CN113945202A - Sea level height prediction method and system and readable storage medium - Google Patents
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Abstract
The invention discloses a sea level height prediction method and a system, which are used for obtaining sea level height data of each effective grid of a target area at a preset moment by using a sea level height prediction model established aiming at the target area, wherein the sea level height prediction model comprises a first model item for describing the change rule of a sea level height trend component of each effective grid of the target area along with time, a second model item for describing the change rule of a sea level height periodic component of each effective grid of the target area along with time and a third model item for describing the change rule of a sea level height residual error component of each effective grid of the target area along with time. The invention realizes the random dynamic prediction of the sea level height through the established sea level height prediction model, can reduce the calculated amount in the process of predicting the sea level height with large space scale, and improves the prediction accuracy. The invention also discloses a computer readable storage medium.
Description
Technical Field
The invention relates to the field of satellite data analysis and application, in particular to a sea level height prediction method and a sea level height prediction system. The invention also relates to a computer-readable storage medium.
Background
In 2018, the international patent on Climate Change (IPCC) issued "special global warming report at 1.5 ℃ in united states, which explains the influence and prospect of global warming control at 1.5 ℃, wherein the rise of sea level is one of the factors that have great influence on human beings. Sea level elevation results in changes in average sea level, particularly increasing the occurrence of extreme sea level events such as storm surge, flood disasters, increased tropical cyclone strength, which severely affect the development of coastal cities.
In order to improve the accuracy of sea level change prediction, a series of researches are carried out by a plurality of scholars, and at present, two methods are mainly used for sea level height prediction, namely mode simulation prediction and empirical statistical prediction. However, the existing method is complex in operation and the accuracy of sea level height prediction needs to be improved.
Disclosure of Invention
The invention aims to provide a sea level height prediction method and a sea level height prediction system, which realize random dynamic prediction of sea level height through an established sea level height prediction model. The invention also provides a computer readable storage medium.
In order to achieve the purpose, the invention provides the following technical scheme:
a sea level height prediction method is characterized in that a sea level height prediction model established for a target area is used for obtaining sea level height data of each effective grid of the target area at a preset moment;
the sea level height prediction model comprises a first model item, a second model item and a third model item, wherein the first model item describes a change rule of a sea level height trend component of each effective grid of the target area along with time, the second model item describes a change rule of a sea level height periodic component of each effective grid of the target area along with time, the third model item describes a change rule of a sea level height residual component of each effective grid of the target area along with time, the sea level height trend component refers to a part which shows a linear change trend along with time in the sea level height, the sea level height periodic component refers to a part which shows a periodic change along with time in the sea level height, and the sea level height residual component refers to a part which is except the trend component and the periodic component in the sea level height.
Preferably, the first model term describes the variation of the sea level altitude trend component of each effective grid of the target area with time as a linear function.
Preferably, the second model term describes the variation of the sea level altitude period component of each effective grid of the target area with time in a sine function or/and a cosine function.
Preferably, constructing the second model term includes: and performing spectrum analysis according to the part of each effective grid in the target area, from which the trend component is subtracted from the sea level height, selecting a main period from each obtained period according to the amplitude corresponding to each obtained period, and constructing the second model term by using a sine function or/and a cosine function represented by the main period.
Preferably, the third model item includes a model obtained by multiplying a prediction matrix of a time sequence of a main spatial matrix of sea level height residual components of each effective grid of the target area by an eigenvector matrix of the main spatial matrix and then accumulating.
Preferably, constructing the third model term includes:
acquiring a main space matrix of a part of each effective grid in the target area, wherein the sea level height of each effective grid in the target area is subtracted by a trend component and a period component, and a corresponding time sequence;
obtaining a characteristic vector matrix of the main space matrix according to the time sequence corresponding to the main space matrix;
and establishing a prediction matrix for the time sequence corresponding to the main space matrix, multiplying the prediction matrix corresponding to the main space matrix and the eigenvector matrix of the main space matrix, and accumulating to construct the third model item.
A sea level height prediction system for performing the sea level height prediction method described above.
Preferably, the method comprises the following steps:
obtaining means for obtaining the sea level altitude prediction model for a target area;
and the prediction device is used for obtaining the sea level height data of each effective grid of the target area at a preset moment by using the sea level height prediction model.
A computer-readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the steps of the sea level altitude prediction method as set forth above.
