Numerical weather forecasting method based on all-weather observation error covariance matrix

Abstract

The invention discloses a numerical weather forecasting method based on an all-weather observation error covariance matrix, and the steps include: assimilating infrared hyperspectral observation data, constructing an observation error covariance matrix, and performing decomposition and inverse calculation to obtain an observation error correlation matrix; realizing the observation error correlation matrix with a cost function; calculating deviations between simulated cloud radiance and observed radiance and clear sky radiance respectively, obtaining cloud radiance of the background field and cloud radiance and cloud characteristic function contained in the observation; constructing expansion factors of different channels, and forming a diagonal expansion matrix by the expansion factors; bringing cloud characteristic function and cloud amount function into the cost function, calculating the newly constructed cost function and its gradient in the assimilation system, and solving the optimal analysis field by minimizing the solution, and performing numerical weather forecasting according to the optimal analysis field. The invention can effectively use observation error correlation to assimilate infrared hyperspectral data for all-weather meteorology.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical weather forecasting, and in particular relates to a numerical weather forecasting method based on an all-weather observation error covariance matrix. Background Art

[0002] Numerical weather prediction (NWP) is a typical initial-boundary value problem of partial differential equations. With the gradual improvement of numerical model prediction models, the accuracy of initial value conditions is increasingly considered to be an important aspect in the field of numerical weather prediction, which directly affects the success or failure of numerical weather prediction. At the same time, with the development of observation technology, the amount and types of observation information are increasing. How to effectively use these observation information and provide more accurate initial values ​​has become the core of numerical weather prediction research. Data assimilation improves the initial conditions of the model by integrating various available known information (including observations, models, and corresponding error statistics). Meteorological satellite observations such as infrared hyperspectral can realize all-weather (All-sky) ground detection from outside the atmosphere, without being restricted by the type of surface, and have the characteristics of large amount of information and high temporal and spatial resolution, which can effectively fill the "information blind spot" that is difficult to detect with conventional observations. Since the use of variational assimilation to process satellite data, numerical forecasting has been significantly improved. Taking the European Center for Medium-Range Weather Forecasts (ECMWF)'s operational four-dimensional variational data assimilation (4DVAR) system as an example, 90% of the observation information comes from satellite data.

[0003] The observation error covariance matrix plays a very important role in the variational assimilation system. It determines the importance of the observation information and how this information spreads in space and between different variables. The more non-zero elements in the observation error covariance matrix, the more information can be extracted from the observation data. In this sense, the observation error covariance matrix should be as full as possible. Generally speaking, the variance of the diagonal elements of the observation error covariance mainly represents the instrument error, which is easy to obtain; the off-diagonal elements represent the correlation between observations, which are estimated a posteriori and are relatively difficult to estimate accurately. Since the development of data assimilation, the background error covariance matrix has developed to a very complex level, but the observation error covariance is extremely simple. Usually, the off-diagonal elements are ignored and only the variance composed of the diagonal elements is considered. For example, when assimilating infrared hyperspectral satellite data, it is simply assumed that the errors between observations are uncorrelated, and the field of view is sparsely spaced and non-adjacent channels are selected accordingly. The error variance is generally given according to statistical experience.

[0004] In order to make up for the deficiency of observation error covariance matrix that does not consider error correlation, observation errors are usually artificially amplified, that is, observation error inflation technology, so that the weight of observation in analysis is consistent with the real weight. However, the observation errors of satellite data are diverse, including not only instrument errors but also representative errors, and there are correlations between observations. These correlations not only include spatial correlations, but also strong channel correlations for tens of thousands of channels of infrared hyperspectral. Studies have shown that the degree of error correlation between these channels varies with atmospheric conditions, with a small degree of correlation under clear sky conditions and more significant channel correlation under all-weather cloud and rain conditions. At present, some studies have made preliminary attempts to consider the correlation between channels for infrared hyperspectral data in the observation error covariance matrix, and use posterior information to diagnose the correlation coefficient and error variance of the channels, but have not fully considered the real-time changes of observation errors with cloud water under all-weather conditions.

