CN110398744A - Ocean thermocline characteristic parameter optimizing and inverting method based on acoustic signals - Google Patents
Ocean thermocline characteristic parameter optimizing and inverting method based on acoustic signals Download PDFInfo
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
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Abstract
The invention provides an ocean thermocline characteristic parameter optimizing and inverting method based on acoustic signals, which comprises the following steps: acquiring the vertical profile distribution of the temperature and salinity of the marine environment; constructing an acoustic echo prediction model based on an acoustic reflection principle, and obtaining an acoustic echo prediction signal according to the acoustic echo prediction model; constructing a thermocline characteristic parameter inversion model by using the temperature vertical profile distribution, the salinity vertical profile distribution and the acoustic echo prediction signal of the marine environment; and solving the constructed thermocline characteristic parameter inversion model to obtain the characteristic parameters of the ocean thermocline. The ocean thermocline characteristic parameter optimizing and inverting method effectively solves the problem of low inversion efficiency of traditional acoustic methods, and provides an effective method for efficient inversion of the ocean thermocline.
Description
Technical field
The present invention relates to a kind of thermocline layer characteristic parameter optimizing inversion method, especially a kind of seas based on acoustical signal
Foreign thermocline characteristic parameter optimizing inversion method.
Background technique
Thermocline layer as a kind of important marine environmental phenomenon, for climate change, sea fishery, underwater communication and
Submarine activity has great influence.Obtaining thermocline information using conventional conventional method has the deficiency that time-consuming, at high cost,
Then a kind of effective method will be become by obtaining thermocline layer characteristic parameter using acoustic method.Therefore, it is necessary to design
A kind of thermocline layer characteristic parameter optimizing inversion method based on acoustical signal out, can be by constructing the ocean based on acoustical signal
Thermocline parameter optimization inverting Optimized model, and solved using population-genetic fusion algorithm, obtain thermocline layer spy
Levy parameter.
Summary of the invention
It is an object of the invention to: a kind of thermocline layer characteristic parameter optimizing inversion method based on acoustical signal is provided,
It can be by constructing the thermocline layer parameter optimization inverting Optimized model based on acoustical signal, and use population-genetic fusion
Algorithm is solved, and thermocline layer characteristic parameter is obtained.
In order to achieve the above-mentioned object of the invention, the present invention provides a kind of, and the thermocline layer characteristic parameter based on acoustical signal is sought
Excellent inversion method, includes the following steps:
Step 1, the vertical section distribution of the temperature and salinity of marine environment is obtained；
Step 2, it is based on sound reflecting principle building sound echo prediction model, it is pre- according to sound echo prediction model acquisition sound echo
Survey signal；
Step 3, believed using the temperature vertical section distribution of marine environment, the distribution of salinity vertical section and sound echo prediction
Number building thermocline characteristic parameter inverse model；
Step 4, the thermocline characteristic parameter inverse model of building is solved, obtains the feature ginseng of thermocline layer
Number.
Further, in step 1, the temperature vertical section of marine environment is distributed expression are as follows:
In formula (1), z is the depth of water, αiFor temperature EOF coefficient, T0It (z) is mean temperature section, fiIt (z) is feature vector.
Further, mean temperature section T0(z) calculation formula are as follows:
In formula (2), N is the number of temperature profile, tiIt (z) is the temperature value of different sections.
Further, feature vector fi(z) calculating process are as follows:
First by obtaining the anomaly value of temperature profile:
ΔTi(z)=ti(z)-T0(z) (3)
Then anomaly value is formed into matrix X:
The covariance matrix S of calculating matrix X again:
S=XXT (5)
Eigenvalues Decomposition is done to covariance matrix S again and obtains feature value vector σ, then eigenvectors matrix F has:
SF=F σ (6)
F=[f1(z), f2(z) ..., fN(z)] (7)
σ=[σ1, σ2..., σN] (8)
Significance test finally is carried out to the feature vector σ decomposited, thus each characteristic value in judging characteristic vector σ
There are physical significance signal or noise signal, examine formula are as follows:
When formula (9) are set up, then characteristic value σkAnd σk+1It is separable, then after testing to Eigenvalues Decomposition, by feature
Value is ranked up by sequence from big to small, and selected characteristic is worth the corresponding feature vector f of biggish preceding m rank characteristic valuei(z)。
Further, the salinity vertical section distribution of marine environment is to carry out fitting of a polynomial to salinity according to T-S relationship,
Fitting formula are as follows:
In formula (10), z is the depth of water, PkFor salinity EOF coefficient, T (z) is the vertical section temperature value of temperature.