According to the technical scheme, the sea level height prediction method and the sea level height prediction system provided by the invention use a sea level height prediction model established aiming at a target area to obtain the sea level height data of each effective grid of the target area at a preset moment, wherein the sea level height prediction model comprises a first model item for describing the change rule of the sea level height trend component of each effective grid of the target area along with time, a second model item for describing the change rule of the sea level height periodic component of each effective grid of the target area along with time and a third model item for describing the change rule of the sea level height residual error component of each effective grid of the target area along with time, the sea level height trend component refers to a part of the sea level height which shows a linear change trend along with time, the sea level height periodic component refers to a part of the sea level height which shows a periodic change along with time, the sea level altitude residual component refers to a portion of the sea level altitude other than the trend component and the periodic component. The invention realizes the random dynamic prediction of the sea level height through the established sea level height prediction model, and compared with the prior art, the invention can reduce the calculated amount and improve the prediction accuracy in the prediction of the sea level height with large space scale.
The invention provides a computer-readable storage medium, which can achieve the beneficial effects.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic diagram of a sea level altitude prediction model used in a sea level altitude prediction method according to an embodiment of the present invention;
FIG. 2 is a diagram of sea level altitude data at a geographic location (110E, 5N) and a first model term established for a trend component in one embodiment;
FIG. 3 is a diagram of sea level altitude data at a geographic location (110E, 5N) and a second model term established for a periodic component in one embodiment;
FIG. 4 is a diagram of the remainder of the sea level altitude data at geographic location (110E, 5N) with the trend component and the periodic component removed in one embodiment;
5-1 to 5-6 are time series and predicted values of the first 6 principal components obtained by analyzing the data shown in FIG. 4 in sequence;
6-1 through 6-6 are the first 6 principal modes obtained by analyzing the data shown in FIG. 4;
FIG. 7-1 is sea level altitude data measured by a satellite altimeter at geographic location (110 ° E,5 ° N) for month 1 2018;
fig. 7-2 is sea level altitude data at geographic location (110 ° E,5 ° N) for month 1 2018 predicted using a method of an embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment provides a sea level height prediction method, which uses a sea level height prediction model established for a target area to obtain sea level height data of each effective grid of the target area at a preset time. Referring to fig. 1, fig. 1 is a schematic diagram of a sea level altitude prediction model used in the sea level altitude prediction method provided in this embodiment, and the sea level altitude prediction model established for a target area as shown in the figure includes a first model item 101, a second model item 102, and a third model item 103.
The first model item 101 describes a change rule of a sea level altitude trend component of each effective grid of the target area along with time, the second model item 102 describes a change rule of a sea level altitude period component of each effective grid of the target area along with time, the third model item 103 describes a change rule of a sea level altitude residual component of each effective grid of the target area along with time, the sea level altitude trend component refers to a part of the sea level altitude showing a linear change trend along with time, the sea level altitude period component refers to a part of the sea level altitude showing a periodic change along with time, and the sea level altitude residual component refers to a part of the sea level altitude except for the trend component and the period component.
In the method of the embodiment, the sea level height is divided into three parts, including a part showing a linear change trend along with time, a part showing a periodic change along with time, and parts except a trend component (i.e. the part showing the linear change trend along with time) and a periodic component (i.e. the part showing the periodic change along with time), corresponding model terms are respectively established for each part of the sea level height, and the change rule of each part of the sea level height along with time is described.
The target area is a geographical area needing sea level height prediction, the target area is divided into grids, and the effective grids are grids with sea level height data. By using the sea level height prediction model established for the target area, the sea level height data of each effective grid of the target area at a preset moment can be obtained. According to the sea level height prediction method, random dynamic prediction of the sea level height is achieved through the established sea level height prediction model, and compared with the prior art, the sea level height prediction method can reduce calculated amount and improve prediction accuracy in the process of predicting the sea level height with large space scale.
The sea level height prediction method will be described in detail with reference to the following embodiments.
Alternatively, the first model term 101 may describe the variation of the sea level altitude trend component of each active mesh of the target area with time as a linear function. I.e. the trend component of sea level height is considered to be the part of sea level height that shows a linear change over time.
Alternatively, the first model term 101 may be constructed by performing linear regression analysis on the sea level height data of the effective grid of the target region to obtain the first model term 101. Performing linear regression analysis on the time series of the sea level altitude data of each effective grid of the target area to obtain a linear regression model, which can be expressed as: a is0+a1x + ε, y denotes the dependent variable, x denotes the independent variable, a0Denotes the intercept, a1Represents the slope, a0And a1Is the model parameter, and ε represents the error value, representing the error sequence for a normal distribution with a mean of 0. Slope a0And representing the variation trend of the time series of the sea level height data.
