CN104992057A - Quasi-ensemble-variation based mixed data assimilation method - Google Patents
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Abstract
The invention discloses a quasi-ensemble-variation based mixed data assimilation method which comprises the following steps of: selecting 12-hour and 24-hour forecast data stored per 6 hours in historical forecast data of a past month, adjacent to forecast moment, and taking the data as a quasi-ensemble forecast sample; calculating the difference between 24-hour forecast and 12-hour forecast at the same moment, and obtaining quasi-ensemble forecast errors; calculating a mean value of the quasi-ensemble forecast errors, and substituting the mean value and the quasi-ensemble forecast errors into an unbiased estimation formula to obtain unbiased estimation; and substituting the unbiased estimation into a quasi-ensemble-variation assimilation algorithm, and carrying out mixed assimilation. The method is used for calculating historical forecast errors to obtain quasi-ensemble background errors, and is applied to quasi-ensemble-variation mixed data assimilation. The quasi-ensemble background errors are generated through adjacent historical forecast results without real ensemble forecast, so that the calculated amount for the ensemble forecast is effectively reduced and the efficiency for business data assimilation and forecast is improved.
Description
Technical Field
The invention relates to a quasi-ensemble-variational-based mixed data assimilation method, and belongs to the technical field of data assimilation in numerical weather forecast.
Background
The numerical weather forecast quality is determined by a numerical forecast mode and a mode initial field. At present, the mode structure and the physical process scheme of numerical forecasting tend to be perfect, and the evolution of a real weather system can be accurately described and simulated. Therefore, the task of improving the accuracy of the numerical weather forecast is more and more directed to improving the accuracy of the initial condition of the mode, namely the requirement of the numerical weather forecast on the accuracy of the initial condition is higher and higher. With the development of software, hardware technology and observation systems, the global meteorological observation network is continuously upgraded, the observation time density and spatial distribution are continuously increased, the types and the quantity of observation data are continuously increased, and the key problem of further improving the numerical weather forecast level is how to effectively utilize the data to provide a more accurate initial field for numerical weather forecast.
Currently, data assimilation has been widely used to fuse various observations to generate a more reasonable initial field for numerical models. Three-dimensional variational assimilation, four-dimensional variational assimilation, ensemble kalman filter assimilation, and ensemble-variational mixed assimilation which is currently receiving much attention from students are mainly used in research and business. The hybrid assimilation scheme combining the variational method and the ensemble Kalman filtering method integrates the advantage that the ambient field error covariance of the ensemble Kalman filtering method can evolve along with the weather situation, and utilizes the variational method to form an effective and mature technical scheme which is considered as a main development direction of data assimilation.
In the hybrid assimilation approach, the aggregate ambient field error covariance, represented by a set of aggregate forecasts, is combined with the ambient field error covariance, which is static in the variation assimilation. The mixed assimilation scheme relieves the problems of insufficient rank and variable incoordination of the set scheme, also improves the problems of isotropy and homogeneity of the variance scheme modeling background field error covariance and incapability of changing according to weather conditions, and a large number of researchers carry out a large number of research tests on the mixed assimilation scheme, wherein most research results show that: the forecasting effect of the mixed assimilation method is superior to that of a pure variation method, and the mixed assimilation method can achieve the effect similar to that of the ensemble Kalman filtering assimilation method under the condition that the number of ensemble members is small. The objective of data assimilation is to find an optimal analysis field to minimize the objective function, which can be expressed as:
wherein J is an objective function, and the objective of assimilation is to continuously correct x to minimize the objective function J. x is the number of1＝x-xb，x1Is the increment of traditional three-dimensional variation assimilation, x is the analysis field, xbAs a background field, B is a static background error covariance matrix, beta1Is the weight coefficient of static covariance, A is the correlation matrix of variable, and plays the role of localization, alphaExtending the control variable, beta, for the set2Is the weight coefficient of flow dependent covariance, H is the linearized observation operator, R is the observation error covariance matrix, d is y-H (x)b) For observation increments, where y is the observation field, H is the linearized observation operator,
for conventional mixed assimilation, in formula (1)Unbiased estimation of ensemble prediction error:
xiis the ith ensemble forecasting member, N is the ensemble forecasting member number,the ensemble prediction average is made. As can be seen from equation (2), when ensemble prediction error covariance is introduced, the mixture needs to calculate the members of the set, and if the members of the set are too few, the problem that the ensemble prediction error covariance is not full-rank and variable is not coordinated is also caused, although the mixture assimilation scheme alleviates the problem, the mixture assimilation method still needs a certain ensemble prediction result as a calculation sample of the ensemble background field error covariance at each assimilation time, for example, 120 samples of the members of the set are needed, and then the method needs to calculate the ensemble background field error covariance120 pattern predictions are required. For some research and business units with insufficient computing conditions, the method still brings about a small computing pressure and influences the business forecasting efficiency.