Further, the specific steps in step 2, when according to sound echo prediction model acquisition sound echo prediction signal
Are as follows:
Building sound echo prediction model first are as follows:
Y (n)=h (n) * x (n) (11)
In formula (11), h (n) is the impulse response of briny environment medium, i.e., received when incoming signal is δ pulse
Echo record, impulse response h (n) includes the characteristic information of thermocline layer structure, and y (n) is the sound echo-signal received,
X (n) is incident acoustical signal, and * indicates convolution；
Then the layered medium model of the times thickness such as foundation is respectively layered when input signal is impulse signal δ (t) again
Impulse response signals indicate are as follows:
In formula (12), f (0,0)=1, f (n, 0)=1, f (n, n)=r0rn, n >=1, riFor the acoustical reflection factor of each layering,
D (0)=δ (t) is impulse signal, and the h (n) being calculated, which is updated to formula (11) just, can obtain sound echo prediction signal.
Further, in step 3, the thermocline characteristic parameter inverse model of building are as follows:
In formula (14), T (z) and S (z) are respectively two elements of temperature and salinity of inverting, and T (z) and S (z) are water
The function of deep z, H are the number of samples of sound echo-signal, and i is the sequence number of sound echo signal sample, yiIndicate what prediction obtained
Sound echo-signal, for the convolution of incident acoustical signal and briny environment medium impulse response, yi' indicate that the sound that actual measurement obtains returns
Wave signal.
Further, in step 4, when solving to the thermocline characteristic parameter inverse model of building, population-is utilized
Genetic fusion algorithm carries out optimizing iterative solution to thermocline characteristic parameter inverse model, obtains temperature profile parameter and salinity is cutd open
Face parameter calculates Sound speed profile parameter further according to temperature profile parameter and salt profile parameter are as follows:
C=1449.14+ Δ cT+ΔcS+ΔcP+ΔcSTP (17)
In formula:
ΔcT=4.5721T-4.4532 × 10-2T2-2.6045×10-4T3+7.985×10-6T4
ΔcS=1.3980 (S-35)+1.692 × 10-3(S-35)2
ΔcP=1.60272 × 10-1P+1.0268×10-5P2+3.5216×10-9P3-3.3603×10-12P4
ΔcSTP=(S-35) (- 1.1244 × 10-2T+7.7711×10-7T2+7.7016×10-5P-1.2943×10-7P2
+3.1580×10-8PT+1.5790×10-9PT2)+P(-1.8607×10-4T+7.4812×10-6T2+4.5283×10-8T3)+
P2(-2.5294×10-7T+1.8563×10-9T2)+P3(-1.9646×10-10T)
P=1.033+1.028126 × 10-1Z+2.38×10-7Z2-6.8×10-17Z4
T is temperature, and unit is degree Celsius；S is salinity, unit ‰；P is pressure, unit dimension gram/cm；Z is deep
Degree, unit is rice.
The beneficial effects of the present invention are: it is anti-that thermocline layer characteristic parameter high efficiency is realized based on sound echo-signal
It drills, solves the problems, such as that conventional acoustic method extracts inverting low efficiency, provide one for the efficient inverting of thermocline layer
The effective method of kind.
Detailed description of the invention
Fig. 1 is inversion method flow chart of the invention；
Fig. 2 is reflection echo schematic illustration of the invention；
Fig. 3 is particle of the invention-genetic dynamics parallel-melt method flow chart.
Specific embodiment
Technical solution of the present invention is described in detail with reference to the accompanying drawing, but protection scope of the present invention is not limited to
The embodiment.
