CN108549961B - Method for predicting sea wave effective wave height based on CMIP5 - Google Patents

Method for predicting sea wave effective wave height based on CMIP5 Download PDF

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CN108549961B
CN108549961B CN201810409041.4A CN201810409041A CN108549961B CN 108549961 B CN108549961 B CN 108549961B CN 201810409041 A CN201810409041 A CN 201810409041A CN 108549961 B CN108549961 B CN 108549961B
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吴玲莉
吴腾
秦杰
梁桂兰
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Abstract

The invention discloses a method for estimating the effective wave height of sea waves based on CMIP5, which comprises the following steps: acquiring original data from ERA-Interim and CMIP5 series tests, and preprocessing the data; selecting a proper sea level air pressure field; correcting the prediction model by adopting data of ERA-Interim in 1981-2000; evaluating the preferred prediction model with data from the corresponding time period in CMIP 5; and predicting the effective wave height of the sea waves in the future by adopting the prediction model. The method adopts data of CMIP5 and long-term stable ERA-Interim reanalysis data of a European mesoscale weather prediction center, extracts data of the estimated wave height of the sea waves from the data, and adopts a method of a multiple regression model to estimate the wave height of the sea waves for many times. On the basis of the traditional atmosphere-ocean coupling mode, the method introduces an earth system mode for the first time, and solves the time interval and reliability problems of observation data by using test data in CMIP 5; the invention can effectively guide the wave protection work in coastal areas and has strong operability.

Description

Method for predicting sea wave effective wave height based on CMIP5
Technical Field
The invention relates to the field of sea wave parameter calculation, in particular to a method for estimating the effective wave height of sea waves based on CMIP5 (Phase 5of Coupled Model Intercom Project, abbreviated as CMIP 5).
Background
Sea waves are the most direct and closest marine phenomena in relation to human beings, and have considerable influence on production and life of people, for example, sea navigation, fishery production, offshore oil platforms, wave energy utilization and the like are closely related to sea waves.
The effective wave height is an important parameter reflecting the characteristics of sea waves, so that the prediction research of the wave height has important practical significance. In order to predict the wave height of the sea waves, long-term stable sea wave observation data are acquired. However, although conventional observation means such as buoys can accurately obtain the information of the change of the wave height of the sea, they can only obtain the change of the sea at a fixed point, and the coverage is relatively limited. The global climate mode is an important tool for predicting future climate change, and has been widely applied to research work in climate change related fields, and multiple disciplines such as hydrology, ocean and the like need to research related climate change influences and adaptation problems based on the prediction result of the climate mode on the future climate change. In recent years, in order to better realize data sharing, pattern comparison and verification, the World Climate Research Plan (WCRP) has implemented an atmospheric pattern comparison plan, an ocean pattern comparison plan, a land process pattern comparison plan and a coupling pattern comparison plan from 1989, but a pattern parameterization scheme, a flux processing scheme, resolution and a coupler technology of the third stage (CMIP3) are to be improved and improved compared with the coupling pattern comparison plan.
Disclosure of Invention
The purpose of the invention is as follows: the method for predicting the wave height of the sea wave based on the CMIP5 is provided, so that the defect of lack of data in the prior art is overcome, and the accuracy of wave height prediction of the sea wave is improved.
The technical scheme is as follows: a method for estimating the effective wave height of sea waves based on CMIP5 comprises the following steps:
s1: acquiring original data from ERA-Interim and CMIP5 series tests, and preprocessing the data;
s2: selecting a proper sea level air pressure field;
s3: correcting the prediction model by adopting preselected data in ERA-Interim;
s4: evaluating the preference of the predictive model using data from the corresponding time period in the CMIP5 series of trials;
s5: and predicting the effective wave height of the sea waves in the future by adopting the prediction model.
