CN111275250B - Strong current region sea surface temperature forecasting method based on anisotropy - Google Patents

Strong current region sea surface temperature forecasting method based on anisotropy Download PDF

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CN111275250B
CN111275250B CN202010044424.3A CN202010044424A CN111275250B CN 111275250 B CN111275250 B CN 111275250B CN 202010044424 A CN202010044424 A CN 202010044424A CN 111275250 B CN111275250 B CN 111275250B
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张亮
胡艳
张学峰
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Abstract

The invention discloses a method for forecasting sea surface temperature in a strong current area based on anisotropy, which comprises the following steps: (1) an initial guess value of a given control variable ω (x, y); (2) let T be the study variable, and get T from "time" T ═ 0 forward integral advection diffusion model to T ═ SS(ii) a And obtaining a diffusion coefficient a by using a parameterization method; (3) integrating the tangent concomitant model to obtain the gradient g (omega) of the target function J (omega); (4) the minimization algorithm optimizes the control variables ω (x, y); (5) and (4) circulating the steps (2) to (4) until the control variable omega (x, y) enables the target function J (omega) to reach the minimum value, and outputting T at the momentS(ii) a (6) T obtained according to step (5)SAnd establishing an analysis field, wherein the established analysis field provides an initial field for sea surface temperature prediction in the strong current region. Aiming at the characteristic of isotropy of original diffusion filtering, the invention adopts a method of adding advection terms and parameterizing diffusion coefficients to a diffusion equation, and adds the influence of ocean currents to the whole assimilation process to ensure that the assimilation result is more close toAnd (6) integrating true values.

