CN102999687B - A kind of astronomical tide and storm tide separation method - Google Patents

Abstract

This application discloses a kind of astronomical tide and storm tide separation method, for just one group of real-time tide water level process that an oceanographic station measures, this real-time process can regard a strong deterministic process (astronomical tide) and a weak stochastic process (atmospheric events interference as, comprise storm tide) superposition, the frequently mathematical measure such as window (frequency field) and wave filter (time domain) now can be utilized to be isolated.Present invention employs a kind of separation method based on wavelet packet analysis, using tidal level as a kind of signal, first the number of plies of wavelet function and WAVELET PACKET DECOMPOSITION is determined, by 170 partial tides according to its parallel compensate to unique leaf node, obtain optimal wavelet tree, then the coefficient of wavelet decomposition including astronomical partial tide is reconstructed, extract the astronomical partial tide signal of each frequency band range, these astronomical partial tide signals remove by optimal utilization wavelet filter from tidal signal, namely obtain Storm Surge curve.

Description

A kind of astronomical tide and storm tide separation method

Technical field

The invention belongs to automatic field, relate to a kind of astronomical tide and storm tide separation method, it is for during storm tide, the astronomical tide water level in total water level and storm tide water level is separated.

Background technology

Storm surge disaster occupies first of all kinds of Oceanic disasters, and the especially big coastal disaster that the overwhelming majority causes because of strong weather system in the world is all caused by storm tide.In China, storm surge disaster, almost throughout China coast, all has generation from south to north. in the southeastern coastal areas that latitude is lower, Disaster of Storm Surges summer and autumn, how to be caused by the typhoon generated in northwest Pacific or tropical cyclone.Astronomical tide is the principal ingredient in tidal observation curve, in tidal observation curve, eliminate astronomical tide, that is astronomical tide and storm tide are separated is primary task.But it seems from dynamic (dynamical) viewpoint, the seawater movement under astronomical power to lead tide and meteorology force the acting in conjunction of power is a kind of nonlinear phenomenon; This nonlinear intercouple be by tidal observation curve the two separate substantially difficulty.The separation method of usual employing deducts tide-prediction curve by tidal observation curve, and institute obtains " difference " namely as " storm tide curve ".Undoubtedly, this separation method based on linear superposition principle, only has when above-mentioned Non-linear coupling is not serious, and side is good being similar to.In some cases, above-mentioned difference curve contains obvious Tidal period.If eliminate the error of astronomical tide forecast and the deficiency of tidal observation technology, then difference curve this phenomenon obviously containing the astronomical tide cycle, just can be summed up as the Non-linear coupling between storm tide and astronomical tide.Storm tide in-situ data and tight theory and successfully experimental data is contrary, very rare and disperse, observation shows, Chinese most of harbours water is shallow, tidal range greatly, astronomical tide and storm tide nonlinear interaction obvious.This nonlinear effect, shows to obtain especially severe in the shallow sea of macrotidal range; Now must adopt other separation method.

The change of water level during storm tide, not only by the effect of Between Celestial Tide-generating Forces, but also be subject to the combined influence of the hydrometeorological factors such as landform, wind-force, wind direction, air pressure, solar irradiance, under the physical agent effect that these periodicity and aperiodicity change, especially in shoal water zone, the nonlinear effect of astronomical tide and storm tide is comparatively strong, makes SEA LEVEL VARIATION process become rather complicated.Major part signal is all the function of time, can using water level time series total during storm tide as signal transacting, and the characteristic of research storm tide and Changing Pattern can be converted into the Time-frequency Analysis of signal.Time frequency analysis can represent energy and the intensity of signal over time and frequency simultaneously, namely time frequency analysis can portray time-frequency structure and the character of all kinds of ripple in storm tide (each astronomy divides tidal wave, Storm events ripple etc.) meticulously, also can extract a certain radio-frequency component in storm tide.