However, in the current business numerical prediction, it is often necessary to continuously calculate and continuously store the relevant result information of the past historical prediction, and whether the historical prediction results can be used as an aggregate sample for calculating the aggregate ambient field error covariance for mixing and assimilating, so as to improve the business prediction efficiency, which is the problem to be solved by the present invention.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for assimilating the quasi-ensemble-variation mixed data based on the historical forecast result effectively introduces anisotropic ambient field error covariance, and simultaneously effectively reduces the calculated amount brought by the forecast ensemble.
The invention adopts the following technical scheme for solving the technical problems:
a quasi-ensemble-variation-based mixed data assimilation method comprises the following steps:
step 1, selecting historical forecast data adjacent to a current forecast time, and taking the data as a quasi-ensemble forecast sample;
step 2, calculating the difference between 24-hour forecast and 12-hour forecast at the same time for the quasi-ensemble forecast sample obtained in the step 1 to obtain a quasi-ensemble forecast error;
step 3, calculating the mean value of the quasi-ensemble prediction errors obtained in the step 2, and substituting the mean value and the quasi-ensemble prediction errors into a formulaUnbiased estimation of quasi-ensemble prediction error
Step 4, the product obtained in the step 3 is processedSubstitution formulaSubstituting the formula into a set-variational assimilation algorithm, performing mixed assimilation, and optimizing a target function of the algorithm to obtain an optimal analysis field;
wherein,the difference between the 24-hour forecast and the 12-hour forecast at the same moment of the ith time, i is 1, …, M, M is the total number of quasi-ensemble forecast errors,is the mean of the quasi ensemble prediction errors, x is the assimilation total analysis increment, x1＝x-xb，x1Is the increment of three-dimensional variation assimilation, x is the analysis field, xbAs a background field, αiControl variables are extended for the set.
As a preferred scheme of the invention, the specific process of the step 1 is as follows: selecting historical forecast data of a past continuous month adjacent to the current forecast time, extracting 12-hour and 24-hour forecast data from 24-hour historical forecast results carried out every 6 hours, and taking the data as quasi-ensemble forecast samples for 240 in total.
As a preferred scheme of the invention, the specific process of the step 2 is as follows: and (3) calculating the pairwise difference between the 24-hour forecast and the 12-hour forecast at the same moment extracted in the step (1) to obtain 120 quasi-ensemble forecast errors.
As a preferred embodiment of the present invention, the method described in step 3Formula (2)Comprises the following steps:wherein,the 24-hour forecast data and the 12-hour forecast data are respectively.
In a preferred embodiment of the present invention, M in step 3 is 120.
As a preferred embodiment of the present invention, the objective function of the quasi-ensemble-variation assimilation algorithm in step 4 is:
wherein J is an objective function, β1Weight coefficient for static covariance, B is a static background error covariance matrix, beta2Is the weight coefficient of flow dependent covariance, alpha is the vector of set extension control variable, A is the variable correlation matrix, H is the observation operator, R is the observation error covariance matrix, d is y-H (x)b) To observe the increment, where y is the observation field.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the quasi-ensemble-variational-based mixed data assimilation method brings anisotropic and heterogeneous background error covariance information to an assimilation system through the introduction of the quasi-ensemble prediction error covariance in a historical prediction result, and establishes a correlation relation between the information and a water vapor field and other control variables, so that the assimilation system can bring more reasonable assimilation results.
