CN114021445B - Ocean vortex mixing non-locality prediction method based on random forest model - Google Patents

Ocean vortex mixing non-locality prediction method based on random forest model Download PDF

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CN114021445B
CN114021445B CN202111270420.8A CN202111270420A CN114021445B CN 114021445 B CN114021445 B CN 114021445B CN 202111270420 A CN202111270420 A CN 202111270420A CN 114021445 B CN114021445 B CN 114021445B
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陈儒
管文婷
邓增安
张翠翠
陈阳
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Tianjin University
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Abstract

The invention discloses a prediction method of ocean vortex mixing non-locality based on a random forest model. In order to solve the problem of insufficient research on the nonlinear relation between the Lagrange balance time and the vortex speed and the mixed non-local degree in the existing method, the invention constructs a random forest model by calculating the vortex diffusivity and the vortex diffusivity error value, the Lagrange balance time, the mixed non-local ellipse and the vortex speed at all self-adaptive box positions based on a standard deviation method, takes the Lagrange balance time and the vortex speed as input samples and takes the mixed non-local degree as output samples, so as to obtain the ocean mixed non-local degree predicted value. The invention is helpful for correctly knowing the importance degree of vortex mixing non-locality in ocean and climate simulation and forecast, provides a new thought for improving the existing vortex mixing parameterization scheme, and indicates the direction for further improving the accuracy of mode simulation and forecast.

Description

Ocean vortex mixing non-locality prediction method based on random forest model
Technical Field
The invention relates to the field of marine vortex mixing non-locality prediction, in particular to prediction of vortex mixing non-locality degree by using a machine learning method.
Background
Some subgrid processes in existing marine climate modes require parameterization. Wherein, the marine vortex mixing parameterization is an important component of marine climate mode simulation. The vortex flow is assumed in vortex mixing parameterization to be represented by the diffusivity coefficient multiplied by the local tracer gradient, but the tracer flow is extended to a form by the green function method, which clearly shows that the tracer flow at a given point depends on both local and non-local large scale tracer gradients [1], and the lagrangian vortex diffusivity coefficient is also non-local in nature. However, the current climate modes do not provide adequate knowledge and application of vortex mixing. Neglecting the climate pattern to mix non-localized features of the ocean limits the accuracy and precision of forecasting the climate pattern.
There have been studies to predict the degree of mixing non-locality by a scale method by constructing a mixing non-locality ellipse in a positive pressure ideal model [2]. However, in high resolution simulation model experiments, the correlation between the scale method and the non-local degree of mixing based on lagrangian magnitude particles is significant, but the root mean square error is large. The prior art has a certain limitation in quantitatively predicting mixing non-locality.
Random forests are a machine learning algorithm, essentially a collection of decision trees with subsampled samples. For the regression problem related to the invention, the prediction result of the random forest model is the average value of the decision tree. The random forest model has strong nonlinear fitting capability, can capture nonlinear relation between the predictive factor and the predictive response value and avoid overfitting. There is currently no study relating hybrid non-localized prediction to machine learning methods. There is a complex nonlinear relationship between the two characteristic parameters of Lagrangian equilibrium time and scroll speed magnitude and the degree of mixing non-locality, but existing methods cannot characterize this nonlinear relationship. Therefore, the invention provides an ocean vortex mixing non-locality prediction method based on a random forest model so as to improve the accuracy of predicting mixing non-locality.
[ reference ]
[1]Kraichnan R H.Eddy viscosity and diffusivity:exact formulas and approximations[J].Complex Systems,1987,1(4-6):805-820.Chen R,Gille S T,McClean J L,et al.A multiwavenumber theory for eddy diffusivities and its application to the southeast Pacific (DIMES)region[J].Journal of Physical Oceanography,2015,45(7):1877-1896.
[2]Chen R,Waterman S.Mixing Nonlocality and Mixing Anisotropy in an Idealized Western Boundary Current Jet[J].Journal of Physical Oceanography,2017,47(12):3015-3036.
Disclosure of Invention
Aiming at the prior art, the invention provides an ocean vortex mixing non-locality prediction method based on a random forest model, which utilizes the random forest model to construct a nonlinear relation between two input characteristic variables (Lagrange balance time and vortex speed) and an output response variable (mixing non-locality degree). Compared with the traditional linear prediction method, the method provided by the invention can be used for more accurately predicting the degree of non-locality of ocean mixing.