Wavelet transformation is the one of time frequency analysis, there is the feature of multiresolution, time, frequently two territories all there is the ability of characterization signal local feature, that a kind of window area is constant, window shape is variable, the time frequency localization analytical approach that time window and frequency window can change, is described as " school microscop " of analytic signal.Wavelet package transforms is the popularization of wavelet transformation, it segments the low-frequency component of signal and radio-frequency component simultaneously, and carries out multi-level binary partition by frequency band, selects frequency band adaptively, make it to match with signal spectrum, thus improve time frequency resolution.Present invention employs Wavelet Packet Transform Method, tidal signal is decomposed under a certain decomposition scale parameter, utilize the best orthogonal basis of astronomical partial tide specific frequency value determination wavelet packet, identify and determine the astronomical partial tide that comprises in different frequency range, extract WAVELET PACKET DECOMPOSITION coefficient to be reconstructed, and filtering from tidal signal, finally reach the object that astronomical tide is separated with storm tide.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, propose a kind of astronomical tide based on WAVELET PACKET DECOMPOSITION and storm tide separation method, utilize limited history tidal level observation data and known 170 astronomical tidal frequencies, realize being separated astronomical tide and storm tide.

Concrete step is:

Step (1): choosing of orthgonal mother wavelet;

The wavelet transformation of tidal signal is in fact the wavelet function of different scale and the cross-correlation of this signal, when carrying out wavelet analysis to tidal signal, selects the wavelet function close with astronomical partial tide shape as morther wavelet.

Step (2): determine the WAVELET PACKET DECOMPOSITION number of plies;

If (its frequency range is set to [f to tidal signal ₀, f ₁]) N layer WAVELET PACKET DECOMPOSITION will be carried out, then the frequency range that in wavelet tree n-th layer, each leaf node is corresponding is as following table:

Leaf node [N, 0] is that low-limit frequency is interval, and suppose that it has isolated the minimum astronomical partial tide of frequency, then leaf node [N, 0] the frequency separation upper limit is less than the frequency of time minimum astronomical partial tide, can determine the optimum WAVELET PACKET DECOMPOSITION number of plies thus.

Step (3): determine best wavelet packet basis and optimal wavelet tree;

The principle that best wavelet packet basis is selected is: according to the astronomical tidal frequency knowledge of priori and initial frequency corresponding to each leaf node of wavelet tree, the frequency content calculating each astronomical partial tide is positioned at which frequency range of which layer, then processed by the leaf node of method to wavelet tree of beta pruning or merging, obtain the best wavelet packet basis of tidal signal, thus construct optimal wavelet tree.

Step (4): WAVELET PACKET DECOMPOSITION is carried out to tidal signal;

Successively WAVELET PACKET DECOMPOSITION is carried out to tidal signal, can obtain being positioned at 2 of different frequency range when decomposing L layer ^l-1group sequence, often organizes sequence respectively by low-pass filtering result with high-pass filtering result composition, supposes that original tidal signal f (i) length is 2 ⁿ, sample frequency is f _s, then each W ^llength be N/2 ^l, sample frequency is f _s/ 2 ^l.

Make W ⁰(i)=f (i) (i=0,1 ..., 2 ⁿ-1), then following recursive decomposition formula is had

$\left\{\begin{array}{c}{W}_{2n}^L\left(i\right)=\underset{k}{\mathrm{\Σ}}{h}_{(k-2i)}{W}_n^{L-1}\left(k\right)\\ W_{2n+1}^L\left(i\right)=\underset{k}{\mathrm{\Σ}}{g}_{(k-2i)}{W}_n^{L-1}\left(k\right)\end{array}\right.$

Wherein i=0,1 ..., N/2 ^l-1; N=0,1 ..., 2 ^l-1-1; L=0,1 ..., N, h _kfor conjugate quadrature mirror wave filter, and g _k=(-1) ^k-1h _1-k.

Step (5): astronomical tide is separated with storm tide.

Reconstruct all coefficient of wavelet decomposition containing astronomical partial tide frequency range, reconstruction formula is as follows:

${\mathrm{NW}}_n^L\left(i\right)=2\underset{k}{\mathrm{\Σ}}{h}_{(i-2k)}{\mathrm{NW}}_{2n}^{L+1}\left(k\right)+2\underset{k}{\mathrm{\Σ}}{g}_{(i-2k)}{\mathrm{NW}}_{2n+1}^{L+1}\left(k\right)$

Wherein i=0,1 ..., N/2 ^l-1; N=0,1 ..., 2 ^l-1-1; L=0,1 ..., N.N is original tidal signal length 2 in step (4) ⁿin N, for low-pass filtering result, for high-pass filtering result, be N group sequence low-pass filtering and high-pass filtering reconstruction result.