2. The invention relates to a quasi-ensemble-variation-based mixed data assimilation method, wherein the covariance of quasi-ensemble prediction errors comes from historical prediction data of adjacent moments, and the difference between 24-hour prediction and 12-hour prediction at the same moment in the historical prediction data is calculated to be used as the quasi-ensemble prediction errors. The quasi-ensemble prediction error is generated not by ensemble prediction but by a historical prediction result, so that ensemble prediction is not needed, the calculated amount is equivalent to the three-dimensional variation, the prediction effect is effectively improved, and the calculation resources are greatly saved.
Drawings
FIG. 1 is a flow chart of the operation of the quasi-ensemble-variation-based data assimilation method of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In order to effectively introduce the anisotropic background field error covariance and effectively reduce the calculated amount brought by ensemble prediction, an assimilation scheme which is independent of ensemble prediction, not only combines the advantages of a three-dimensional variational method and is convenient for assimilating various data, but also has the spatial anisotropy and the non-uniform background error covariance is established. The invention provides a quasi-ensemble-variable-component mixed data assimilation method which is characterized in that anisotropic and heterogeneous quasi-ensemble background error covariance is obtained by calculating historical forecast result errors and is combined with three-dimensional variable-component background error covariance.
In order to reduce the calculation amount brought by a forecast set and introduce anisotropic and anisotropic ambient field error covariance at the same time, the difference of mode forecast fields with different timeliness at the same time in a historical forecast sample is used as a quasi-aggregate forecast error, and the forecast error set of the quasi-aggregate forecast error is composed of forecast errors with different forecast timeliness at the same time for a continuous period.
The objective of data assimilation is to find an optimal analysis field to minimize the objective function, which can be expressed as:
wherein, each letter has the same meaning as above.
For conventional mixed assimilation, in formula (1)Unbiased estimation of ensemble prediction error:
wherein, each letter has the same meaning as above.
In order to reduce the calculated amount brought by a forecast set and introduce anisotropic and anisotropic ambient field error covariance at the same time, the difference of mode forecast fields with different timeliness at the same time in a historical forecast sample is used as a quasi-set forecast error covariance, namely the difference is used as a quasi-set forecast error covarianceUnbiased estimation of prediction error set considered as a mode quasi-ensemble:
wherein,the difference of the mode prediction fields of different ages at the same time at the ith time is as follows:
t1 and T2 are forecast aging, whereinFor the time-averaging of the historical forecast (in order to eliminate the time-averaged deviation), M is the total number of errors in the historical forecast, and M may be equal to N. It is obvious from the above derivation that the method of the present invention not only avoids the large calculation amount brought by ensemble prediction, but also enables the assimilation system to have anisotropic and non-uniform background field error covariance information.
As shown in fig. 1, the historical forecast data generally selects the past continuous month time of adjacent time, and may be 15 days or 45 days, but the month data is more reasonable in consideration of the sufficiency of the statistical sample. Taking the collection-variation mixing assimilation at 7/16/12/2011 as an example, the mixed data assimilation method based on the quasi-collection-variation comprises the following steps:
step 1, extracting continuous historical prediction results of adjacent months to obtain historical prediction samples. Namely: from the historical forecast results of every 6 hours from 2011 6/15/00 to 2011 7/16/00, the forecast results of 12 hours and 24 hours are extracted, the results are taken as quasi-aggregate forecast samples, namely, the forecast results of 12 hours and 24 hours (namely, the next day 00) are extracted from the forecast results reported from 2011 6/15/00, the forecast results of 18 hours and the next day 06 are extracted from the forecast results reported from 2011 6/15/06, and the like.
