CN105447593A - Rapid updating mixing assimilation method based on time lag set - Google Patents

Abstract

The invention provides a rapid updating mixing assimilation method based on a time lag set. According to a characteristic that a service value forecast system assimilates observation data in a high frequency mode and outputs a forecast field in the high frequency mode, in order to effectively introduce a flow-dependent background error covariance and simultaneously effectively reducing a calculated amount brought by ensemble forecast, the flow-dependent background error covariance obtained and calculated by the time lag set formed by a same moment forecast field obtained by initial fields of different moments based on a history sample is combined with a modeling static background error covariance of a three-dimensional variation so as to expect that assimilation and forecast effects of a current value forecast system based on a variation assimilation method are increased under the condition that calculating cost and storage cost are not increased or only increased a little.

Description

Based on the quick renewal mixing assimilation method of set time lag

Technical field:

The invention belongs to Atmospheric Sciences, relate to a kind of quick renewal mixing assimilation method based on set time lag.

Background technology:

The weather forecast of socio-economic development logarithm value has higher requirement, and the effect of numerical weather forecast depends on the precision of initial fields to a great extent, and how to obtain appropriate initial fields is a very important job in numerical weather forecast research always.Operational forecast center often adopts the method for Data Assimilation to estimate or optimizes initial fields.For surprised severe weather weather, such as heavy rain, carry out the high frequency Data Assimilation at short period interval according to up-to-date observational data, so that initial fields comprises the effective information of weather system as far as possible, just seem very necessary (Benjaminetal.2004).

Current use more widely Data Assimilation method mainly contains the three-dimensional variational method (3DVar), the four-dimensional variational method (4DVar), Ensemble Kalman Filter method (EnKF) and set-variation mixing assimilation method (Hybrid) etc.In view of three-dimensional variational calculation cost is low, be convenient to the advantage of assimilating multiple observational data, the assimilation technique in most of operational forecast system is still the three-dimensional variational method (Barkeretal.2004).But the background error covariance of the height model that the three-dimensional variational method adopts is static, cannot develop with weather situation, describes accurate not to sky airflow; For the four-dimensional variational method (Huangetal.2009), although background error covariance is along with the integration implicit expression of adjoint mode develops, but the tangent linear mode needed for four-dimensional variation and adjoint mode ask for relative complex, and still need static background error covariance time window is initial; Ensemble Kalman Filter method obtains along with weather situation develops the background error covariance (Evensen1994) of (flow-dependent) by the error statistics of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM, but the method also exists the more difficult accurate estimated background error of finite aggregate number, full rank, situational variables are not difficult to the problems such as balance to matrix.

For the assimilation scheme of the comparatively effective ripe multiple observational data of the variational method can be utilized, the advantage that in Ensemble Kalman Filter method, background error covariance can develop with weather situation can be utilized again, in recent years, the set variational method and Ensemble Kalman Filter method combined-variation mixing assimilation becomes the focus (HamillandSnyder2000 of research; Wangetal.2008a, b; Zhangetal.2013).Mixing assimilation method is incorporated into the covariance information that the collective flow describing sky airflow relies in variation cost function, for the assimilation technique in operational forecast provides a kind of selection newly.

The stream that background error covariance in mixing assimilation normally comes from DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM sample error statistics relies on the combination of the background error covariance of static state in background error covariance and variational Assimilation.Mixing assimilation method alleviates Ensemble Kalman Filter method matrix not full rank, variable problem of disharmony, the problem that also improve variation scheme modelling background error covariance isotropy and homogeneity, cannot become according to weather situation, many scholars have also carried out large quantifier elimination test to mixing assimilation scheme, most result of study all shows: the value of forecasting of mixing assimilation method is better than simple variational method, and when set member is less, the effect (Wangetal.2007 similar to Ensemble Kalman Filter method also can be reached; Zhangetal.2013).But mixing assimilation method is secondary when each assimilation still needs certain DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM result as calculating sample, this is not for very abundant researches and operations unit for some design conditions, still can bring no small calculating pressure, more affect operational forecast efficiency.