The step S1 further includes:
s11, collecting ERA-Interim re-analysis data of a long-period weather forecast data set based on a European mesoscale weather prediction center of a lattice point mode, and experimental data in a fifth stage (Phase 5of Coupled Model Intercomparison Project, abbreviated as CMIP5) of a global coupling mode comparison plan, wherein the experimental data comprises sea level air pressure SLP once in 6 hours and effective wave height Hs;
s12, obtaining coordinates of grid points marked by the collected ERA-Interim and CMIP5 time weather forecast data, and taking the coordinates as a basis, extracting sea level air pressure corresponding to the coordinates of the grid points marked by the time weather forecast data, wherein the sea level air pressure matrix of the extracted ERA-Interim is E, the effective wave height matrix is H, and the sea level air pressure matrix of the extracted CMIP5 is C, wherein the sea level air pressure matrix comprises m space points, and each space point comprises n times of observation data:
Figure BDA0001647509820000031
Figure BDA0001647509820000032
wherein E ismnIs the sea level air pressure value of the nth time of the mth space point of ERA-Interim, HmnIs the effective wave height of the nth time of the mth space point, CmnThe sea level air pressure value at the nth time of the mth space point of CMIP5, m is the number of space points, and n is the observation time.
The step S3 further includes:
s31, calculating the average value M of sea level air pressure SLP of each time of ERA-Interim based on the lattice point mode; subtracting the mean value M from the original value E to obtain the interval value P of SLP of each time based on the lattice point mode; calculating the standard deviation S of the SLP from the flat value P:
Figure BDA0001647509820000033
wherein the content of the first and second substances,
Figure BDA0001647509820000034
n is the observed hour, i represents a spatial point, and j represents the hour.
S32, performing EOF analysis on the SLP pitch average value P to obtain different components and the contribution rate of each component to the total variance, and reserving the first 30 EOFs and principal components;
carrying out covariance calculation on P to obtain a real symmetric matrix Lm×m：
Figure BDA0001647509820000041
T denotes the transpose of the matrix.
Then, a covariance matrix L is obtainedm×mThe eigenvector V and the eigenvalue Λ of (a), satisfy LV ═ Λ V,
Figure BDA0001647509820000042
the matrix V is an orthogonal matrix, and the j-th column element of the matrix V is the characteristic value lambdajA corresponding feature vector;
according to the real symmetric matrix Lm×mCalculating the variance contribution rate of each eigenvector and the accumulated variance contribution rates of the first eigenvectors, wherein the larger the variance contribution, the more obvious the evolution rule of the corresponding eigenvector and time coefficient in the data is, sorting L according to the sequence of the eigenvalues from large to small, and the first ranked eigenvector is EOF1And so on;
s33: carrying out Box-Cox conversion on the original sea level air pressure SLP and the effective wave height Hs of each time based on the lattice points collected in the step S1 to obtain the converted sea level air pressure treT and the converted effective wave height trHt;
s34: for the transformed trEt and trHt corresponding to each lattice point, the k-th principal component PC is usedk，tAnd the k-th principal component PC delayed by 4 hoursk，t-4Calculating the correlation coefficient, and taking the 28 PCs with the highest correlation numberk,tOr PCk,t-4As a predictor of effective wave height;
s35: calculating the standard deviation S of the effective wave heightHtAnd 30 predictors Xk,tStandard deviation of (S)XkStoring for later use;
s36: substituting the prediction factor into a prediction model, and comparing the prediction results of the ith model and the (i + 1) th model by using F statistic so as to select the optimal prediction factor; the model is as follows:
Figure BDA0001647509820000051
in the formula, HtIs the transformed effective wave height at each grid point, a is a constant term, P is the lag coefficient of a parameter related to the prediction quantity, Xk,tIs the kth SLP-based predictor, t is the time, bkIs corresponding to Xk,tK is the total number of predictor factors, Ht-pIs the effective wave height of the lag p, cpIs corresponding to Ht-pThe coefficient of (a) is determined,
utcan be expressed by an autoregressive model of order M, if M is 0, utIs white noise.
The step S4 further includes:
s41: calculating a mean value Mc of sea level air pressure SLP of each time of CMIP5 based on the lattice point mode, and subtracting the mean value Mc from the original value C to obtain a distance flat value Cp of SLP of each time based on the lattice point mode;
Figure BDA0001647509820000052
wherein the content of the first and second substances,
Figure BDA0001647509820000053
n is the observed hour, i represents a spatial point, and j represents the hour.