And 2, calculating the difference of mode prediction fields with different timeliness at the same time in quasi-ensemble prediction samples obtained within one continuous month as a quasi-ensemble prediction error. For example, from the historical prediction results of every 6 hours from 2011 6 month and 15 day 00 to 2011 7 month and 16 day 00, the difference between the 24 hour prediction and the 12 hour prediction is selected as a prediction error (namely, the prediction of 24 hours from 2011 6 month and 15 day 00 can obtain a result of 2011 6 month and 16 day 00, the prediction of 12 hours from 2011 6 month and 15 day 12 can also obtain a result of 2011 6 month and 16 day 00, and the difference between the two prediction results is used as a prediction error), and an error field is obtained every 6 hours, so that 120 prediction error samples can be obtained in the month. The set of historical prediction errors is generated not by ensemble prediction but by a one-month continuous historical prediction, so that the prediction errors are referred to as "quasi-ensemble prediction errors".
And 3, calculating the mean value of the prediction errors by using the prediction error set obtained in the step 2, substituting the prediction error set and the mean value into a formula (3) for calculation, and obtaining the unbiased estimation of the quasi-prediction error set at 7, 16 and 12 months in 2011.
Step 4, substituting the quasi-ensemble prediction error obtained in the step 3 into a formulaA mixed assimilation system, namely formula (1), is introduced to carry out normal mixed assimilation at 7/16/12/2011 in combination with static covariance B.
And 5, during mixing and assimilating, assimilating observation data at 2011, 7, 16 and 12 to obtain an analysis field at the moment based on a background field at 2011, 7, 16 and 12, and performing numerical weather forecast on the basis of the analysis field to obtain a forecast field at the next moment.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (6)
1. A quasi-ensemble-variation-based hybrid data assimilation method is characterized in that: the method comprises the following steps:
step 1, selecting historical forecast data adjacent to a current forecast time, and taking the data as a quasi-ensemble forecast sample;
step 2, calculating the difference between 24-hour forecast and 12-hour forecast at the same time for the quasi-ensemble forecast sample obtained in the step 1 to obtain a quasi-ensemble forecast error;
step 3, calculating the mean value of the quasi-ensemble prediction errors obtained in the step 2, and pre-collecting the mean value and the quasi-ensembleFormula for substituting reported errorUnbiased estimation of quasi-ensemble prediction error
Step 4, the product obtained in the step 3 is processedSubstitution formulaSubstituting the formula into a set-variational assimilation algorithm, performing mixed assimilation, and optimizing a target function of the algorithm to obtain an optimal analysis field;
wherein,the difference between the 24-hour forecast and the 12-hour forecast at the same moment of the ith time, i is 1, …, M, M is the total number of quasi-ensemble forecast errors,is the mean of the quasi ensemble prediction errors, x is the assimilation total analysis increment, x1＝x-xb，x1Is the increment of three-dimensional variation assimilation, x is the analysis field, xbAs a background field, αiControl variables are extended for the set.
2. The method of claim 1, wherein: the specific process of the step 1 is as follows: selecting historical forecast data of a past continuous month adjacent to the current forecast time, extracting 12-hour and 24-hour forecast data from 24-hour historical forecast results carried out every 6 hours, and taking the data as quasi-ensemble forecast samples for 240 in total.
3. The method of claim 1, wherein: the specific process of the step 2 is as follows: and (3) calculating the pairwise difference between the 24-hour forecast and the 12-hour forecast at the same moment extracted in the step (1) to obtain 120 quasi-ensemble forecast errors.
4. The method of claim 1, wherein: step 3 theThe formula of (1) is:wherein,the 24-hour forecast data and the 12-hour forecast data are respectively.
5. The method of claim 1, wherein: step 3, wherein M is 120.
6. The method of claim 1, wherein: and 4, the objective function of the quasi-ensemble-variation assimilation algorithm is as follows:
wherein J is an objective function, β1Weight coefficient for static covariance, B is a static background error covariance matrix, beta2Is the weight coefficient of flow dependent covariance, alpha is the vector of set extension control variable, A is the variable correlation matrix, H is the observation operator, R is the observation error covariance matrix, d is y-H (x)b) To observe the increment, where y is the observation field.
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Application publication date: 20151021 |