[0005] At present, the operational data assimilation systems of numerical forecast centers such as ECMWF mainly use the clear sky assimilation method to assimilate infrared hyperspectral data. The observation error covariance model used in its data assimilation system is relatively simple, and it is difficult to accurately describe the error level of infrared hyperspectral data in cloud and rain areas under all-weather conditions. In order to give full play to the numerical simulation application value of infrared hyperspectral observation data, it is necessary to use advanced observation error covariance models to build an all-weather data assimilation system. This error model should change in real time with the cloud water conditions and establish a close connection with the cloud water material in the field of view.

[0006] The current four-dimensional variational assimilation method of infrared hyperspectral data can only assimilate the channels above the cloud top in the clear sky field and the full cloud field that are not affected by clouds to a certain extent due to the relatively simple observation error covariance model. The available effective observations are very limited (approximately less than 10% of the total number of observations), and the application value of infrared hyperspectral data is not fully utilized. Summary of the invention

[0007] In view of this, the present invention proposes a numerical weather forecasting method based on the all-weather observation error covariance matrix. Aiming at the problem that the observation error covariance model adopted by the current business variational assimilation system cannot accurately describe the channel correlation and observation error variance level of infrared hyperspectral observation under all-weather conditions, an infrared hyperspectral all-weather observation error covariance model based on cloud scenes is proposed to solve the infrared hyperspectral observation error covariance channel correlation technology based on cloud characteristic function and the observation error variance expansion technology based on cloud amount.

[0008] The numerical weather forecasting method based on the all-weather observation error covariance matrix disclosed in the present invention comprises the following steps:

[0009] S1: Select a period of infrared hyperspectral observation data for assimilation, construct an observation error covariance matrix for satellite observation data errors, and decompose and inversely calculate the observation error covariance matrix to obtain an observation error correlation matrix;

[0010] S2: Implementing the observation error correlation matrix using a cost function;

[0011] S3: Calculate the deviation between the simulated cloud radiance and the observed radiance and the clear sky radiance to obtain the cloud radiance of the background field and the cloud radiance and cloud characteristic function included in the observation;

[0012] S4: constructing expansion factors of different channels, and forming a diagonal expansion matrix by the expansion factors;

[0013] S5: Bringing the cloud characteristic function and cloud amount function into the cost function, calculating the newly constructed cost function and its gradient in the assimilation system, and solving the optimal analysis field by minimization, and performing numerical weather forecasting based on the optimal analysis field.

[0014] Furthermore, the step S1 includes the following sub-steps:

[0015] S11: Select a period of infrared hyperspectral observation data for assimilation, perform diagnostic analysis on satellite observation data errors, and use the posterior observation error covariance matrix The calculation formula calculates the observation error covariance matrix, the posterior observation error covariance matrix The calculation is as follows:

[0016]

[0017] Where E[] represents the mathematical expectation. is the difference between observation and analysis;

[0018] S12: Count the covariance of each channel combination to obtain the observation error covariance matrix, where the observation error covariance R(i, j) of the i-th channel and the j-th channel is:

[0019]

[0020] S13: Construct the elements of the observation error covariance matrix R from the observation error covariance R(i, j) between each channel.

[0021]

[0022] S14: performing block diagonal decomposition on the error covariance matrix of the infrared hyperspectral observation data;

[0023] S15: Block diagonalize the observation error covariance matrix Rk The diagonal transformation is carried out using the empirical orthogonal expansion method. The steps are as follows:

[0024] R k =∑C∑

[0025] Among them, ∑ is the observation error standard deviation matrix, which is a diagonal matrix, and the diagonal element is the observation error standard deviation σ of the i-th channel i , C is the correlation coefficient matrix between observation error channels;

[0026] S16: The decomposed observation error covariance matrix R k Inverse The inverse formula is as follows:

[0027]

[0028] Where Λ is the eigenvalue λ of the matrix C, the correlation coefficient matrix between the observation errors. j The diagonal matrix E is composed of the eigenvectors e of the matrix C of the correlation coefficient matrix between the observation errors. j An orthogonal matrix.