In order to solve the technical problems, the invention provides a random forest model-based ocean vortex mixing non-locality prediction method, which mainly comprises the following steps:
step 1: calculating vortex diffusivity and vortex diffusivity error value;
step 2: calculating Lagrangian balance time at all the adaptive bin positions;
step 3: calculating a mixed non-local ellipse;
step 4: calculating the vortex speed;
step 5: predicting the magnitude of the vortex mixing non-local degree by using a random forest model, and obtaining a mixing non-local degree prediction value.
The specific content of the step 1 of the invention is as follows: firstly, lagrangian numerical particles are deployed, ocean surface velocity field data are interpolated on the numerical particles, and a fourth-order Longgot-Kutta method (or other similar numerical methods) is utilized to form a long-time sequence particle track; intercepting tracks with fixed time length on each long track by taking different moments as starting points to serve as particle quasi-tracks; clustering all particle quasi trajectories by using a K-means clustering algorithm (K-means) to obtain a self-adaptive box center; calculating the vortex diffusivity kappa over time at each adaptive bin center position ij (x,τ)，
In the formula (1), u i ′(t 0 |x,t 0 ) Representing t 0 A vortex residual speed in a specific direction i at a moment, wherein the vortex residual speed represents a difference between a particle speed and a local time average euler speed, (x, t) 0 ) The initial position and initial time of a particular quasi-trajectory are indicated, τ indicates the number of days of particle advection,<·> L representation pair passing adaptationIntegrating and averaging all quasi-track autocorrelation functions at the box position x; vortex diffusivity kappa obtained for each adaptive bin according to self-sampling (Bootstrapping) ij Error estimation is performed, i.e. N is set for the remaining vortex speed per day boot Repeating the experiment group, randomly selecting N in the self-adaptive box every time of experiment subset A quasi-track, and calculating a corresponding vortex diffusivity; further utilize N boot Standard deviation sigma of individual vortex diffusivity boot To determine a vortex diffusivity error value error with a 95% confidence level,
the specific content of the step 2 of the invention is as follows:
step 2-1) vortex diffusion coefficient at adaptive bin position x based on formula (2)Diagnostic equation, let τ 1 Initial value is 1, τ 2 Initial value of τ 1 +N-1, N is the particle quasi-trajectory length τ 0 A period of time of upper interception;
in formula (2), the vortex diffusivity κ ij (x, τ) is the integral over time of the velocity autocorrelation function for a particular direction i and j of the bin position x with respect to the number of days τ of particle advection;
step 2-2) at time τ 1 To tau 2 And (3) the upper integration, and judging whether vortex diffusivity integration converges or not according to the following process:
judging tau 2 Whether or not to exceed tau 0 If τ 2 <τ 0 Then according to τ 1 To tau 2 Average value of vortex diffusivity corresponding to the timeObtaining the markThe standard deviation std is equal to the minimum value e of the error value error of the vortex diffusivity in the period min Comparing, if std<e min Then the vortex diffusivity integral at the adaptive bin position x is considered to converge and the Lagrangian balance time τ eq Is tau 1 And τ 2 Average value of (2); if std is greater than or equal to e min Executing the step 2-3);
step 2-3) τ 1 And τ 2 Respectively adding 1 and returning to the step 2-2); up to τ 2 Exceeding τ 0 The convergence criterion std is still not satisfied<e min The convergence of the vortex diffusivity of the self-adaptive box position x is considered to be uncertain, and the Lagrange balance time is considered to be uncertain;
step 2-4) the Lagrangian equilibrium time at all adaptive bin positions is obtained according to steps 2-1) to 2-3).