Embodiment 1:
As shown in Figure 1, the thermocline layer characteristic parameter optimizing inversion method disclosed by the invention based on acoustical signal, including
Following steps:
Step 1, the vertical section distribution of the temperature and salinity of marine environment is obtained；
Step 2, it is based on sound reflecting principle building sound echo prediction model, it is pre- according to sound echo prediction model acquisition sound echo
Survey signal；
Step 3, believed using the temperature vertical section distribution of marine environment, the distribution of salinity vertical section and sound echo prediction
Number building thermocline characteristic parameter inverse model；
Step 4, the thermocline characteristic parameter inverse model of building is solved, obtains the feature ginseng of thermocline layer
Number.
Sound wave is influenced maximum to be temperature in ocean, followed by salinity.In common inversion, usually with the velocity of sound
For inverting object, and the basic parameter of Seawater is temperature and salinity etc., can conveniently be sent using temperature and salinity
Livelihood calculates the physical quantity of other care, therefore inversion result can be summed up in the point that the basic parameter of Seawater itself as much as possible
Form；Meanwhile the unknown number of inverse model should lack as best one can, to improve the efficiency of inverting.Based on these considerations, to ocean
On the basis of temperature profile and salt profile property research, temperature profile can be characterized using Empirical Orthogonal Function method and salinity is cutd open
EDS maps, therefore, in step 1, the temperature vertical section of marine environment is distributed expression are as follows:
In formula (1), z is the depth of water, αiFor temperature EOF coefficient, T0It (z) is mean temperature section, fiIt (z) is feature vector.
Further, mean temperature section T0(z) calculation formula are as follows:
In formula (2), N is the number of temperature profile, tiIt (z) is the temperature value of different sections.
Further, feature vector fi(z) calculating process are as follows:
First by obtaining the anomaly value of temperature profile:
ΔTi(z)=ti(z)-T0(z) (3)
Then anomaly value is formed into matrix X:
The covariance matrix S of calculating matrix X again:
S=XXT (5)
Eigenvalues Decomposition is done to covariance matrix S again and obtains feature value vector σ, then eigenvectors matrix F has:
SF=F σ (6)
F=[f1(z), f2(z) ..., fN(z)] (7)
σ=[σ1, σ2..., σN] (8)
Significance test finally is carried out to the feature vector σ decomposited, thus each characteristic value in judging characteristic vector σ
There are physical significance signal or noise signal, examine formula are as follows:
When formula (9) are set up, then characteristic value σkAnd σk+1Be it is separable, characteristic value has physical significance, to characteristic value
After decomposition is tested, characteristic value is ranked up by sequence from big to small, selected characteristic is worth biggish preceding m rank characteristic value pair
The feature vector f answeredi(z)。
Further, the salinity vertical section distribution of marine environment is to carry out fitting of a polynomial to salinity according to T-S relationship,
Fitting formula are as follows:
In formula (10), z is the depth of water, PkFor salinity EOF coefficient, T (z) is the vertical section temperature value of temperature.It establishes with temperature
Degree and salinity are the marine environment dielectric model of major parameter, pass through experimental analysis, temperature, seven rank experiences of saline environment parameter
Orthogonal function more can accurately describe temperature, the vertical distribution of salinity.
Have the characteristics that heterogeneity for seawater, then use for reference layered medium model, a small range can be by seawater
It is approximately layered medium model, as shown in Fig. 2, thinking is uniform in Seawater horizontal direction, and in vertical direction
Using etc. whens thickness model, seawater is considered as to the fine and closely woven plane layer of U equal times thickness, the inner parameter in each layer is identical
, i.e. conforming layer；And between every layer it is mutation, in each layering transmission time Δ t having the same, rather than identical sky
Between thickness deltat x.However, this and real medium are that continuous situation has a certain difference, if by fine and closely woven plane layer thickness control
System is in incidence wave wavelengthThe reflection characteristics of so layered medium are consistent with continuous media, if layering number U obtains foot
Enough big, then thickness layering and actual seawater section are close whens waiting.