[0029] Furthermore, the cost function J includes the observation term J o and background field term J b , expressed as:

[0030] J=J o +J b

[0031] Cost function observation term J o It is expressed as:

[0032]

[0033] Where d is the observation increment, σ o is the standard deviation of the observation error. When the cost function is solved in an incremental manner, the observation term J o The gradient of is:

[0034]

[0035] Among them, H T is the transpose of the tangent linear observation operator, whose column vector is h i , used to measure the sensitivity of observations to changes in atmospheric conditions, σ o is the standard deviation of the observation error.

[0036] Furthermore, the cloud characteristic function C cld The calculation is as follows:

[0037]

[0038] Among them, H clr (x b ) is the cloud emissivity, H cld (x b ) is the clear sky emissivity.

[0039] Furthermore, the expansion factor S of different channels j is constructed j , by S i Construct a diagonal expansion matrix S to expand the observation error:

[0040] R=ES 0.5 ΛS 0.5 E T ≡ESΛE T ,

[0041] where E is the eigenvector e of the matrix of the correlation coefficients between the observed error channels. j An orthogonal matrix.

[0042] Furthermore, the first eigenvalue expansion factor is S1, and the other eigenvalue expansion factors are set to constants, that is, S j The value strategy of is expressed as:

[0043]

[0044] Among them, S1 is expressed as:

[0045]

[0046] a is the minimum expansion factor coefficient under clear sky conditions, b is the maximum expansion factor coefficient under cloudy conditions, C a is a function of cloud cover.

[0047] Furthermore, the cloud cover function C a The simulated cloud cover C m and observed cloud amount C o Calculated, it is expressed as follows:

[0048] C m =B cld -B clr

[0049] C o =O cld -B clr

[0050] C a =(C m +C o ) / 2

[0051] Among them B cldrepresents the brightness temperature simulated by RTTOV for the cloud profile, B clr represents the brightness temperature simulated by RTTOV for the cloud profile, O cld It indicates the observed cloud brightness temperature.

[0052] The beneficial effects of the present invention are as follows:

[0053] Aiming at the upper tropospheric water vapor channel in satellite infrared hyperspectral observation data, the observation error covariance model based on the observation error correlation of cloud characteristic function is studied. By constructing the cloud characteristic function in the field of view, the characteristic deviation and characteristic Jacobian related to the observation error covariance matrix error are obtained, and the observation error correlation is effectively used to assimilate the infrared hyperspectral data.

[0054] Aiming at the application needs of infrared hyperspectral all-weather observation error covariance, an observation error inflation technology based on cloud cover is proposed, and the functional correspondence between the observation error variance and the cloud cover is established. The use of different cloud cover inflation values ​​and observation error covariance eigenvalue threshold truncation inflation schemes for different feature channels are explored, providing an effective and practical way to achieve different degrees of influence of channels with different error levels on the cost function. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The present invention provides a flow chart of a numerical weather forecasting method based on an all-weather observation error covariance matrix. DETAILED DESCRIPTION

[0056] The present invention is further described below in conjunction with the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention belong to the protection scope of the present invention.

[0057] like Figure 1 As shown, the numerical weather forecasting method of the present invention is based on the all-weather observation error covariance matrix, and the steps of the method are as follows:

[0058] S1: Select a period of infrared hyperspectral observation data for assimilation, construct an observation error covariance matrix for the satellite observation data error, and decompose and inversely calculate the observation error covariance matrix to obtain an observation error correlation matrix.

[0059] Under all-weather observation conditions, infrared hyperspectral observations are affected by cloud water, and the error level is more complex than that of clear sky observations. The construction of observation error patterns is critical for assimilating all-weather infrared hyperspectral observation data. First, the posterior information of the assimilation system is used to diagnose the infrared hyperspectral observation error covariance matrix under clear sky conditions, and the basic observation error covariance matrix is ​​constructed for introducing the influence of cloud water. The specific steps are as follows:

[0060] S11: Select a period of infrared hyperspectral observation data for assimilation, perform diagnostic analysis on satellite observation data errors, and use the posterior observation error covariance matrix The calculation formula calculates the GIIRS (interferometric atmospheric vertical sounder) observation error covariance matrix.