Description

Strong current region sea surface temperature forecasting method based on anisotropy
Technical Field
The invention relates to marine environmental engineering, in particular to a method for forecasting sea surface temperature in a strong current area based on anisotropy.
Background
The ocean numerical prediction is a method for performing numerical calculation through a large computer under certain initial value and boundary value conditions according to the actual ocean conditions, solving a hydrodynamics and thermodynamics equation system describing the ocean evolution process and predicting the ocean motion state and the ocean phenomenon in a certain time period, namely a means for performing ocean prediction by using the current ocean conditions as input data. The most important aspect of how to obtain a more accurate prediction result is the initial value problem, and at present, a more accurate initial field can be obtained by adopting a data assimilation method so as to improve the prediction accuracy.
In general, the standard three-dimensional variational data assimilation method can be written as the following objective function minimization problem:
Figure BDA0002368870540000011
where x is the analysis vector, xbIs the background field, y is the observation vector, H is the interpolation operator from the model point interpolation to the observation point, R is the observation error covariance matrix, (.)TIs a transposition of-1Refers to the inverse matrix. If the matrix is overestimated, the effect of the background term in the objective function will be diminished, so that the minimization is mainly directed at the observation term, and the observation field will be over-fitted, ignoring better background information. Similarly, if the background field is over-fitted, the contribution of the good quality observation field is diminished.
Since the actual marine environment is complex and the real situation is unknown, the determination of the covariance matrix B including the three-dimensional variation background error in any data assimilation method is a challenge, how to solve the problem becomes the key scientific research content of data assimilation researchers, and two methods are currently used for determining BThe scale-off method, but this method cannot find B-1And a large storage space is required for storage, which has certain limitations. The second approach is to introduce a new variable ω, defined as:
ω＝B-1(x-xb) (2)
b is described with recursive filtering:
Yi＝αYi-1+(1-α)Xi (3)
Zi＝αZi+1+(1-α)Yi (4)
wherein XiIs the initial value at grid point i, YiIs the value after filtering from i-1 to n, ZiIs the initial value after one filtering pass in each direction and alpha is the filter coefficient that determines the speed at which the observed information propagates through the analysis domain. The operations of (2) and (3) are repeated for multiple filtering. The multi-dimensional filtering may be constructed by performing one-dimensional filtering in each direction.
The matrix B considered gaussian can be considered as a gaussian filtering process in recursive filtering, and gaussian filtering is diffusion filtering. The final analysis field can be obtained by solving the diffusion equation in combination with a minimization algorithm. However, the determination experience of the diffusion coefficient in the process is relatively strong, and the method has an isotropic property, so that the assimilation result is not ideal in a strong flow region, and the prediction result is poor in numerical prediction of the strong flow region.
Disclosure of Invention
Aiming at the characteristic of isotropy of original diffusion filtering, the invention adopts a method of adding an advection term to a diffusion equation and parameterizing a diffusion coefficient, and adds the influence of sea current to the whole assimilation process to enable the assimilation result to be more fit with a true value.
The technical scheme adopted by the invention is as follows: a strong current region sea surface temperature forecasting method based on anisotropy comprises the following steps:
step 1, giving an initial guess value of a control variable omega (x, y);
and 2, setting T as a research variable, and obtaining T from the forward integral advection diffusion model with time T being 0 to the forward integral advection diffusion model with time T being SS(ii) a And obtaining a diffusion coefficient a by using a parameterization method;
step 3, integrating the tangent concomitant model to obtain the gradient g (omega) of the target function J (omega);
step 4, optimizing a control variable omega (x, y) by a minimization algorithm;
and 5, circulating the steps 2 to 4 until the control variable omega (x, y) enables the target function J (omega) to reach the minimum value, and outputting T at the momentS；
Step 6, obtaining T according to step 5SAnd establishing an analysis field, wherein the established analysis field provides an initial field for sea surface temperature prediction in the strong current region.
Further, in step 2, the advection diffusion model is:
Figure BDA0002368870540000031
wherein t represents time; u represents the flow rate of the fluid under the east-west; v represents the flow velocity in the north and south; t represents a study variable; a represents a diffusion coefficient; s represents an integration time length;
Figure BDA0002368870540000032
d represents the width of the study region, and L represents the length of the study region; omega is
Figure BDA0002368870540000033
The central domain of (a) is,
Figure BDA0002368870540000034
gamma is
Figure BDA0002368870540000035
The boundary of (2); n is the outer normal vector of Γ.
Further, in step 2, the obtaining of the diffusion coefficient a by using the parameterization method includes:
by TSRepresents T-t＝STo achieve the goalThe scaling function J (ω) is expressed as:
Figure BDA0002368870540000036
in the formula, H represents an interpolation operator from a model point to an observation point, R represents an observation error covariance matrix, and d is an observation increment;
parameterizing the diffusion coefficient a by Smagorinsky diffusion formula (6):
Figure BDA0002368870540000037
wherein, C represents HORCON parameter, and C is 0.1; Δ x represents the x-direction spatial step; Δ y represents the y-direction spatial step;
Figure BDA0002368870540000038
further, in step 3, said integrating the gradient g (ω) of the objective function J (ω) obtained by the tangential adjoint model comprises:
calling a tapenade compiler to automatically generate a tangent linear adjoint model code by adopting a code2code form;
from "time" t-S to t-0, the integral tangent adjoint model is used to obtain the solution R of the tangent adjoint model at t-00(ω)；
The gradient g (omega) of the objective function J (omega) is-R0(ω)。
The beneficial effects of the invention are: the invention discloses a strong flow region sea surface temperature forecasting method based on anisotropy, which adopts a three-dimensional variational data assimilation method based on traditional diffusion filtering construction flow dependence to provide an initial field for numerical forecasting. The invention adds the advection term to the diffusion equation, solves the advection diffusion equation according to the same method, and parameterizes the diffusion coefficient to replace the constant in the traditional method. Compared with the traditional diffusion filtering data assimilation method, the method has the characteristic of anisotropy, the influence of ocean current information is considered in the assimilation process, especially in a strong current area such as a black tide area, an analysis field with smaller error than that of the traditional method can be obtained, and certain guarantee is provided for the accuracy of numerical prediction.
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FIG. 1: the invention discloses a flow schematic diagram of a strong current region sea surface temperature forecasting method based on anisotropy.
Detailed Description
In order to further understand the contents, features and effects of the present invention, the following embodiments are illustrated and described in detail with reference to the accompanying drawings:
the diffusion coefficient of the traditional diffusion filter is generally fixed as a constant, the defect of isotropy exists, and the assimilation result error of the sea area with a strong flow field is large. The method adds the influence of ocean current information in the assimilation process, uses advection diffusion equation to filter, and uses Smagorinsky equation to parameterize the diffusion coefficient, so that an analysis field which is closer to a real field can be obtained in a strong current area compared with the traditional method.
As shown in the attached figure 1, the important content of the invention is that a strong-current-region sea surface temperature forecasting method based on anisotropy adopts a three-dimensional variation data assimilation method based on flow dependence, and the traditional diffusion filtering data assimilation method is improved by adding sea current information. The method specifically comprises the following steps:
in step 1, an initial guess of the control variable ω (x, y) is given, typically set to ω (x, y) equal to 0.
And 2, setting T as a research variable, and obtaining T from the forward integral advection diffusion model with time T being 0 to the forward integral advection diffusion model with time T being SS：
Figure BDA0002368870540000051
Wherein t represents time; u represents the flow rate of the fluid under the east-west; v represents the flow velocity in the north and south; t (ω) represents the study variable; a represents a diffusion coefficient; s represents an integration time length;
Figure BDA0002368870540000052
d denotes the width of the investigation region and L denotesThe length of the study area; omega is
Figure BDA0002368870540000053
The central domain of (a) is,
Figure BDA0002368870540000054
gamma is
Figure BDA0002368870540000055
The boundary of (a); n is the outer normal vector of Γ.
If using TSRepresents T-t＝SThe objective function J (ω) can then be expressed as:
Figure BDA0002368870540000056
where H denotes an interpolation operator for interpolating from a model point to an observation point, R denotes an observation error covariance matrix, and d is an observation increment.
Parameterizing the diffusion coefficient a by using Smagorinsky diffusion formula (6):
Figure BDA0002368870540000057
wherein, C represents HORCON parameter, and C is 0.1; Δ x represents the x-direction spatial step; Δ y represents the y-direction spatial step;
Figure BDA0002368870540000058
and 3, integrating the tangent concomitant model to obtain the gradient g (omega) of the target function J (omega).
Step 3.1, obtaining a tangent concomitant model:
and (3) changing the three-dimensional variational into a special four-dimensional variational due to the introduction of a diffusion equation, solving the gradient of the target function by using a commonly used adjoint method in the four-dimensional variational, and calling a tapenade compiler to automatically generate a tangent linear adjoint model code in a code2code form.
Step 3.2, from "time" t ═ S to t ═ 0Integrating the tangent adjoint model to obtain the solution R of the tangent adjoint model at the moment when t is 00(ω); the gradient g (omega) of the objective function J (omega) is-R0(ω)。
And 4, optimizing the control variable omega (x, y) by a minimization algorithm, namely a descent algorithm.
And 5, circulating the steps 2 to 4 until the control variable omega (x, y) enables the target function J (omega) to reach the minimum value, and outputting T at the momentS。
Step 6, obtaining T according to step 5SIf x is equal to TS+xbI.e. the analysis field we need, where xbThe analysis field provides an initial field for forecasting the sea surface temperature in the strong current area as a background field.
Although the preferred embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and those skilled in the art can make many modifications without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims (1)