S42: carrying out Box-Cox conversion on the range-to-range values Cp of the sea level air pressure at each time obtained in the step S41 to obtain a converted sea level air pressure field trGt;
s43: performing EOF analysis on trGt to obtain contribution rates of different components and each component to total variance, and reserving the first 30 EOFs and the main component PCk,tK, t represent ordinal and chronological;
s44: for trGt corresponding to each lattice point, use principal component PCk，tAnd PCk，t-4Calculating the correlation coefficient, and taking the 28 PCs with the highest correlation numberk,tOr PCk,t-4As a predictor of effective wave height;
s45: substituting the prediction factor into a prediction model, and comparing the prediction results of the ith model and the (i + 1) th model by using F statistic so as to select the optimal prediction factor; wherein the model is shown as formula (5).
The step S5 further includes:
s51: and (3) bringing the effective wave height lagging by one step into the model, taking the effective wave height as one of the prediction factors, comprehensively predicting the effective wave height of each lattice point at the next time, and optimizing the parameters of the model to obtain a final model, wherein the model is shown as a formula (5).
S52: substituting all the prediction factors into the final model in the step S51, predicting the effective wave height of each time in the target period, reducing the predicted effective wave height value to the value before Box-Cox conversion, and storing the value as a lattice point mode file;
s53: the prediction level of the index is evaluated by using RMSE (root-mean-square error, also called standard error) and the like, and is defined as follows:
Figure BDA0001647509820000061
in a limited number of measurements, the RMSE is represented by:
Figure BDA0001647509820000062
in the formula, n is the number of measurement times; diThe deviation of the i-th set of measurements from the mean value.
Has the advantages that: the CMIP5 mode utilized by the invention adopts a more reasonable parameterization scheme, a flux processing scheme and a coupler technology, and introduces an earth system mode for the first time on the basis of the traditional atmosphere-ocean coupling mode; in addition, the horizontal resolution of the CMIP5 mode is improved, the number of vertical layers is increased, the description of the physical process is more detailed, and the flux adjustment is not required in the coupling mode. The invention utilizes the global coupling mode to compare the test data in the fifth stage (Phase 5of Coupled Model Intercom Project, abbreviated as CMIP5), and solves the problems of time interval and reliability of the observed data; according to the method, the Box-Cox transformation is adopted to correct original data, and then the effective wave height of the sea waves in the future is estimated by adopting a multivariate regression analysis method according to corrected meteorological data such as sea level air pressure, effective wave height of the sea waves and the like; the wave protection device can effectively guide the wave protection work in coastal areas, plays an important and indispensable role in maintaining the safety and stability of coastal zones and lightening wave disasters, and has very strong operability.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is an algorithmic flow diagram of an embodiment of the present invention;
FIG. 3 is a schematic diagram of estimating annual average wave height in a certain sea area in China by using the embodiment of the invention.
Detailed Description
FIG. 2 is an algorithmic flow diagram of an embodiment of the present invention; with reference to fig. 2 and taking a certain sea area in china as an example, the method for estimating the effective wave height of sea waves based on the CMIP5 modified parameters of the present invention specifically includes the following steps:
s11: collecting the long-period weather forecast data of the ERA-Interim re-analysis data set of a certain sea area in China based on the lattice point mode and the experimental data in the fifth stage (Phase 5of Coupled Model Intercom Project, abbreviated as CMIP5) of the global coupling mode comparison plan,
s12, obtaining coordinates of grid points marked by the collected ERA-Interim and CMIP5 time weather forecast data, and taking the coordinates as a basis, extracting sea level air pressure corresponding to the coordinates of the grid points marked by the time weather forecast data, wherein the sea level air pressure matrix of the extracted ERA-Interim is E, the effective wave height matrix is H, and the sea level air pressure matrix of the extracted CMIP5 is C, wherein the sea level air pressure matrix comprises m space points, and each space point comprises n times of observation data:
Figure BDA0001647509820000081
Figure BDA0001647509820000082
s2: and selecting a proper sea level air pressure field. The selection of different sea level air pressure fields can lead to different prediction effects of the model, so that the suitable sea level air pressure fields are selected by comparison;
s3: correcting the model with data from the first decades of ERA-Interim, once in 6 hours; preferably, ERA-Interim1981-2000 data is selected.