Summary of the invention:

In view of operational forecast system high-frequency assimilates observational data and the feature of high frequency output forecast fields, for effectively introducing the background error covariance that stream relies on, effectively reduce again the calculated amount that DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM is brought simultaneously, is gathered the stream dependence background error covariance calculated the time lag be made up of the phase forecast fields in the same time that initial fields does not obtain in the same time based on historical sample to combine with the modelling static background error covariance of three-dimensional variation, propose a kind of quick renewal mixing assimilation method based on set time lag, to under the prerequisite not increasing or only increase very little calculation cost and carrying cost, improve at present based on assimilation and the value of forecasting of the Numerical Prediction System of variational Assimilation method.

The object of the invention is to be realized by following measures:

Based on a quick renewal mixing assimilation method for set time lag, the method comprises the following steps:

The first step: choose adjacent with the assimilation moment before the history forecast data of t days as sample, assimilation interval is set to T hour, obtain mutually forecast fields in the same time with each moment initial fields integration forecast and build set time lag, Time effect forecast is 24t hour, forecast fields exported once at interval of T hour, in this time lag of set, total N (N=24t/T, T get 1 or 3 usually) individual member, is respectively x ₁, x ₂, x ₃... x _n;

Second step: calculate the difference between set member's above-mentioned time lag, i.e. x ₂-x ₁, x ₃-x ₁..., x _n-x ₁, x ₃-x ₂, x ₄-x ₂..., x _n-x _2,, x _n-x _n-1;

3rd step, substitutes into following formula by the difference between upper step set member's time lag, obtains the unbiased esti-mator of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error

$x_{n,b}^e=(x_j-x_i)/\sqrt{N-1},1\&le;i<j\&le;N$

In formula, x _iand x _jfor the model predictions field of the different timeliness of synchronization in history forecast sample, two members namely in above-mentioned set time lag, x _i-x _jthe time lag obtained for upper step the difference between set member; N is set member's number; total individual; B represents ambient field mark, and n represents sequence number, be less than or equal to

4th step: utilize the 3rd step to obtain substitute into formula ), the δ x obtained is substituted in set-variational Assimilation algorithm, carries out mixing assimilation, optimize the objective function of this algorithm, obtain mixing assimilation field;

Wherein, δ x is assimilation bulk analysis increment, δ x ₁static covariance analysis increment, α _nfor set expansion control variable;

5th step: forecast in t days is carried out in the mixing assimilation field utilizing the 4th step to obtain, exports once for the every T of forecast result hour.

Further design of the present invention is:

The method also comprises: the 6th step: the method according to the first step builds set time lag in next moment, proceeds assimilation and forecast.

Wherein, desirable 2 days of t, assimilation interval is set to 3 hours, and Time effect forecast is 48 hours, and forecast fields exports once for every 3 hours, and time lag has 16 members in set.

The present invention has following beneficial effect:

The present invention is based in the quick renewal mixing assimilation method of set time lag, gather the stream dependence that covariance can react weather modification time lag, the correlativity between each variable is more coordinated.Set covariance weight coefficient is larger, and the stream dependence of covariance is more obvious, can reduce remote false relevant impact by the Constraints of Equilibrium ability by static covariance with on the application localization technology of set covariance.

Under rational localization yardstick and set covariance weight, all obviously to be better than three-dimensional variation scheme based on the wind field of the quick renewal mixing assimilation method of set time lag, temperature field and moisture field.The background error covariance information that this mixing assimilation scheme relies on owing to effectively introducing stream, improves water vapor condition and the aerodynamic field structure of the simulation of three-dimensional variation.Especially near forward line, create Cyclonic increment, strengthen bottom convergence, the vertical movement of precipitation region is strengthened.In mixing assimilation scheme, due to the existence of localization correlation matrix, steam correlated variables and other control variable in aggregate error covariance matrix are set up and contacts, make steam field be provided with more rational structure.