[0061]

[0062] Where E[] represents the mathematical expectation. represents the difference between the observation and background fields (information increment or observation increment), where x b is the background field, y is the satellite GIIRS observation value, H is the observation operator, if the deviation correction is considered, then Where b is the deviation correction parameter. is the difference between the observed and analyzed values, where δx a is the analysis increment. Assuming the error is Gaussian, the observation and background errors are uncorrelated, and the weight of the observation in the analysis is the same as when using the true error characteristics, then

[0063] S12: Count the covariance of each channel combination respectively. The covariance of the observation error between the i-th channel and the j-th channel R(i,,) is:

[0064]

[0065] S13: Construct the elements of the observation error covariance matrix R from the observation error covariance R(i, j) between each channel.

[0066]

[0067] S14: Use the error covariance matrix of the infrared hyperspectral observation data diagnosed in step S12 to perform block diagonal decomposition. It is assumed that the error covariance block of the water vapor channel selected for study is R k (Considering the correlation of observation errors, it is an n×n dimensional square matrix), which represents the observation error covariance matrix of n channels in the kth observation set of the entire infrared hyperspectral channel set. If 7 GIIRS water vapor channels are planned to be selected, then n=7.

[0068] S14: Block diagonalized observation error covariance matrix R obtained in S13 k Diagonal transformation is performed and achieved by using methods such as empirical orthogonal expansion.

[0069] R k =∑C∑

[0070] Among them, ∑ is the observation error standard deviation matrix, which is a diagonal matrix, and the diagonal elements are the observation error standard deviation σ of the i-th channel i , C is the matrix of correlation coefficients between observation error channels.

[0071] S15: R after decomposition of S14 k Inverse The inverse formula is as follows:

[0072]

[0073]

[0074] The coefficient matrix needs to be decomposed again, then It is expressed as:

[0075]

[0076] where Λ is the eigenvalue λ of the C matrix j The diagonal matrix E is composed of the eigenvectors e of the C matrix. j An orthogonal matrix.

[0077] S2: Implementation of the observation error correlation matrix in the cost function

[0078] The data assimilation cost function J contains the observation term J o and background field term J b , expressed as:

[0079] J=J o +J b

[0080] When channel correlation is not considered, R is a diagonal matrix that only considers variance, and the cost function observation term J o It is expressed as:

[0081]

[0082] Among them, d is the observation increment. When the cost function is solved in an incremental way, the gradient of the observation term is:

[0083]

[0084] Among them, H T is the transpose of the tangent linear observation operator, also known as the Jacobian matrix, whose column vector is h i , which is often used to measure the sensitivity of observations to changes in the atmospheric state.

[0085] When considering channel correlation, the inversion of the R matrix cannot be simply expressed as the inversion of the variance diagonal matrix. It is necessary to use the form of the observation error correlation coefficient matrix decomposition to invert it. The cost function observation term is expressed as:

[0086]

[0087] in, is the transpose of the eigenvector, is the characteristic deviation term, λ j is the eigenvalue of the matrix of correlation coefficients between observation error channels.

[0088] The gradient of the corresponding observation is:

[0089]

[0090] H T e j is the characteristic Jacobian, which measures the sensitivity of the observations to changes in the atmospheric state.

[0091] S3: Calculate the deviation between the simulated cloudy radiance and the observed radiance and the clear sky radiance to obtain the cloud radiance of the background field and the cloud radiance and cloud characteristic function included in the observation.