Preferably, in order to accurately describe the relationship between the independent variable and the dependent variable, the least square method may be used to estimate the model parameters, which is expressed as:
wherein, yiThe value of a dependent variable, x, representing time iiDenotes the argument value at time i and n denotes the length of the time series. Dependent variable y ═ y1，y2，…，yn]The independent variable x ═ x1，x2，…，xn]。
Thus, a first model term of the sea level altitude prediction model is constructed from the obtained linear regression model, and the first model term can be expressed as: t (t) ═ a0+a1t。
Alternatively, the second model term 102 may describe the variation of the sea level altitude period component of each effective grid of the target area with time in a sine function or/and a cosine function.
Optionally, the second model item 102 may be constructed by the following method, performing spectrum analysis on data obtained by subtracting the trend component from the sea level height of each effective grid of the target area, selecting a main period from the obtained periods according to the amplitude value corresponding to each obtained period, and constructing the second model item 102 by using a sine function or/and a cosine function represented by the main period.
Further, the second model item 102 may be constructed according to the following process, which essentially comprises the following steps:
s20: and carrying out spectrum analysis on the part of each effective grid in the target area, from which the trend component is subtracted from the sea level height, so as to obtain a plurality of periods.
And (3) performing spectrum analysis on the data obtained by subtracting the trend component T (t) from the original sea level height data SLH (t), wherein the spectrum analysis can be specifically Fourier spectrum analysis to obtain a plurality of periods. Exemplary can be expressed as:
wherein, Y (t) represents the rest of the sea level height data after the trend component is removed, Y (ω) represents the frequency spectrum obtained by performing fourier transform on N points of Y (t), and ω represents the period value.
S21: and selecting a main period from the obtained periods according to the amplitude value corresponding to each period.
Optionally, according to the obtained amplitude corresponding to each period, a period with an amplitude greater than a preset value may be selected from the obtained periods as a main period. Illustratively, the amplitude corresponding to each period in the spectrum sequence Y (ω) is traversed to obtain the highest amplitude, which is denoted as amaxAlternatively, higher than 0.1AmaxThe period corresponding to the amplitude of (c) is the dominant period.
S22: the second model term is constructed as a sine function or/and a cosine function represented by a dominant period.
Optionally, the obtained main period may be used to construct a second model term 102 of the sea level height prediction model based on the harmonic analysis model, that is, a model term describing a change rule of a sea level height period component of each effective grid of the target area with time is constructed. For example, assuming that the sequence contains K major cycles, the second model term 102 can be represented by the following formula:
wherein A iskAnd BkRelated to the main cycle:
optionally, the third model item 103 may include a model obtained by multiplying a prediction matrix of a time sequence of a main spatial matrix of sea level height residual components of each effective grid of the target area by an eigenvector matrix of the main spatial matrix and then accumulating the multiplication result.
Alternatively, the third model item 103 may be constructed by the following method, which mainly includes the following steps:
s30: and acquiring a main space matrix of a part obtained by subtracting the trend component and the period component from the sea level height of each effective grid of the target area and a corresponding time sequence.
Optionally, an empirical orthogonal function analysis may be performed on a part obtained by subtracting the trend component t (t) and the period component p (t) from the sea level height slh (t) of each effective grid of the target area, that is, a residual data part of the sea level height of each effective grid of the target area, to calculate each spatial matrix and a time sequence corresponding to each spatial matrix, so as to obtain each EOF mode and a time sequence corresponding to each EOF mode.
And selecting a main mode from the obtained EOF modes. Optionally, the main mode may be selected according to the cumulative variance of each EOF mode. For example, an EOF mode with a cumulative variance of 90% or more may be selected from the obtained EOF modes as a main mode. So that the time series corresponding to the main mode, i.e. the main component, is recorded accordingly.
S31: and obtaining the eigenvector matrix of the main space matrix according to the time sequence corresponding to the main space matrix.
The eigenvector matrix of the principal spatial matrix may be obtained by: and representing the time sequence corresponding to the main space matrix as a matrix, and solving the eigenvalue and the eigenvector of the matrix to obtain the eigenvector matrix of the main space matrix.
Specifically, the long-time sequence, i.e., the principal component time sequence, may be represented as a matrix F, and the covariance matrix of the matrix F may be represented as R ═ FTF, wherein R is a square matrix. Obtaining the eigenvalue and the eigenvector of the matrix R, specifically obtaining the eigenvalue and the eigenvector of the matrix R according to the following formula, that is: RC ═ C Λ, where C is the eigenvector matrix of matrix R,is a diagonal matrix with diagonal elements lambdaiThe characteristic value is represented. Column vector C of matrix CiIs the eigenvector corresponding to the eigenvalue. The covariance matrix R can be decomposed into R ═ ca C-1。
The feature vector can be regarded as a set of bases to be found, representing features of the original data in the new coordinate system. The eigenvalues in Λ then represent the degree of importance of the corresponding feature in the new coordinate system. The first of which is the eigenvector c corresponding to the largest eigenvalue1Is EOF1In turn, obtaining EOFj. Thereby obtaining the feature vector matrix EOF.