Time lag, set can regard the forecast result obtained by initial value disturbance integration as, each member's boundary condition length difference also can cause the difference between set, and take full advantage of history observation, each set member is made to contain it to assimilation during correspondence and forecast information, coordinate with dynamic mode and have power growth structure, thus time lag, set embodied the stream dependence of day airflow and prediction error conariance.From calculating and carrying cost, the member of set time lag is owing to coming from already present model predictions field, avoiding Monte Carlo method must by random forcing functions parameterized trouble in addition when determining the probability density function of original state, relative to Ensemble Kalman Filter, Incremental rate model etc., some need the initial disturbance DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM method be coupled in forecast system, substantially do not need extra integral and calculating and storage space.Therefore for business numerical weather forecast system, especially assimilation forecast system is upgraded fast, set-variation mixing assimilation time lag in this paper scheme effectively can be introduced stream and rely on covariance information, and assesses the cost in saving and save on storage resources and have obviously advantage.

In addition, this method by the difference field between computing time delayed set different members as set disturbance information, both the change of the prediction error of different time lag set member with integral time and the difference of confidence level had been taken into full account, too increase the sample number that set covariance calculates, thus provide more rational error covariance information for mixing assimilation system.

Accompanying drawing illustrates:

Fig. 1 is the quick renewal mixing assimilation flow process that the present invention is based on set time lag.

Embodiment:

Embodiment one:

For saving computational resource, improve operational forecast efficiency, up-to-date observational data assimilated for higher-frequency time and exports for the operational forecast system of forecast fields, can be made up of the phase forecast fields in the same time that initial fields does not obtain in the same time and gather (Zhouetal.2010) time lag.Time lag, DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM method was suggested in order to alternative Monte Carlo DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM method (HoffmanandKalnay1983) at first, the uncertainty of this set mainly comes from the difference of not initial fields, lateral boundaries and observational data in the same time, thus can reflect the prediction error conariance information (Luetal.2007 that the stream developed in time relies on; Vogeletal.2014).And in the history forecast fields directly utilizing systemic circulation to forecast due to the method different initial time for the forecast result of synchronization as set sample, save calculation cost and carrying cost largely.Time lag, collection approach was widely used in ensemble prediction system research and development, and achieved good effect (Yuanetal.2008; Chenetal.2013; Jieetal.2014).

Set in current WRFDA-variation mixing assimilation method is (Wangetal.2008a, b),

$J({\mathrm{\&delta;x}}_1,\mathrm{\&alpha;})={\mathrm{\&beta;}}_1\frac{1}{2}{\mathrm{\&delta;x}}_1^T{B}^{-1}{\mathrm{\&delta;x}}_1+{\mathrm{\&beta;}}_2\frac{1}{2}{\mathrm{\&alpha;}}^T{A}^{-1}\mathrm{\&alpha;}+\frac{1}{2}{(y^{o^{\&prime;}}-H\mathrm{\&delta;}x)}^T{R}^{-1}(y^{o^{\&prime;}}-H\mathrm{\&delta;}x)---\left(1\right)$

In formula (1), J is objective function, and B is static background error co-variance matrix, is generally added up obtaining by 12 hours forecast fieldses of historical simulation and the difference of 24 hours forecast fieldses, β ₁it is the weight coefficient of static covariance.δ x ₁be static covariance analysis increment, this can be calculated by the 3DVar function in WRFDA.δ x is assimilation bulk analysis increment, and the bulk analysis increment δ x of assimilation is the static covariance analysis increment δ x relevant to variational Assimilation ₁with the stream relevant to set relies on increment ) sum, namely ), N is set member's number, it is the disturbance quantity of the n-th set member.β ₂it is the weight coefficient that stream relies on covariance.A is localization correlation matrix, is specially diagonal matrix, and the element on diagonal line is pre-set localization related coefficient (experience is determined).α is the vector of set expansion control variable, is provided by DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM Perturbation, mainly comprises wind field, temperature field and moisture field.H is linearization Observation Operators, is responsible for observation field to map (interpolation) on ambient field.R is observational error covariance, and the statistics such as stochastic error, systematic error according to observation data obtains (as in the assimilation system that glue file is Already in commonly used).Y ^o'=y ^o-Hx _bnewly cease vector, i.e. the difference of ambient field and observation field, wherein y ^ofor observation, usually obtained by meteorological observation instrument, as radar, satellite, ground automatic Weather Station etc., x _bfor ambient field, usually provided by forecast fields.Covariance weight coefficient β ₁and β ₂meet relation: 1/ β ₁+ 1/ β ₂=1, β ₁and β ₂value is determined for experience at present, wherein β ₂be generally 0.5 or 0.75.