1. A strong current region sea surface temperature forecasting method based on anisotropy is characterized by comprising the following steps:
step 1, giving an initial guess value of a control variable omega (x, y);
and 2, setting T as a research variable, and obtaining T from the forward integral advection diffusion model with time T being 0 to the forward integral advection diffusion model with time T being SS(ii) a And obtaining a diffusion coefficient a by using a parameterization method;
wherein, the advection diffusion model is as follows:
Figure FDA0003494411660000011
wherein t represents time; u represents the flow rate of the fluid under the east-west; v represents the flow velocity in the north and south; t represents a study variable; a represents a diffusion coefficient; s meterShowing the integration time length;
Figure FDA0003494411660000012
d represents the width of the study region, and L represents the length of the study region; omega is
Figure FDA0003494411660000013
The central domain of (a) is,
Figure FDA0003494411660000014
gamma is
Figure FDA0003494411660000015
The boundary of (2); n is the outer normal vector of Γ;
wherein, the obtaining of the diffusion coefficient a by using the parameterization method comprises the following steps:
by TSRepresents T-t＝SThen the objective function J (ω) is expressed as:
Figure FDA0003494411660000016
in the formula, H represents an interpolation operator from a model point to an observation point, R represents an observation error covariance matrix, and d is an observation increment;
parameterizing the diffusion coefficient a by Smagorinsky diffusion formula (6):
Figure FDA0003494411660000017
wherein, C represents HORCON parameter, and C is 0.1; Δ x represents the x-direction spatial step; Δ y represents the y-direction spatial step;
Figure FDA0003494411660000018
step 3, integrating the tangent adjoint model to obtain the gradient g (ω) of the target function J (ω), including:
calling a tapenade compiler to automatically generate a tangent linear adjoint model code by adopting a code2code form;
from the time t, S to the time t, 0, the integral tangent adjoint model is obtained to obtain the solution R of the tangent adjoint model at the time t, 00(ω)；
The gradient g (omega) of the objective function J (omega) is-R0(ω)；
Step 4, optimizing a control variable omega (x, y) by a minimization algorithm;
and 5, circulating the steps 2 to 4 until the control variable omega (x, y) enables the target function J (omega) to reach the minimum value, and outputting T at the momentS；
Step 6, obtaining T according to the step 5SAnd establishing an analysis field, wherein the established analysis field provides an initial field for sea surface temperature prediction in the strong current region.
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