If the eigenvector matrix EOF is projected onto the raw data, then an EOF represents a quasi-periodic oscillation whose variation in time can be calculated as:
wherein the content of the first and second substances,
representing the time coefficients or principal components of the eigenvector matrix EOF. And performing power spectrum analysis on the principal component to obtain a time period corresponding to the change of the feature vector matrix EOF. Data can be reconstructed by the EOF and the principal component at the same time, and is expressed as:
s32: and establishing a prediction matrix for the time sequence corresponding to the main space matrix, multiplying the prediction matrix corresponding to the main space matrix and the eigenvector matrix of the main space matrix, and accumulating to construct the third model item.
And the prediction matrix established for the time sequence corresponding to the main space matrix is used for predicting the representation matrix of the time sequence corresponding to the main space matrix. The expression matrix of time series refers to a matrix for expressing time series.
Optionally, an autoregressive moving average model may be constructed for the time sequence corresponding to the main spatial matrix, so as to construct a prediction matrix for the time sequence corresponding to the main spatial matrix, and construct a prediction matrix for the time sequence corresponding to the main spatial matrix. For example, the prediction matrix of the ith principal component time series can be expressed as:
Xi(t)＝A1Xt-1+…+ApXt-p-B1εt-1-…-Bqεt-q。
wherein p represents the autoregressive order of the model, q represents the moving average order, A, B represents the coefficient to be determined which is not zero in the model, and epsilon represents the independent error term.
Further, the prediction matrix of the time sequence of the main spatial matrix is multiplied by the eigenvector matrix of the corresponding main spatial matrix and then accumulated, so as to construct a third model item 103, that is, a model item describing the change rule of the sea level height residual error component of each effective grid of the target area along with time is constructed.
Specifically, the method can be calculated by matrix multiplication and can be expressed as:
R(t)＝∑Ri(t)×EOFi；
Ri(t)＝A1Rt-1+…+ApRt-p-B1εt-1-…-Bqεt-q。
wherein R (t) represents a third model term, Ri(t) a prediction matrix, EOF, representing the time sequence of the ith primary spatial matrixiAnd representing the characteristic vector matrix corresponding to the ith main space matrix.
Preferably, in the process of calculating the eigenvector matrix of the obtained main space matrix, the significance of the obtained modal function may be checked, and the error of the k-th eigenvalue at the confidence level of 95% may be expressed as:
n represents the effective number of samples of data. When adjacent characteristic values satisfy Δ λj≤λj+1-λjThe mode selection is performed to determine whether the mode is the main mode. This can reduce the number of selected modalities.
In the method of the embodiment, when the third model item 103 for describing the change rule of the sea level height residual component of each effective grid of the target area with time is constructed, a method of combining an Empirical Orthogonal Function (EOF) and an autoregressive moving average (ARMA) model is adopted, so that the operation cost can be reduced compared with the method.
Then, based on the first model term 101, the second model term 102, and the third model term 103 constructed as above, the sea level height prediction model can be expressed as:
in practical application, the sea level height data of a target area is obtained, and the sea level height data of an effective grid is obtained from the sea level height data. Preferably, the sea level height data of the target area may be input into the base map template for data masking to obtain the sea level height data of the effective grid, specifically, the sea level height data may be cut according to the base map template of the target area, and divided into grids, and the grid representing land is marked as an invalid grid, and thereafter, the grid will not participate in the calculation.
According to the sea level height prediction method and device, random dynamic prediction of the sea level height is achieved through the established sea level height prediction model, and the advantages that the model is simple and the calculation cost can be reduced when the sea level height in a large space scale range is predicted are achieved.
In one embodiment, fig. 2 is a diagram of sea level altitude data at a geographic location (110 ° E,5 ° N) and a first model term established for a trend component. A unary linear regression model is established for the sea level height data to describe the change rule of the trend component of the sea level height data along with time. Fig. 3 is a schematic diagram of sea level altitude data at a geographic location (110 ° E,5 ° N) and a second model term established for the periodic component, and fig. 4 is a diagram of sea level altitude data at the geographic location (110 ° E,5 ° N) with the trend component and the remainder of the periodic component removed from the sea level altitude data, i.e., a sea level altitude data residual at the geographic location (110 ° E,5 ° N), which can be seen as a random sequence.
