first m leading modes of the monthly mean model error and the corresponding principal component time series, and take the error principal components as the forecast object X, which can be expressed as: X(t + τ) = exp(Lτ)X(t) + ξ(t + τ) ≡ G(τ)X(t) + ξ(t + τ) (1) S4: Model the first m principal component time series of the intercepted model error according to formula (1): Use the principal component time series of the model error within the fitting period to inversely calculate the formal construction operator L of the model error; S5: According to the inversely obtained formal construction operator L of the model error, perform linear forecasting on X to obtain the principal component time series of the model error based on linear inversion technology for the prediction period; S6: Use the distribution spatial patterns of the model error leading modes within the modeling period and the principal component time series of the model error for the prediction period obtained in S5 to obtain the target monthly model error result based on linear inversion technology; S7: Use the original forecast for the target forecast month of the dynamical model and the target forecast month model error based on linear inversion technology to obtain the forecast correction result for the target forecast month; In S3, X represents the object of m - dimensional forecasting, the first m principal components intercepted by the EOF analysis of the X - field, so it is actually m - dimensional, L is an m×m - order deterministic coefficient matrix, G(τ) is the Green's function, which is determined by the sequence X itself, and the value of G(τ) can be calculated through the sequence X of the fitting period, and then L can be inversely obtained, and ξ is an m - dimensional Gaussian white noise vector.

2. A climate prediction method based on linear inversion and correction of pattern error operators according to claim 1, characterized in that: According to the idea that the pattern error also changes continuously with the state of the climate system, regard the forecast error E of the dynamical model as a function of time and space for forecasting, where , Y M represents the model forecast result, and the left side of the equal sign represents the corrected model forecast result.

3. A climate prediction method based on linear inversion and correction of pattern error operators according to claim 1, characterized in that: Assume that there is also a linearly predictable part in the dynamical processes not represented in the actual model, and then use historical model error data to establish a linear forecasting model for the model forecast error, as shown in formula (1).

4. A climate prediction method based on linear inversion and correction of pattern error operators according to claim 1, characterized in that: In S2, use sea surface temperature, precipitation, and wind field as factor variables in the climate prediction process, and perform correlation tests according to the characteristics of the forecast object and the historical model forecasts and climate factors, and screen to obtain a key factor set with physical meaning for the forecast object.

5. A climate prediction method based on linear inversion and correction of pattern error operators according to claim 1, characterized in that: In S3, specifically, the empirical orthogonal decomposition method is used to screen and obtain a key factor set with physical meaning for the prediction object for decomposition, so as to obtain the main mode distribution spatial pattern of the factors and the corresponding principal component time series.

6. A climate prediction method based on linear inversion and correction of pattern error operators according to claim 1, characterized in that: In S4, specifically, the intercepted factor principal component time series and the pattern error principal component time series are used as input data for modeling together.

7. A climate prediction method based on linear inversion and correction of pattern error operators according to claim 1, characterized in that: In S3, the specific method process and formula of the empirical orthogonal decomposition method: For any meteorological variable field Y, where l is the number of stations or grid points, perform anomaly or standardization processing, and then calculate its covariance matrix: S = YY T , (3) Use the Jacobi method to find the eigenvalues (λ) and eigenvectors (V) of the covariance matrix S, and arrange the eigenvalues in descending order: λ 1 ≥ λ 2 ≥ … ≥ λ l ≥ 0, (4) And calculate its corresponding time coefficients: T = V T Y, (5) Then calculate the variance contribution of each eigenvector respectively: (k = 1, 2, 3,..., p < l), and the cumulative variance contribution of the first p eigenvectors:

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