Mixing for routine is assimilated, for the unbiased esti-mator of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error, namely

$x_{n,b}^e=(x_{n,b}-\stackrel{\&OverBar;}{x_b})/\sqrt{N-1}---\left(2\right)$

In formula, x _n,bbe the n-th DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM member, x _bfor DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM is average.Can find out, when introducing DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error covariance, need the calculating of set member.And if set member very little, also can bring DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error covariance not full rank, variable problem of disharmony, although mixing assimilation method alleviates this problem, assessing the cost required for DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM still brings impact to the counting yield of mixing assimilation.

The calculated amount brought for avoiding DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM, the background error covariance that stream relies on can be introduced again simultaneously, based on the quick renewal mixing assimilation method gathered time lag, history is forecast that the difference of the model predictions field of the different timeliness of synchronization in sample is considered as the unbiased esti-mator of the DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error in (2) formula, namely

$x_{n,b}^e=(x_j-x_i)/\sqrt{N-1},1\&le;i<j\&le;N---\left(3\right)$

X in formula _iand x _jfor the model predictions field of the different timeliness of synchronization in history forecast sample, i, j are integer, total individual.As, if every 3h does once assimilation and 48h forecast, every 3h preservation single prediction result, just have 16 time lag set member.Difference so between set member is just x ₂-x ₁, x ₃-x ₁..., x ₁₆-x ₁, x ₃-x ₂, x ₄-x ₂..., x ₁₆-x ₂..., x ₁₆-x ₁₅.Therefore 16 time lag set member will obtain individual difference field, provides set disturbance information with these difference fields for mixing assimilation system, carries out circulation mixing assimilation and forecast.

Application example:

As shown in Figure 1, the present invention is based on the quick renewal mixing assimilation method of set time lag, concrete steps are as follows:

The first step: utilize system to the circulation assimilation in adjacent first 2 days of moment of forecast and forecast, assimilation is spaced apart 3 hours, and Time effect forecast is 48 hours, and forecast fields exports once for every 3 hours;

Second step: the forecast fields being integrated to the identical forecast moment with each moment initial fields builds set time lag, as set time lag during 3 days 00 July in 2014 is made up of the 9 hours forecast fieldses etc. when 6 hours forecast fieldses when 3 hours forecast fieldses during 2 days 21 July in 2014,2 days 18 July in 2014,2 days 15 July in 2014, because Time effect forecast in this method is 48 hours, set time lag therefore obtained has 16 members;

3rd step: calculate the difference between different time lag set member according to (3) formula, i.e. x ₂-x ₁, x ₃-x ₁..., x ₁₆-x ₁, x ₃-x ₂, x ₄-x ₂..., x ₁₆-x ₂,

4th step: the esodisparity utilize (2) formula to try to achieve the unbiased esti-mator of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error time lag obtained with the 3rd step with the last time assimilation (first time assimilation ambient field by the whole world from American NCEP again analysis of data FNL provide) 3 hours forecast fieldses field x as a setting _b, Perturbation, ambient field and observational data y will be gathered ^osubstitute into (1) formula respectively, first try to achieve the vectorial y of new breath ^o', when objective function reaches minimal value, obtain static covariance analysis increment δ x respectively ₁the stream relevant to set relies on increment ), the bulk analysis increment δ x of mixing assimilation is front two sums, and final mixing assimilation field is that ambient field adds bulk analysis increment;

Adopt the set-variation mixing assimilation method in WRFDA, optimized the objective function of former three-dimensional variational algorithm by formula (1), obtain mixing assimilation field,

$J({\mathrm{\&delta;x}}_1,\mathrm{\&alpha;})={\mathrm{\&beta;}}_1\frac{1}{2}{\mathrm{\&delta;x}}_1^T{B}^{-1}{\mathrm{\&delta;x}}_1+{\mathrm{\&beta;}}_2\frac{1}{2}{\mathrm{\&alpha;}}^T{A}^{-1}\mathrm{\&alpha;}+\frac{1}{2}{(y^{o^{\&prime;}}-H\mathrm{\&delta;}x)}^T{R}^{-1}(y^{o^{\&prime;}}-H\mathrm{\&delta;}x)---\left(1\right)$