For primary detection, variation of the Seawater in time scale is much smaller than the variation on space scale, thus,
Can be by Seawater as a linear time invariant system, the reflection echo of thermocline layer is considered as incident acoustic wave and sea
The convolution of the impulse response of foreign environmental parameter.Then in step 2, according to sound echo prediction model acquisition sound echo prediction signal
When specific steps are as follows:
Building sound echo prediction model first are as follows:
Y (n)=h (n) * x (n) (11)
In formula (11), h (n) is the impulse response of briny environment medium, i.e., received when incoming signal is δ pulse
Echo record, impulse response h (n) includes the characteristic information of thermocline layer structure, and y (n) is the sound echo-signal received,
X (n) is incident acoustical signal, and * indicates convolution；
Then the layered medium model of the times thickness such as foundation is respectively layered when input signal is impulse signal δ (t) again
Impulse response signals indicate are as follows:
In formula (12), f (0,0)=1, f (n, 0)=1, f (n, n)=r0rn, n >=1, riFor the acoustical reflection factor of each layering,
D (0)=δ (t) is impulse signal, and the h (n) being calculated, which is updated to formula (11) just, can obtain sound echo prediction signal.
Since sound wave propagates the mainly influence by ocean environment parameters such as temperature, salinity, present invention building in the seawater
Thermocline layer parametric inversion mathematical model, using temperature, salinity as research object, essence is namely based on to be worked as inverting object
Simulate inverting sound analogue echoes signal and measurement field sound echo-signal closest to when, it is believed that the thermocline parameter of simulation with
Actual measurement field thermocline layer parameter optimal approximation, therefore, in step 3, the thermocline characteristic parameter inverse model of building are as follows:
In formula (14), T (z) and S (z) are respectively two elements of temperature and salinity of inverting, and T (z) and S (z) are water
The function of deep z, H are the number of samples of sound echo-signal, and i is the sequence number of sound echo signal sample, yiIndicate what prediction obtained
Sound echo-signal, for the convolution of incident acoustical signal and briny environment medium impulse response, yi' indicate that the sound that actual measurement obtains returns
Wave signal.
Further, in step 4, when solving to the thermocline characteristic parameter inverse model of building, population-is utilized
Genetic fusion algorithm carries out optimizing iterative solution to thermocline characteristic parameter inverse model, obtains temperature profile parameter and salinity is cutd open
Face parameter calculates Sound speed profile parameter further according to temperature profile parameter and salt profile parameter are as follows:
C=1449.14+ Δ cT+ΔcS+ΔcP+ΔcSTP (17)
In formula:
ΔcT=4.5721T-4.4532 × 10-2T2-2.6045×10-4T3+7.985×10-6T4
ΔcS=1.3980 (S-35)+1.692 × 10-3(S-35)2
ΔcP=1.60272 × 10-1P+1.0268×10-5P2+3.5216×10-9P3-3.3603×10-12P4
ΔcSTP=(S-35) (- 1.1244 × 10-2T+7.7711×10-7T2+7.7016×10-5P-1.2943×10-7P2
+3.1580×10-8PT+1.5790×10-9PT2)+P(-1.8607×10-4T+7.4812×10-6T2+4.5283×10-8T3)+
P2(-2.5294×10-7T+1.8563×10-9T2)+P3(-1.9646×10-10T)
P=1.033+1.028126 × 10-1Z+2.38×10-7Z2-6.8×10-17Z4
C is the velocity of sound, and unit is meter per second；T is temperature, and unit is degree Celsius；S is salinity, unit ‰；P is pressure, single
Position dimension gram/cm；Z is depth, and unit is rice.