[0092] For the calculation of cloud characteristic function and cloud amount, it is necessary to use RTTOV fast radiative transfer model to calculate the cloud radiance H for each channel. clr (x b ) and clear sky radiance H cld (x b ). The channel with the greatest impact from clouds, i.e., the one with the weight function at the bottom layer, is taken as the research object. Then, the simulated radiance with clouds and the observed radiance are compared with the clear sky radiance to calculate the deviation. That is, the cloud radiance of the background field and the cloud radiance included in the observation are obtained based on the simulated clear sky radiance. Finally, the cloud characteristic function C is obtained by weighted average. cld :

[0093]

[0094] When considering channel correlation, It is expressed as a normalized feature information increment term, using C cld Instead, it is possible to consider the error correlation based on cloud characteristics in the observation error model.

[0095] S4: constructing expansion factors of different channels, and forming a diagonal expansion matrix by the expansion factors;

[0096] For the observation error standard deviation, considering the influence of cloud cover, it is necessary to construct the expansion factor S for different channels j. j , by S iConstruct a diagonal expansion matrix S.

[0097]

[0098] Therefore, the expansion of the observation error can be expressed as:

[0099] R=ES 0.5 ΛS 0.5 E T ≡ESΛE T

[0100] R k The expansion of the eigenvalues ​​of the matrix is ​​proposed to adopt a strategy of different eigenvalue types. The expansion factor of the first eigenvalue is S1, and the expansion coefficients of other eigenvalues ​​are set to 1 (or other constants for expansion, which need to be tested based on experiments to obtain empirical values), that is, S j The value strategy can be expressed as:

[0101]

[0102] Among them, S1 is expressed as:

[0103]

[0104] a is the minimum expansion factor coefficient under clear sky conditions (for example, a value of 0.2), b is the maximum expansion factor coefficient under cloudy conditions (for example, a value of 3.2), C a is a function of cloud cover.

[0105] Cloud cover function C a The simulated cloud cover C m and observed cloud amount C o Calculated, it is expressed as follows:

[0106] C m =B cld -B clr

[0107] C o =O cld -B clr

[0108] C a =(C m +C o ) / 2

[0109] Among them B cld represents the brightness temperature simulated by RTTOV for the cloud profile, B clr represents the brightness temperature simulated by RTTOV for the cloud profile, O cld When the emissivity brightness temperature is used to represent the cloud amount, the cloud amount function C aand cloud characteristic function C cld Are equivalent.

[0110] S5: Bringing the cloud characteristic function and cloud amount function into the cost function, calculating the newly constructed cost function and its gradient in the assimilation system, and solving the optimal analysis field by minimization, and performing numerical weather forecasting based on the optimal analysis field.

[0111] The cloud characteristic function and cloud amount function calculated in steps S3 and S4 are applied to the observation term of the cost function in step S2 to realize the observation error covariance model based on the cloud scene and the corresponding assimilation cost function.

[0112] The newly constructed cost function and its gradient are calculated in the assimilation system, and the optimal analysis field is solved by minimization, and the convergence of the cost function is verified.

[0113] The beneficial effects of the present invention are as follows:

[0114] Aiming at the upper tropospheric water vapor channel in the FY-4A satellite infrared hyperspectral observation data, the observation error covariance model based on the observation error correlation of cloud characteristic function is studied. By constructing the cloud characteristic function in the field of view, the characteristic deviation and characteristic Jacobian related to the observation error covariance matrix error are obtained, and the infrared hyperspectral data are assimilated effectively by using the observation error correlation.

[0115] Aiming at the application needs of infrared hyperspectral all-weather observation error covariance, an observation error inflation technology based on cloud cover is proposed, and the functional correspondence between the observation error variance and the cloud cover is established. The use of different cloud cover inflation values ​​and observation error covariance eigenvalue threshold truncation inflation schemes for different feature channels are explored, providing an effective and practical way to achieve different degrees of influence of channels with different error levels on the cost function.