Further comprising:
s31, calculating the average value M of sea level air pressure SLP of each time of ERA-Interim based on the lattice point mode; subtracting the mean value M from the original value E to obtain the interval value P of SLP of each time based on the lattice point mode; calculating the standard deviation S of the SLP from the flat value P:
Figure BDA0001647509820000083
wherein the content of the first and second substances,
Figure BDA0001647509820000084
s32, performing EOF analysis on the SLP pitch average value P to obtain different components and the contribution rate of each component to the total variance, and reserving the first 30 EOFs and principal components;
the EOF method is a dimension reduction analysis method, and can extract the most typical space type and time evolution law in the data according to the variance maximization principle.
Carrying out covariance calculation on P to obtain a real symmetric matrix Lm×m：
Figure BDA0001647509820000091
T denotes the transpose of the matrix.
Then, a covariance matrix L is obtainedm×mSatisfies LV ═ Λ V, where
Figure BDA0001647509820000092
The matrix V is an orthogonal matrix, and the j-th column element of the matrix V is the characteristic value lambdajA corresponding feature vector;
according to the real symmetric matrix Lm×mCalculating the variance contribution rate of each eigenvector and the accumulated variance contribution rates of the first eigenvectors, wherein the larger the variance contribution, the more obvious the evolution rule of the corresponding eigenvector and time coefficient in the data is, sorting L according to the sequence of the eigenvalues from large to small, and the first ranked eigenvector is EOF1And so on;
s33: carrying out Box-Cox conversion on the original sea level air pressure SLP and the effective wave height Hs of each time based on the lattice points collected in the step S1 to obtain the converted sea level air pressure treT and the converted effective wave height trHt;
s34: for the transformed trEt and trHt corresponding to each lattice point, the k-th principal component PC is usedk，tAnd the k-th principal component PC delayed by 4 hoursk，t-4Calculating the correlation coefficient, and taking the 28 PCs with the highest correlation numberk,tOr PCk,t-4As a predictor of effective wave height;
s35: calculating the standard deviation S of the effective wave heightHtAnd 30 predictors Xk,tStandard deviation of (S)XkStoring for later use;
s36: and substituting the prediction factor into the prediction model, and comparing the prediction results of the ith model and the (i + 1) th model by using the F statistic so as to select the optimal prediction factor. The model is as follows:
Figure BDA0001647509820000101
in the formula, HtIs the transformed effective wave height at each grid point, a is a constant term, P is the lag coefficient of a parameter related to the prediction quantity, Xk,tIs the kth SLP-based predictor, t is the time, bkIs corresponding to Xk,tK is the total number of predictor factors, Ht-pIs the effective wave height of the lag p, cpIs corresponding to Ht-pThe coefficient of (a) is determined,
utcan be expressed by an autoregressive model of order M, if M is 0, utIs white noise.
S4: the preference of the predictive model was evaluated using data from the CMIP5 series of trials at 6 hours for the corresponding period (e.g., 1980-1999);
further comprising:
s41: calculating a mean value Mc of sea level air pressure SLP of each time of CMIP5 based on the lattice point mode, and subtracting the mean value Mc from the original value C to obtain a distance flat value Cp of SLP of each time based on the lattice point mode;
Figure BDA0001647509820000102
wherein the content of the first and second substances,
Figure BDA0001647509820000103
n is the observed hour, i represents a spatial point, and j represents the hour.
S42: carrying out Box-Cox conversion on the range-to-range values Cp of the sea level air pressure at each time obtained in the step S41 to obtain a converted sea level air pressure field trGt;
s43: performing EOF analysis on trGt to obtain contribution rates of different components and each component to total variance, and reserving the first 30 EOFs and the main component PCk,tK, t represent ordinal and chronological;
s44: for trGt corresponding to each lattice point, use principal component PCk，tAnd PCk，t-4Calculating the correlation coefficient, and taking the 28 PCs with the highest correlation numberk,tOr PCk,t-4As a predictor of effective wave height;
s45: substituting the prediction factor into a prediction model, and comparing the prediction results of the ith model and the (i + 1) th model by using F statistic so as to select the optimal prediction factor; wherein the model is shown as formula (5).
S5: the effective wave height of the sea waves in the future of a certain sea area in China is estimated.
Specifically, in the implementation process, the step five further includes:
s51: and (3) introducing the effective wave height lagging by one step into the model, comprehensively predicting the effective wave height of each lattice point at the next time, and optimizing the model parameters to obtain the final model as shown in the formula (5).