The specific content of the step 3 of the invention is as follows: within each adaptation box, the Lagrangian equilibrium time τ from time 0 is truncated eq Respectively calculating longitude and latitude coordinate average values on all the intercepted quasi-trajectories, and taking the longitude and latitude coordinate average values as trajectory centroids; constructing a hybrid non-local ellipse using equation set (3),
in the formula group (3), the average variances of the quasi-track coordinates in different directions relative to the track centroid are respectively recorded as the latitudinal variancesWarp variance->And Cross variance->The method comprises the steps of carrying out a first treatment on the surface of the Calculating the degree S of vortex mixing non-localization by using (4) ellipse ，
In the formula (4), the amino acid sequence of the compound,for mixing non-local elliptic half-length axis length, < >>For mixing non-local elliptical semi-short axial lengths.
In step 4 of the present invention, the scroll speed u is calculated according to the formula (5) rms In the formula (5), u 'is the residual velocity of the latitudinal vortex, and v' is the residual velocity of the meridional vortex.
The specific process of the step 5 of the invention is as follows:
step 5-1) determining an original sample set: the Lagrangian balance time tau at all the adaptive bin positions obtained in step 2 is calculated eq And obtaining the vortex speed u according to the step 4 rms As input feature samples in the original sample set; mixing the vortex obtained in the step 3 into a non-local degree S ellipse As output response samples in the original sample set; each sample point in the original sample set is provided with two characteristic input values and a response output value, and the sample points are mutually independent; performing Z-score standardization on an original sample set, randomly selecting a% of original samples in the original sample set as a training sample set, and taking the rest (100-a)% of original samples as a test sample set;
step 5-2), constructing a random forest model by using the training sample set;
step 5-3) taking input characteristic sample values in the test sample set as the input of the random forest model;
and 5-4) carrying out inverse standardization on the output value of the random forest model to obtain a mixed non-local degree predicted value.
Compared with the prior art, the invention has the beneficial effects that:
the convergence of the vortex mixed diffusivity can be accurately and rapidly judged by using a standard deviation method, the corresponding Lagrange balance time is determined, the result is similar to that of the existing least square fitting method, and the two methods are mutually evidence, so that the Lagrange balance time is objectively, accurately and convincingly determined. In addition, the Lagrangian equilibrium time characterizes the time required for the particle velocity to reach a degree of decorrelation from the initial velocity, and is an important input component in a random forest model, whose accurate judgment is beneficial to improving the accuracy of the degree of hybrid non-locality. Compared with the existing method, the mixed non-locality prediction method based on the random forest model provided by the invention takes the non-linear relationship among Lagrange balance time, vortex speed and mixed non-locality degree into more comprehensive consideration and effectively constructs, and improves the accuracy of mixed non-locality prediction. Compared with the prior art, the method has the advantages that root mean square error is greatly reduced, and the prediction accuracy of vortex mixing non-locality is remarkably improved.
Drawings
FIG. 1 is a flow chart of a prediction method of the present invention;
FIG. 2 is a comparison of the predicted outcome of the present invention with the predicted outcome of the prior art, wherein (a) is the predicted outcome of the prior art scale method and (b) is the predicted outcome of the random forest model.
Detailed Description
The invention will now be further described with reference to the accompanying drawings and specific examples, which are in no way limiting.
In order to further understand the nature, features and effects of the present invention, specific embodiments of annual average cross-flow vortex mixing for black tide extender regions (110 DEG E-170 DEG W,20 DEG N-45 DEG N) are described in detail below with reference to the accompanying drawings:
as shown in a flow chart of the attached figure 1, in the method for predicting the mixing non-locality of the ocean vortex based on the random forest model, firstly, the vortex diffusivity and the vortex diffusivity error are calculated through a Lagrange number particle experiment, then, the Lagrange balance time is judged according to the standard deviation method provided by the invention, and then, the mixing non-locality ellipse is calculated, so as to obtain the mixing non-locality degree, then, the Lagrange balance time and the vortex speed are respectively used as input characteristic variables, the mixing non-locality degree is used as output response variables, 70% of sample size is imported as a random forest model training set of the invention, a random forest model is constructed, and finally, a prediction result corresponding to a 30% test set, which is not repeated by the training set sample, is derived as the predicting value of the mixing non-locality degree of the ocean vortex. The specific technical operation is as follows:
step 1: calculating the annual average cross-flow vortex diffusivity and the error value thereof, including:
firstly, a plurality of months are allocated with Lagrange numerical particles with the spatial resolution of 0.2 DEG, MITgcm-llc4320 ocean surface velocity field data are interpolated on the numerical particles, a four-order Dragon-Kutta method (other similar numerical methods are not excluded) is utilized to form 180-day particle tracks, and the advection tracks of all the allocated Lagrange numerical particles are distributed on a annual time scale;
taking a track with a length of 100 days as a particle quasi-track on each long track by taking different moments as starting points; clustering all particle quasi trajectories by using a K-means clustering algorithm (K-means) to ensure that about 1000 quasi trajectories exist in each self-adaptive box, and obtaining the center of the self-adaptive box;
calculating the annual average cross-flow vortex diffusivity kappa over time at each adaptive bin center position ⊥ (x,τ)，
In the formula (1), u' ⊥ (t 0 |x,t 0 ) Representing t 0 A vortex residual speed in a moment cross-flow direction, wherein the vortex residual speed represents the difference between a particle speed and a local time average Euler speed, and the cross-flow direction refers to the direction crossing the local time average Euler speed, (x, t) 0 ) Representing initial position and specific quasi-trajectoryThe initial time, τ, represents the number of days of particle advection,<·> L representing the integration and averaging of all quasi-trajectory autocorrelation functions at the passing adaptive bin position x over a year;
annual average cross-flow vortex diffusivity κ obtained for each adaptive bin according to self-sampling (Bootstrapping) ⊥ Error estimation is performed, i.e. N is set for the residual speed of the cross-flow vortex of each day boot Repeating the experiment group, randomly selecting N in the self-adaptive box every time of experiment subset The quasi-track is adopted, and the corresponding annual average cross-flow vortex diffusivity is calculated;
further utilize N boot Standard deviation sigma of individual vortex diffusivity boot To determine an annual average cross-flow vortex diffusivity error value error with a 95% confidence level,
step 2: calculating Lagrange balance time tau of all self-adaptive box positions based on standard deviation method eq Comprising:
step 2-1) annual average cross-flow vortex diffusion coefficient at adaptive bin position x as shown in equation (2)Diagnostic equation, let τ 1 Initial value is 1, τ 2 Initial value of τ 1 +N-1, N is the particle quasi-trajectory length τ 0 Length of time of up cut, τ 0 ＝100，N＝30；
In the formula (2), κ is ⊥ (x, τ) is the integral over time of the velocity autocorrelation function for the cross-stream direction of the adaptive bin position x and the number of days τ of particle advection;
step 2-2) at time τ 1 To tau 2 And (3) the upper integration, and judging whether vortex diffusivity integration converges or not according to the following process:
judging tau 2 Whether or not to exceed tau 0 If τ 2 <τ 0 Then according to τ 1 To tau 2 Average value of vortex diffusivity corresponding to the timeObtaining the standard deviation std and the minimum value e of the vortex diffusivity error value error in the corresponding period of time min Comparing, if std<e min Then the vortex diffusivity integral at the adaptive bin position x is considered to converge and the Lagrangian balance time τ eq Is tau 1 And τ 2 Average value of (2); if std is greater than or equal to e min Executing the step 2-3);
step 2-3) τ 1 And τ 2 Respectively adding 1 and returning to the step 2-2); up to τ 2 Exceeding τ 0 The convergence criterion std is still not satisfied<e min The convergence of the vortex diffusivity of the self-adaptive box position x is considered to be uncertain, and the Lagrange balance time is considered to be uncertain;
step 2-4) the Lagrangian equilibrium time at all adaptive bin positions is obtained according to steps 2-1) to 2-3).