As shown in figure 3, further, population-genetic fusion algorithm basic principle are as follows: the individual in group is each
In secondary optimizing iteration journey, firstly, selecting the big individual of certain amount fitness value using sequencing selection method carries out crossover operation
The next generation is generated, then, mutation operation is carried out according to certain mutation probability to the filial generation that crossover operation generates, obtains filial generation
Position and speed, meanwhile, for being not carried out father's individual of crossover operation still according to particle swarm algorithm speed and location updating
Formula generates the next generation, and the optimal location of optimal location and group individual in two kinds of modes of operation is shared.Population-something lost
Pass the execution step of blending algorithm are as follows:
Step (I), to position and speed individual in population size, initial population, weight factor, maximum speed, intersection
Probability, mutation probability and maximum number of iterations are initialized, and individual position and speed is to be randomly generated in initial population
Temperature EOF coefficient and salinity EOF coefficient, initialization population size is set as 50, weight factor 1.0, maximum speed 5.0,
Crossover probability is 0.8, mutation probability 0.05；
Step (II) calculates the functional value of each individual according to formula (14), chooses the current function value of an individual,
And be compared with history optimal function value, if current function value is higher than history optimal function value, updated with current function value
History optimal function value, conversely, then retaining history optimal function value；
Step (III) one by one compares the functional value of the current function value of each individual and group's overall situation optimum position
Compared with if current function value is higher, global optimum position being updated with the position of current function value, conversely, then retaining original
Global optimum position；
Step (IV) is ranked up all individuals according to the size of functional value, 2M optimal individual is selected to be handed over
Fork and mutation operator；
Step (V), the individual in group in addition to 2M individual carry out more according to population position and speed more new formula
Newly；
Step (VI), if meeting the termination condition of maximum number of iterations, optimizing iteration terminates, otherwise, return step
(Ⅱ)。
Further, in step (V), when carrying out crossing operation, individual adaptation degree is ranked up, obtains coming front
2M individual, by 2M it is individual match two-by-two, the formula of crossing operation are as follows:
In formula (15),Speed and the position of filial generation are represented,Represent the speed of parent
Degree and position, k are the number of iteration, and random number of the r between [0,1] is indicated with the random number for meeting Gaussian Profile；
In step (V), the formula of mutation operator are as follows:
In formula (16),Speed and the position of filial generation are represented,Speed and the position of parent are represented, k is repeatedly
The number in generation, CiFor the random number between [0,1].
As described above, must not be explained although the present invention has been indicated and described referring to specific preferred embodiment
For the limitation to invention itself.It without prejudice to the spirit and scope of the invention as defined in the appended claims, can be right
Various changes can be made in the form and details for it.
Claims (8)
1. a kind of thermocline layer characteristic parameter optimizing inversion method based on acoustical signal, which comprises the steps of:
Step 1, the vertical section distribution of the temperature and salinity of marine environment is obtained；
Step 2, it is based on sound reflecting principle building sound echo prediction model, is believed according to sound echo prediction model acquisition sound echo prediction
Number；
Step 3, the temperature vertical section distribution of marine environment, the distribution of salinity vertical section and sound echo prediction signal structure are utilized
Build thermocline characteristic parameter inverse model；
Step 4, the thermocline characteristic parameter inverse model of building is solved, obtains the characteristic parameter of thermocline layer.
2. the thermocline layer characteristic parameter optimizing inversion method according to claim 1 based on acoustical signal, feature exist
In in step 1, the temperature vertical section of marine environment is distributed expression are as follows:
In formula (1), z is the depth of water, αiFor temperature EOF coefficient, T0It (z) is mean temperature section, fiIt (z) is feature vector.
3. the thermocline layer characteristic parameter optimizing inversion method according to claim 2 based on acoustical signal, feature exist
In mean temperature section T0(z) calculation formula are as follows:
In formula (2), N is the number of temperature profile, tiIt (z) is the temperature value of different sections.
4. the thermocline layer characteristic parameter optimizing inversion method according to claim 2 based on acoustical signal, feature exist
In feature vector fi(z) calculating process are as follows:
First by obtaining the anomaly value of temperature profile:
ΔTi(z)=ti(z)-T0(z) (3)
Then anomaly value is formed into matrix X:
The covariance matrix S of calculating matrix X again:
S=XXT (5)
Eigenvalues Decomposition is done to covariance matrix S again and obtains feature value vector σ, then eigenvectors matrix F has:
SF=F σ (6)
F=[f1(z), f2(z) ..., fN(z)] (7)
σ=[σ1,σ2..., σN] (8)
Significance test finally is carried out to the feature vector σ decomposited, so that each characteristic value in judging characteristic vector σ is that have
Physical significance signal or noise signal examine formula are as follows:
When formula (9) are set up, then characteristic value σkAnd σk+1It is separable, then after testing to Eigenvalues Decomposition, characteristic value is pressed
Sequence from big to small is ranked up, and selected characteristic is worth the corresponding feature vector f of biggish preceding m rank characteristic valuei(z)。
5. the thermocline layer characteristic parameter optimizing inversion method according to claim 2 based on acoustical signal, feature exist
In the salinity vertical section distribution of marine environment is to carry out fitting of a polynomial, fitting formula to salinity according to T-S relationship are as follows:
In formula (10), z is the depth of water, PkFor salinity EOF coefficient, T (z) is the vertical section temperature value of temperature.