S52: substituting all the prediction factors into the final model in the step S51, predicting the effective wave height of each time in the target period, reducing the predicted effective wave height value to the value before Box-Cox conversion, and storing the value as a lattice point mode file;
s53: the prediction level of the index is evaluated by using RMSE (root-mean-square error, also called standard error) and the like, and is defined as follows:
Figure BDA0001647509820000111
in a limited number of measurements, the RMSE is represented by:
Figure BDA0001647509820000112
in the formula, n is the number of measurement times; diThe deviation of the i-th set of measurements from the mean value.
Repeated tests prove that the method can play a good guiding role in predicting the effective wave height of the sea waves and preventing sea wave disasters.
Aiming at the problem that long-term stable wave height observation data cannot be obtained in the current wave height prediction research, the invention utilizes the test data in the fifth stage (Phase 5of Coupled Model Intercom Project, abbreviated as CMIP5) of the global coupling mode comparison plan and the ERA-Interim reanalysis data of the European mesoscale weather prediction center, corrects the original data by adopting Box-Cox transformation, and can predict the effective wave height of the sea waves for many times by adopting a multiple regression method according to the corrected meteorological data such as sea level air pressure, effective wave height and the like, thereby having strong operability and high accuracy.
The embodiments of the present invention are described in detail with reference to the prior art, and the description thereof is not limited thereto.
Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the details of the embodiments, and various equivalent modifications can be made within the technical spirit of the present invention, and the scope of the present invention is also within the scope of the present invention. It should be noted that the various features described in the above embodiments may be combined in any suitable manner without departing from the scope of the invention. The invention is not described in detail in order to avoid unnecessary repetition.

Claims (5)

1. A method for estimating the effective wave height of sea waves based on CMIP5 is characterized by comprising the following steps:
s1: acquiring original data from ERA-Interim and CMIP5 series tests, and preprocessing the data;
s2: selecting a proper sea level air pressure field;
s3: correcting the prediction model by adopting data preselected in ERA-Interim;
s4: evaluating the preference of the predictive model using data from the corresponding time period in the CMIP5 series of trials;
s5: the effective wave height lagged by one step is also brought into the model to be used as one of prediction factors, the effective wave height of each grid point at the next time is comprehensively predicted, model parameters are optimized to obtain a final model, and the optimal prediction model is adopted to predict the effective wave height of the sea wave in the future;
the step S4 further includes:
s41: calculating a mean value Mc of sea level air pressure SLP of each time of CMIP5 based on the lattice point mode, and subtracting the mean value Mc from the original value C to obtain a distance flat value Cp of SLP of each time based on the lattice point mode;
Figure FDA0003188316570000011
wherein the content of the first and second substances,
Figure FDA0003188316570000012
n is the observation time, i represents a space point, and j represents the time;
s42: carrying out Box-Cox conversion on the range-to-range values Cp of the sea level air pressure at each time obtained in the step S41 to obtain a converted sea level air pressure field trGt;
s43: performing EOF analysis on trGt to obtain contribution rates of different components and each component to total variance, and reserving the first 30 EOFs and the main component PCk,tK, t represent ordinal and chronological;
s44: for trGt corresponding to each lattice point, use principal component PCk，tAnd PCk，t-4Calculating the correlation coefficient, and taking the 28 PCs with the highest correlation numberk,tOr PCk,t-4As a predictor of effective wave height;
s45: substituting the prediction factor into a prediction model, and comparing the prediction results of the ith model and the (i + 1) th model by using F statistic so as to select the optimal prediction factor; wherein the model is shown as a formula (5),
Figure FDA0003188316570000013
in the formula, HtIs the transformed effective wave height at each grid point, a is a constant term, P is the lag coefficient of a parameter related to the prediction quantity, Xk,tIs the kth SLP-based predictor, t is the time, bkIs corresponding to Xk,tK is the total number of predictor factors, Ht-pIs the effective wave height of the lag p, cpIs corresponding to Ht-pCoefficient of (a), utCan be expressed by an autoregressive model of order M, if M is 0, utIs white noise.