Suppose that the frequency content of astronomical partial tide signal is for { p ₁, p ₂..., p _m, order

$\left\{\begin{array}{cc}{\mathrm{NW}}_n^L=W_n^L& n=\{p_1,p_2,...,p_m\}\\ {\mathrm{NW}}_n^L=0& n\≠\{p_1,p_2,...,p_m\}\end{array}\right.$

Thus can the filter result of stick signal, reach object astronomical tide be separated with storm tide.

The present invention adopts and tidal signal is regularly carried out WAVELET PACKET DECOMPOSITION, and its maximum feature is the angle from signal analysis, and utilize the thought of wavelet transformation multiresolution astronomical tide and storm tide to be separated, algorithm flow chart of the present invention is shown in Figure of description 1.

Accompanying drawing explanation

Fig. 1 is algorithm flow chart;

Fig. 2 is isolated Sa partial tide curve;

Fig. 3 is isolated storm tide curve;

Embodiment

Actual measurement tide water level for Laizhou Wan tidal station (east longitude 119.762, north latitude 36.9762) isolates astronomical tide and storm tide, and concrete implementation step is as follows:

Based on MATLAB wavelet toolbox wavelet function storehouse and Laizhou Wan actual measurement tide level data in 2009, utilize wavelet package transforms to carry out astronomical tide and be separated with storm tide.Concrete grammar is:

1. the local characteristics that had of Daubechies small echo, can extract useful signal composition preferably, finally choose db4 strict support orthogonal wavelet as wavelet packet generating function in various transition waveform.

2. consider the astronomical tide of 170 partial tides, the frequency (/h) scope of tidal signal is [0.0001141,0.4887123], then that frequency is minimum is Sa partial tide (f _sa=0.0001141), secondary minimum be partial tide Ssa, its frequency is 0.0002282, then

$\frac{(2^N-1)f_0+f_1}{2^N}<0.0002282$

By f ₀=0.0001141, f ₁=0.4887123 substitutes into above formula, and draw N > 12, namely minimum N=13, namely obtaining the WAVELET PACKET DECOMPOSITION number of plies is 13 layers.

3. following table is the wavelet packet node serial number (wherein (M, N) represents M once N number of frequency range) that 170 astronomical partial tides are corresponding.

4. according to wavelet function db4, the wavelet decomposition number of plies and the optimal wavelet tree determined above, wpdec () function in Calling MATLAB wavelet toolbox carries out 13 layers of WAVELET PACKET DECOMPOSITION to tidal signal s: wpt=wpdec (s, 13, ' db4 ').

5. the wprcoef () function in Calling MATLAB wavelet toolbox, as reconstructed the astronomical partial tide of Ssa, leaf node numbering in the wavelet tree wpt at its place is [13,1], then reconstruction parameter can be designated as Ssa=wprcoef (wpt, [13,1]), the rest may be inferred, reconstructs all coefficient of wavelet decomposition containing astronomical partial tide frequency range, thus isolate each astronomical partial tide and storm tide.

By using the Laizhou Wan actual measurement tide level data of 2009, the method based on wavelet package transforms of the present invention is adopted to test, result shows that the gross energy shared by astronomical tide is 79.12939%, and the energy shared by storm tide is 19.4910%, and energy loss is 1.3796%.

Claims (1)

1. astronomical tide and a storm tide separation method, is characterized in that:

(1) step 1: choosing of orthgonal mother wavelet

The wavelet transformation of tidal signal is in fact the wavelet function of different scale and the cross-correlation of this signal, when carrying out wavelet analysis to tidal signal, select the wavelet function close with astronomical partial tide shape as morther wavelet, the local characteristics that Daubechies small echo has had, useful signal composition can be extracted preferably in various transition waveform, choose db4 strict support orthogonal wavelet as wavelet packet generating function;

(2) step 2: determine the WAVELET PACKET DECOMPOSITION number of plies

Be [f by frequency range ₀, f ₁] tidal signal carry out N layer WAVELET PACKET DECOMPOSITION, then the frequency range that in wavelet tree n-th layer, each leaf node is corresponding is as following table:

Leaf node [N, 0] is that low-limit frequency is interval, and suppose that it has isolated the minimum astronomical partial tide of frequency, then leaf node [N, 0] the frequency separation upper limit is less than the frequency of time minimum astronomical partial tide, can determine the optimum WAVELET PACKET DECOMPOSITION number of plies thus; Consider the astronomical tide of 170 partial tides, the frequency (/h) scope of tidal signal is [0.0001141,0.4887123], then what frequency was minimum is Sa partial tide, and its frequency is 0.0001141, secondary minimum be partial tide Ssa, its frequency is 0.0002282, then by f ₀=0.0001141, f ₁=0.4887123 substitutes into above formula, and draw N > 12, namely minimum N=13, namely obtaining the WAVELET PACKET DECOMPOSITION number of plies is 13 layers;

(3) step 3: determine best wavelet packet basis and optimal wavelet tree

The principle that best wavelet packet basis is selected is: according to the astronomical tidal frequency knowledge of priori and initial frequency corresponding to each leaf node of wavelet tree, the frequency content calculating each astronomical partial tide is positioned at which frequency range of which layer, then processed by the leaf node of method to wavelet tree of beta pruning or merging, obtain the best wavelet packet basis of tidal signal, thus construct optimal wavelet tree;

(4) step 4: WAVELET PACKET DECOMPOSITION is carried out to tidal signal

Successively WAVELET PACKET DECOMPOSITION is carried out to tidal signal, can obtain being positioned at 2 of different frequency range when decomposing L layer ^l-1group sequence, often organizes sequence respectively by low-pass filtering result with high-pass filtering result composition, supposes that original tidal signal f (i) length is 2 ⁿ, sample frequency is f _s, then each W ^llength be N/2 ^l, sample frequency is f _s/ 2 ^l,

Make W ⁰(i)=f (i), wherein i=0,1 ..., 2 ⁿ-1, then there is following recursive decomposition formula

$\left\{\begin{array}{c}{W}_{2n}^L\left(i\right)=\underset{k}{\mathrm{\&Sigma;}}{h}_{(k-2i)}{W}_n^{L-1}\left(k\right)\\ W_{2n+1}^L\left(i\right)=\underset{k}{\mathrm{\&Sigma;}}{g}_{(k-2i)}{W}_n^{L-1}\left(k\right)\end{array}\right.$

Wherein i=0,1 ..., N/2 ^l-1; N=0,1 ..., 2 ^l-1-1; L=0,1 ..., N, h _kfor conjugate quadrature mirror wave filter, and g _k=(-1) ^k-1h _1-k,

According to the wavelet function db4 determined above, the wavelet decomposition number of plies and optimal wavelet tree, the wpdec function in Calling MATLAB wavelet toolbox to tidal signal s carry out 13 layers of WAVELET PACKET DECOMPOSITION: wpt=wpdec (s, 13, ' db4 ');

(5) step 5: astronomical tide is separated with storm tide

Reconstruct all coefficient of wavelet decomposition containing astronomical partial tide frequency range, reconstruction formula is as follows:

${\mathrm{NW}}_n^L\left(i\right)=2\underset{k}{\mathrm{\&Sigma;}}{h}_{(i-2k)}{\mathrm{NW}}_{2n}^{L+1}\left(k\right)+2\underset{k}{\mathrm{\&Sigma;}}{g}_{(i-2k)}{\mathrm{NW}}_{2n+1}^{L+1}\left(k\right)$

Wherein i=0,1 ..., N/2 ^l-1; N=0,1 ..., 2 ^l-1-1; L=0,1 ..., N,

Suppose that the frequency content of astronomical partial tide signal is for { p ₁, p ₂..., p _m, order

$\left\{\begin{array}{cc}{\mathrm{NW}}_n^L=W_n^L& n=\{p_1,p_2,...,p_m\}\\ {\mathrm{NW}}_n^L=0& n\&NotEqual;\{p_1,p_2,...,p_m\}\end{array}\right.$

N is original tidal signal length 2 in step (4) herein ⁿin N, for low-pass filtering result, for high-pass filtering result, be the filter result of N group sequence low-pass filtering and high-pass filtering reconstruction result, stick signal, reach object astronomical tide be separated with storm tide;

Wprcoef function in Calling MATLAB wavelet toolbox, the astronomical partial tide of reconstruct Ssa, leaf node numbering in the wavelet tree wpt at its place is [13,1], then reconstruction parameter can be designated as Ssa=wprcoef (wpt, [13,1]), the rest may be inferred, reconstructs all coefficient of wavelet decomposition containing astronomical partial tide frequency range, thus isolate each astronomical partial tide and storm tide.