Step 3: computing a hybrid non-local ellipse comprising:
within each adaptation box, the Lagrangian equilibrium time τ from time 0 is truncated eq Respectively solving the average value of longitude and latitude coordinates on all the quasi-trajectories and taking the average value as a trajectory centroid;
constructing a hybrid non-local ellipse using equation set (3),
in the formula group (3), the average variances of the quasi-track coordinates in different directions relative to the track centroid are respectively recorded as the latitudinal variancesWarp variance->And Cross variance->
Calculating the degree S of vortex mixing non-localization by using (4) ellipse ，
In the formula (4), the amino acid sequence of the compound,for mixing non-local elliptic half-length axis length, < >>Is a mixed non-local elliptic semi-short axial length;
step 4: calculating the scroll speed u rms ，
In the formula (5), u 'is the residual velocity of the latitudinal vortex, and v' is the residual velocity of the meridional vortex;
step 5: predicting vortex mixing non-local extent magnitude using a random forest model, comprising:
step 5-1) determining the original sample set
The Lagrangian balance time tau at all the adaptive bin positions obtained in step 2 is calculated eq And obtaining the vortex speed u according to the step 4 rms As input feature samples in the original sample set; mixing the vortex obtained in the step 3 into a non-local degree S ellipse As output response samples in the original sample set; each sample point in the original sample set is provided with two characteristic input values and a response output value, and the sample points are mutually independent; z-score (Z-score) normalization to the original sample set, at the originalIn the sample set, 30% of original samples are randomly selected as a training sample set, and the rest 70% of original samples are used as a test sample set;
step 5-2), constructing a random forest model by using the training sample set;
step 5-3) taking input characteristic sample values in the test sample set as the input of the random forest model;
and 5-4) carrying out inverse standardization on the output value of the random forest model to obtain a mixed non-local degree predicted value.
Root mean square error RMSE and determinable coefficient R can be calculated from the mixed non-local degree of prediction and test values 2 The prediction effect of the random forest model can be evaluated and analyzed by comprehensively considering the two. The construction of the random forest model can be realized by MATLAB software, and the detailed construction process can be realized by using a manual for MATLAB.
In the specific examples, reference [2]]The instant scale method predicts hybrid non-locality. The scale method predictor (a) and the random forest model predictor (b) are compared as shown in fig. 2, wherein the black line represents a regression line for linear fitting of the predicted value and the test value, and the confidence interval with 95% confidence level is represented inside the two gray lines. Can find both R 2 The method is relatively high, reaches about 0.8, but the RMSE of the predicted value of the random forest model is reduced to 8.9% of the prior art, and the prediction precision is greatly improved. According to the ocean vortex mixing non-locality prediction method based on the random forest model, a non-linear relation between two characteristic variables of Lagrange balance time and vortex speed and mixing non-locality degree is established, and the mixing non-locality degree can be predicted more accurately.
In summary, the invention solves the problem of insufficient research on the nonlinear relation between the Lagrange balance time and the vortex speed and the mixed non-local degree in the existing method, and constructs a random forest model by calculating the vortex diffusivity and the vortex diffusivity error value, the Lagrange balance time, the mixed non-local ellipse and the vortex speed at all self-adaptive box positions based on the standard deviation method, taking the Lagrange balance time and the vortex speed as input samples and the mixed non-local degree as output samples, so as to obtain the ocean mixed non-local degree predicted value. The invention is helpful for correctly knowing the importance degree of vortex mixing non-locality in ocean and climate simulation and forecast, provides a new thought for improving the existing vortex mixing parameterization scheme, and indicates the direction for further improving the accuracy of mode simulation and forecast.
Although the invention has been described above with reference to the accompanying drawings, the invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many modifications may be made by those of ordinary skill in the art without departing from the spirit of the invention, which fall within the protection of the invention.