Fig. 5-1 to 5-6 are a time series and a predicted value of the first 6 principal components obtained by analyzing the data shown in fig. 4 in sequence. Fig. 6-1 to 6-6 are sequential diagrams illustrating the first 6 principal modes obtained by analyzing the data shown in fig. 4.
Fig. 7-1 and 7-2 are a comparison of the true and predicted values of the sea level height in month 1 of 2018, fig. 7-1 is sea level height data at the geographical location (110 ° E,5 ° N) in month 1 of 2018 measured by a satellite altimeter, and fig. 7-2 is sea level height data at the geographical location (110 ° E,5 ° N) in month 1 of 2018 predicted using the method of the present embodiment. It can be seen that although the predicted values of part of sea areas have slight deviation and the average absolute error is 50.5mm, the predicted result is close to the true value in the spatial distribution trend, so that the model can be used for sea level height prediction.
Accordingly, the present embodiment also provides a sea level height prediction system, which is used for implementing the sea level height prediction method described above.
According to the sea level height prediction system, random dynamic prediction of the sea level height is achieved through the established sea level height prediction model, and compared with the prior art, the sea level height prediction system can reduce calculated amount in the process of predicting the sea level height with large space scale and improve prediction accuracy.
Optionally, the sea level height prediction system of this embodiment includes: obtaining means for obtaining the sea level altitude prediction model for a target area; and the prediction device is used for obtaining the sea level height data of each effective grid of the target area at a preset moment by using the sea level height prediction model.
Accordingly, the present embodiment also provides a computer-readable storage medium having stored thereon a computer program which, when being executed by a processor, implements the steps of the sea level height prediction method as described above.
The sea level height prediction method, the sea level height prediction system and the readable storage medium provided by the invention are described in detail above. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
Claims (9)
1. A sea level height prediction method is characterized in that a sea level height prediction model established for a target area is used to obtain sea level height data of each effective grid of the target area at a preset moment;
the sea level height prediction model comprises a first model item, a second model item and a third model item, wherein the first model item describes a change rule of a sea level height trend component of each effective grid of the target area along with time, the second model item describes a change rule of a sea level height periodic component of each effective grid of the target area along with time, the third model item describes a change rule of a sea level height residual component of each effective grid of the target area along with time, the sea level height trend component refers to a part which shows a linear change trend along with time in the sea level height, the sea level height periodic component refers to a part which shows a periodic change along with time in the sea level height, and the sea level height residual component refers to a part which is except the trend component and the periodic component in the sea level height.
2. The sea level altitude prediction method of claim 1, wherein the first model term describes a change over time of a sea level altitude trend component of each active mesh of the target area as a linear function.
3. The sea level altitude prediction method of claim 1, wherein the second model term describes a variation with time of a sea level altitude period component of each active mesh of the target area in a sine function or/and a cosine function.
4. The sea level altitude prediction method of claim 3, wherein constructing the second model term comprises: and performing spectrum analysis according to the part of each effective grid in the target area, from which the trend component is subtracted from the sea level height, selecting a main period from each obtained period according to the amplitude corresponding to each obtained period, and constructing the second model term by using a sine function or/and a cosine function represented by the main period.
5. The sea level altitude prediction method of claim 1, wherein the third model term comprises a model obtained by adding up a prediction matrix of a time sequence of a main spatial matrix of the sea level altitude residual components of each effective grid of the target area multiplied by an eigenvector matrix of the main spatial matrix.
6. The sea level altitude prediction method of claim 5, wherein constructing the third model term comprises:
acquiring a main space matrix of a part of each effective grid in the target area, wherein the sea level height of each effective grid in the target area is subtracted by a trend component and a period component, and a corresponding time sequence;
obtaining a characteristic vector matrix of the main space matrix according to the time sequence corresponding to the main space matrix;
and establishing a prediction matrix for the time sequence corresponding to the main space matrix, multiplying the prediction matrix corresponding to the main space matrix and the eigenvector matrix of the main space matrix, and accumulating to construct the third model item.
7. Sea level height prediction system for performing the sea level height prediction method according to any one of claims 1-6.
8. Sea level altitude prediction system according to claim 7, characterized in that it comprises:
obtaining means for obtaining the sea level altitude prediction model for a target area;
and the prediction device is used for obtaining the sea level height data of each effective grid of the target area at a preset moment by using the sea level height prediction model.
9. A computer-readable storage medium, characterized in that a computer program is stored thereon, which computer program, when being executed by a processor, carries out the steps of the sea level altitude prediction method according to any one of claims 1 to 6.
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