In formula (1), J is objective function, and B is static background error co-variance matrix, is generally added up obtaining by 12 hours forecast fieldses of historical simulation and the difference of 24 hours forecast fieldses, β ₁it is the weight coefficient of static covariance.δ x ₁be static covariance analysis increment, this can be calculated by the 3DVar function in WRFDA., δ x is assimilation bulk analysis increment, and the bulk analysis increment δ x of assimilation is the static covariance analysis increment δ x relevant to variational Assimilation ₁with the stream relevant to set relies on increment sum, namely _nset member's number, the disturbance quantity of the n-th set member, β ₂it is the weight coefficient that stream relies on covariance.A is localization correlation matrix, is specially diagonal matrix, and the element on diagonal line is pre-set localization related coefficient (experience is determined).α _nbe the vector of set expansion control variable, provided by DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM Perturbation, mainly comprise wind field, temperature field and moisture field.H is linearization Observation Operators, is responsible for observation field to map (interpolation) on ambient field.R is observational error covariance, and the statistics such as stochastic error, systematic error according to observation data obtains (as in the assimilation system that glue file is Already in commonly used).Y ^o'=y ^o-Hx _bnewly cease vector, i.e. the difference of ambient field and observation field, wherein y ^ofor observation, usually obtained by meteorological observation instrument, as radar, satellite, ground automatic Weather Station etc., x _bfor ambient field, usually provided by forecast fields.Covariance weight coefficient β ₁and β ₂meet relation: 1/ β ₁+ 1/ β ₂=1, β ₁and β ₂value is determined for experience at present, wherein β ₂be generally 0.5 or 0.75.

5th step: forecast in 48 hours is carried out in the mixing assimilation field utilizing the 4th step to obtain, forecast result exports once for every 3 hours;

6th step: the method according to second step builds set time lag in next moment, proceeds assimilation and forecast.

Claims (3)

1., based on a quick renewal mixing assimilation method for set time lag, the method comprises the following steps:

The first step: choose adjacent with the assimilation moment before the history forecast data of t days as sample, assimilation interval is set to T hour, obtain mutually forecast fields in the same time with each moment initial fields integration forecast and build set time lag, Time effect forecast is 24t hour, forecast fields exported once at interval of T hour, in this time lag of set, total N number of member, is respectively x ₁, x ₂, x ₃... x _n;

Second step: calculate the difference between set member's above-mentioned time lag, i.e. x ₂-x ₁, x ₃-x ₁..., x _n-x ₁, x ₃-x ₂, x ₄-x ₂..., x _n-x ₂..., x _n-x _n-1;

3rd step, substitutes into following formula by the difference between upper step set member's time lag, obtains the unbiased esti-mator of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM error $x_{n,b}^e=(x_j-x_i)/\sqrt{N-1},1\&le;i<j\&le;N$

In formula, x _iand x _jfor two members in above-mentioned set time lag, x _i-x _jthe time lag obtained for upper step the difference between set member; N is set member's number; total individual; B represents ambient field mark; N represents sequence number; Wherein 1≤i<j≤N;

4th step: utilize the 3rd step to obtain substitute into formula the δ x obtained is substituted in set-variational Assimilation algorithm, carries out mixing assimilation, optimize the objective function of this algorithm, obtain mixing assimilation field;

Wherein, δ x is assimilation bulk analysis increment, δ x ₁static covariance analysis increment, α _nfor set expansion control variable;

5th step: forecast in t days is carried out in the mixing assimilation field utilizing the 4th step to obtain, exports once for the every T of forecast result hour.

2. according to claim 1 based on the quick renewal mixing assimilation method of set time lag, the method also comprises: the 6th step: the method according to the first step builds set time lag in next moment, proceeds assimilation and forecast.

3. according to claim 1 or 2 based on the quick renewal mixing assimilation method of set time lag, wherein, t gets 2 days, and assimilation interval is set to 3 hours, and Time effect forecast is 48 hours, and every 3 hours of forecast fields exports once, has 16 members in gathering time lag.