Claims (2)

1. The method for predicting the non-locality of the ocean vortex mixture based on the random forest model is characterized by comprising the following steps:
step 1: calculating the vortex diffusivity and the vortex diffusivity error value, comprising:
firstly, lagrangian numerical particles are deployed, marine surface velocity field data are interpolated at space-time positions where the numerical particles are located, and a fourth-order Dragon-Algorithm method is utilized to form a long-time-series particle track;
intercepting a track with a fixed time length on each particle track by taking different moments as starting points to serve as a particle quasi-track; clustering all particle alignment tracks by using a K-means clustering algorithm to obtain a self-adaptive box center;
calculating the vortex diffusivity kappa over time at each adaptive bin center position ij (x,τ)，
In the formula (1), κ is ij (x, τ) is the number of days τ related to particle advection and the specific direction i and j of the adaptive bin position xIntegrating the velocity autocorrelation function over time; u (u) i ′(t 0 |x,t 0 ) Representing t 0 A vortex residual speed in a specific direction i at a moment, wherein the vortex residual speed represents a difference between a particle speed and a local time average euler speed, (x, t) 0 ) The initial position and initial time of a particular quasi-trajectory are indicated, τ indicates the number of days of particle advection,<·> L representing the integral averaging of all quasi-trajectory autocorrelation functions at the passing adaptive bin position x;
vortex diffusivity kappa obtained for each self-adaptive tank according to self-sampling method ij Error estimation is performed, i.e. N is set for the remaining vortex speed per day boot Repeating the experiment group, randomly selecting N in the self-adaptive box every time of experiment subset Calculating corresponding vortex diffusivity by the strip quasi-track;
further utilize N boot Standard deviation sigma of individual vortex diffusivity boot To determine a vortex diffusivity error value error with a 95% confidence level,
step 2: calculating Lagrange equilibrium time τ at all adaptive bin positions eq ；
Step 3: computing a hybrid non-local ellipse comprising:
within each adaptation box, the Lagrangian equilibrium time τ from time 0 is truncated eq Respectively calculating longitude and latitude coordinate average values on all the intercepted quasi-trajectories, and taking the longitude and latitude coordinate average values as trajectory centroids;
constructing a hybrid non-local ellipse using equation set (3),
in the formula group (3), the average variances of the quasi-track coordinates in different directions relative to the track centroid are respectively recorded as the latitudinal variancesWarp variance->And Cross variance->
Calculating the degree S of vortex mixing non-localization by using (4) ellipse ，
In the formula (4), the amino acid sequence of the compound,for mixing non-local elliptic half-length axis length, < >>Is a mixed non-local elliptic semi-short axial length;
step 4: calculating the scroll speed u rms ，
In the formula (5), u 'is the residual velocity of the latitudinal vortex, and v' is the residual velocity of the meridional vortex;
step 5: predicting vortex mixing non-local extent magnitude using a random forest model, comprising:
step 5-1) determining the original sample set
The Lagrangian balance time tau at all the adaptive bin positions obtained in step 2 is calculated eq And obtaining the vortex speed u according to the step 4 rms As input feature samples in the original sample set; mixing the vortex obtained in the step 3 into a non-local degree S ellipse As output in the original sample setResponding to the sample; each sample point in the original sample set is provided with two characteristic input values and a response output value, and the sample points are mutually independent; z fraction standardization is carried out on an original sample set, a% of original samples are randomly selected in the original sample set to serve as a training sample set, and the rest (100-a)% of original samples are used as a test sample set;
step 5-2), constructing a random forest model by using the training sample set;
step 5-3) taking input characteristic sample values in the test sample set as the input of the random forest model;
and 5-4) carrying out inverse standardization on the output value of the random forest model to obtain a mixed non-local degree predicted value.
2. The prediction method according to claim 1, wherein in step 2, the standard deviation method is used to calculate the lagrangian balance time of all the adaptive bin positions, comprising the steps of:
step 2-1) vortex diffusion coefficient at adaptive bin position x based on formula (2)Diagnostic equation, let τ 1 Initial value is 1, τ 2 Initial value of τ 1 +N-1, N is the particle quasi-trajectory length τ 0 A period of time of upper interception;
step 2-2) at time τ 1 To tau 2 And (3) the upper integration, and judging whether vortex diffusivity integration converges or not according to the following process:
judging tau 2 Whether or not to exceed tau 0 If τ 2 <τ 0 Then according to τ 1 To tau 2 Average value of vortex diffusivity corresponding to the timeObtaining the standard deviation std and the minimum value e of the vortex diffusivity error value error in the corresponding period of time min Comparing, if std<e min Then the vortex diffusivity integral at the adaptive bin position x is considered to converge and the Lagrangian balance time τ eq Is tau 1 And τ 2 Average value of (2); if std is greater than or equal to e min Executing the step 2-3);
step 2-3) τ 1 And τ 2 Respectively adding 1 and returning to the step 2-2); up to τ 2 Exceeding τ 0 The convergence criterion std is still not satisfied<e min The convergence of the vortex diffusivity of the self-adaptive box position x is considered to be uncertain, and the Lagrange balance time is considered to be uncertain;
step 2-4) the Lagrangian equilibrium time at all adaptive bin positions is obtained according to steps 2-1) to 2-3).
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