[0116] The above embodiment is an implementation mode of the present invention, but the implementation mode of the present invention is not limited to the described embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A numerical weather forecasting method based on the all-weather observation error covariance matrix, applied to the assimilation system, characterized in that: The following steps are involved: S1: Select a period of infrared hyperspectral observation data for assimilation, construct an observation error covariance matrix for satellite observation data errors, and decompose and inversely calculate the observation error covariance matrix to obtain an observation error correlation matrix; S2: Implementing the observation error correlation matrix using a cost function; S3: Calculate the deviation between the simulated cloud radiance and the observed radiance and the clear sky radiance to obtain the cloud radiance of the background field and the cloud radiance and cloud characteristic function included in the observation; S4: constructing expansion factors of different channels, and forming a diagonal expansion matrix by the expansion factors; S5: Bringing the cloud characteristic function and the cloud amount function into the cost function, calculating the newly constructed cost function and its gradient in the assimilation system, and solving the optimal analysis field by minimizing the solution, and performing numerical weather forecasting according to the optimal analysis field; Cloud characteristic function C cld The calculation is as follows: Among them, H clr (x b ) is the cloud emissivity, H cld (x b ) is the clear sky radiance; Construct the expansion factor S of different channels j j , by S i Construct a diagonal expansion matrix S to expand the observation error: R=ES 0.5 ΛS 0.5 AND T ≡ES∧E T , Where E is an orthogonal matrix composed of the eigenvectors ej of the matrix of the correlation coefficients between the observation error channels; The first eigenvalue expansion factor is S1, and the other eigenvalue expansion factors are set to constants, that is, S j The value strategy of is expressed as: Among them, S1 is expressed as: a is the minimum expansion factor coefficient under clear sky conditions, b is the maximum expansion factor coefficient under cloudy conditions, C a is the cloud cover function; The cloud cover function C a The simulated cloud cover is expressed as follows: C m and the observed cloud amount C, C m =B cld -B clr C o =O cld -B clr C a =(C m +C o ) / 2 Among them B cld represents the brightness temperature simulated by RTTOV for the cloud profile, B clr represents the brightness temperature simulated by RTTOV for the cloud profile, O cld It indicates the observed cloud brightness temperature.

2. The numerical weather forecasting method based on the all-weather observation error covariance matrix according to claim 1, characterized in that: The step of S1 includes the following sub-steps: S11: Select a period of infrared hyperspectral observation data for assimilation, and perform diagnostic analysis on the satellite observation data error; the observation data error ε0=yy t , where y represents the infrared hyperspectral observation value measured by the instrument, y t Indicates the true value of infrared hyperspectral of atmosphere; Compute the posterior observation error covariance matrix The specific formula is as follows: Where E[] represents the mathematical expectation. is the difference between observation and analysis; S12: Count the covariance of each channel combination to obtain the observation error covariance matrix R, where the observation error covariance R(i, j) of the i-th channel and the j-th channel is: in, represents the difference between the observation and background fields, and N is the number of channels; S13: constructing elements of the observation error covariance matrix R from the observation error covariance R(i, j) between each channel; S14: performing block diagonal decomposition on the error covariance matrix of the infrared hyperspectral observation data; S15: Block diagonalize the observation error covariance matrix R k The diagonal transformation is carried out using the empirical orthogonal expansion method. The steps are as follows: R k =∑C∑ Among them, ∑ is the observation error standard deviation matrix, which is a diagonal matrix, and the diagonal elements are the observation error standard deviation σ of the th channel. i , C is the correlation coefficient matrix between observation error channels; S16: The decomposed observation error covariance matrix R k Inverse The inverse formula is as follows: Where Λ is the eigenvalue λ of the matrix C, the correlation coefficient matrix between the observation errors. j The diagonal matrix E is composed of the eigenvectors e of the matrix C of the correlation coefficient matrix between the observation errors. j An orthogonal matrix.

3. The numerical weather forecasting method based on the all-weather observation error covariance matrix according to claim 1, characterized in that: The cost function J includes the observation term J o and background field term J b , expressed as: J=J o =J b Cost function observation term J o It is expressed as: Where d is the observation increment, σ° is the standard deviation of the observation error, and when the cost function is solved by the incremental method, the observation term J o The gradient of is: Among them, H T is the transpose of the tangent linear observation operator, whose column vector is h i , used to measure the sensitivity of observations to changes in atmospheric conditions, σ o is the standard deviation of the observation error.

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