6. the thermocline layer characteristic parameter optimizing inversion method according to claim 5 based on acoustical signal, feature exist
In specific steps in step 2, when according to sound echo prediction model acquisition sound echo prediction signal are as follows:
Building sound echo prediction model first are as follows:
Y (n)=h (n) * x (n) (11)
In formula (11), h (n) is the impulse response of briny environment medium, i.e. the echo received when incoming signal is δ pulse
Record, impulse response h (n) includes the characteristic information of thermocline layer structure, and y (n) is the sound echo-signal received, x (n)
For incident acoustical signal, * indicates convolution；
Then again according to etc. times thickness layered medium model, when input signal be impulse signal δ (t) when, what is be respectively layered rushes
Swashing response signal indicates are as follows:
In formula (12), f (0,0)=1, f (n, 0)=1, f (n, n)=r0rn, n >=1, riFor the acoustical reflection factor of each layering, D (0)
=δ (t) is impulse signal, and the h (n) being calculated, which is updated to formula (11) just, can obtain sound echo prediction signal.
7. the thermocline layer characteristic parameter optimizing inversion method according to claim 1 based on acoustical signal, feature exist
In, in step 3, the thermocline characteristic parameter inverse model of building are as follows:
In formula (14), T (z) and S (z) are respectively two elements of temperature and salinity of inverting, and T (z) and S (z) are depth of water z
Function, H are the number of samples of sound echo-signal, and i is the sequence number of sound echo signal sample, yiIndicate the sound echo that prediction obtains
Signal, for the convolution of incident acoustical signal and briny environment medium impulse response, yi' indicate the sound echo letter that actual measurement obtains
Number.
8. the thermocline layer characteristic parameter optimizing inversion method according to claim 7 based on acoustical signal, feature exist
In when solving to the thermocline characteristic parameter inverse model of building, utilizing population-genetic fusion algorithm pair in step 4
Thermocline characteristic parameter inverse model carries out optimizing iterative solution, obtains temperature profile parameter and salt profile parameter, further according to
Temperature profile parameter and salt profile parameter calculate Sound speed profile parameter are as follows:
C=1449.14+ Δ cT+ΔcS+ΔcP+ΔcSTP (17)
In formula:
ΔcT=4.5721T-4.4532 × 10-2T2-2.6045×10-4T3+7.985×10-6T4
ΔcS=1.3980 (S-35)+1.692 × 10-3(S-35)2
ΔcP=1.60272 × 10-1P+1.0268×10-5P2+3.5216×10-9P3-3.3603×10-12P4
ΔcSTP=(S-35) (- 1.1244 × 10-2T+7.7711×10-7T2+7.7016×10-5P-1.2943×10-7P2+
3.1580×10-8PT+1.5790×10-9PT2)+P(-1.8607×10-4T+7.4812×10-6T2+4.5283×10-8T3)+P2
(-2.5294×10-7T+1.8563×10-9T2)+P3(-1.9646×10-10T)
P=1.033+1.028126 × 10-1Z+2.38×10-7Z2-6.8×10-17Z4
T is temperature, and unit is degree Celsius；S is salinity, unit ‰；P is pressure, unit dimension gram/cm；Z is depth,
Unit is rice.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111144666A (en) * | 2020-01-02 | 2020-05-12 | 吉林大学 | Ocean thermocline prediction method based on deep space-time residual error network |
| CN111259943A (en) * | 2020-01-10 | 2020-06-09 | 天津大学 | Thermocline prediction method based on machine learning |
| CN112115406A (en) * | 2020-09-28 | 2020-12-22 | 自然资源部第二海洋研究所 | Ocean internal mesoscale vortex inversion method and system based on remote sensing sea surface data |
| CN113051795A (en) * | 2021-03-15 | 2021-06-29 | 哈尔滨工程大学 | Three-dimensional temperature-salinity field analysis and prediction method for offshore platform guarantee |
| CN113218493A (en) * | 2021-04-08 | 2021-08-06 | 中国人民解放军国防科技大学 | Sound velocity profile inversion method based on empirical orthogonal function method |
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