2. The method for estimating sea wave effective wave height based on CMIP 5of claim 1, wherein the step S1 further comprises:
s11, collecting ERA-Interim re-analysis data of a long-period meteorological forecast data set based on a grid point mode in the European mesoscale weather prediction center, and test data in a CMIP5 in a fifth stage of a global coupling mode comparison plan, wherein the test data comprise sea level air pressure SLP once in 6 hours and effective wave height Hs;
s12, obtaining coordinates of grid points marked by the collected ERA-Interim and CMIP5 time weather forecast data, and taking the coordinates as a basis, extracting sea level air pressure corresponding to the coordinates of the grid points marked by the time weather forecast data, wherein the sea level air pressure matrix of the extracted ERA-Interim is E, the effective wave height matrix is H, and the sea level air pressure matrix of the extracted CMIP5 is C, wherein the sea level air pressure matrix comprises m space points, and each space point comprises n times of observation data:
Figure FDA0003188316570000021
Figure FDA0003188316570000022
wherein E ismnIs the sea level air pressure value of the nth time of the mth space point of ERA-Interim, HmnIs the effective wave height of the nth time of the mth space point, CmnThe sea level air pressure value at the nth time of the mth space point of CMIP5, m is the number of space points, and n is the observation time.
3. The method for estimating sea wave effective wave height based on CMIP 5of claim 2, wherein the step S3 further comprises:
s31, calculating the average value M of sea level air pressure SLP of each time of ERA-Interim based on the lattice point mode; subtracting the mean value M from the original value E to obtain the interval value P of SLP of each time based on the lattice point mode; calculating the standard deviation S of the SLP from the flat value P:
Figure FDA0003188316570000031
wherein the content of the first and second substances,
Figure FDA0003188316570000032
n is the observation time, i represents a space point, and j represents the time;
s32, performing EOF analysis on the SLP pitch average value P to obtain different components and the contribution rate of each component to the total variance, and reserving the first 30 EOFs and principal components;
carrying out covariance calculation on P to obtain a real symmetric matrix Lm×m：
Figure FDA0003188316570000033
T represents the transpose of the matrix;
then, a covariance matrix L is obtainedm×mThe eigenvector V and the eigenvalue Λ of (a), satisfy LV ═ Λ V,
Figure FDA0003188316570000034
the matrix V is an orthogonal matrix, and the j-th column element of the matrix V is the characteristic value lambdajA corresponding feature vector;
according to the real symmetric matrix Lm×mCalculating the variance contribution rate of each eigenvector and the accumulated variance contribution rates of the first eigenvectors, wherein the larger the variance contribution, the more obvious the evolution rule of the corresponding eigenvector and time coefficient in the data is, sorting L according to the sequence of the eigenvalues from large to small, and the first ranked eigenvector is EOF1And so on;
s33: carrying out Box-Cox conversion on the original sea level air pressure SLP and the effective wave height Hs of each time based on the lattice points collected in the step S1 to obtain the converted sea level air pressure treT and the converted effective wave height trHt;
s34: for the transformed trEt and trHt corresponding to each lattice point, the k-th principal component PC is usedk，tAnd the k-th principal component PC delayed by 4 hoursk，t-4Calculating the correlation coefficient, and taking the 28 PCs with the highest correlation numberk,tOr PCk,t-4As effective asA predictor of wave height;
s35: calculating the standard deviation S of the effective wave heightHtAnd 30 predictors Xk,tStandard deviation of (S)XkStoring for later use;
s36: and substituting the prediction factor into the prediction model, and comparing the prediction results of the ith model and the (i + 1) th model by using the F statistic so as to select the optimal prediction factor.
4. The method for estimating sea wave effective wave height based on CMIP 5of claim 1, wherein the step S5 further comprises:
s51: substituting all the prediction factors into the final model in the step S51, predicting the effective wave height of each time in the target period, reducing the predicted effective wave height value to the value before Box-Cox conversion, and storing the value as a lattice point mode file;
s52: the prediction level of the index is evaluated by RMSE and the like, and is defined as:
Figure FDA0003188316570000041
in a limited number of measurements, the RMSE is represented by:
Figure FDA0003188316570000042
in the formulas (7) and (8), n is the number of measurements; diThe deviation of the i-th set of measurements from the mean value.
5. The method for estimating the effective wave height of sea waves based on CMIP5 as claimed in claim 1, wherein the data pre-selected in ERA-Interim is data from 1981-2000.
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