WO2020218626A2 - Εορ prediction method, εορ prediction apparatus, eop prediction program and computer readable recording media recorded with eop prediction program - Google Patents

Εορ prediction method, εορ prediction apparatus, eop prediction program and computer readable recording media recorded with eop prediction program Download PDF

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WO2020218626A2
WO2020218626A2 PCT/KP2019/000049 KP2019000049W WO2020218626A2 WO 2020218626 A2 WO2020218626 A2 WO 2020218626A2 KP 2019000049 W KP2019000049 W KP 2019000049W WO 2020218626 A2 WO2020218626 A2 WO 2020218626A2
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earth
nutation
variation
rotation
predicting
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PCT/KP2019/000049
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French (fr)
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WO2020218626A3 (en
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Kwan U Kim
Sae Yong CHOE
Song Chol RI
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Kwan U Kim
Choe Sae Yong
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    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B19/00—Teaching not covered by other main groups of this subclass
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B27/00—Planetaria; Globes
    • G09B27/02—Tellurions; Orreries
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects

Definitions

  • EOP prediction method EOP prediction apparatus, EOP prediction program and computer readable recording media recorded with EOP prediction program
  • the present invention relates to a technique for predicting the Earth Orientation Parameters (EOP) by using the observation data for variation of length-of-day (LOD) and latitude observation.
  • EOP Earth Orientation Parameters
  • the rotation of the Earth is closely related with human life, thus it has been studied for a long time.
  • the astronomers discovered and proved, on the basis of modem observation means, various kinds of astronomical phenomena related to the rotation of the Earth. They discovered the Chandler Wobble in polar motion through analyzing the observation data related to the latitude variation, several periodic phenomena in the polar motion identified as 14 months-period, annual period, semiannual period and 1 month-period and the secular variation in the mean pole motion.
  • the present invention provides a method of predicting the EOP in real time with high accuracy by using data of the LOD variation and latitude observation on the basis of a new mathematical model which can clearly explain the causes of all the astronomical phenomena related with the rotation of the Earth.
  • the present invention also provides an EOP predicting apparatus and an EOP predicting program, and a computer readable recording medium recorded with the EOP predicting program.
  • the rotation of the Earth can be modeled as follows on the basis of the relativistic movement law.
  • r g ( ( p) are main elements affecting the non-uniformity of the rotation of the Earth, where K(X), as a random variable reflecting the non-uniformity of the rotation of the Earth, is a main element of semiannual oscillation, r g ((p), as the distance between the Earth and the Sun according to the latitude, is a main element of annual oscillation.
  • the present invention provides a method and program which analyze and predict, in a quantitative manner, various kinds of astronomical phenomena including the non-uniformity of the rotation of the Earth, the precession-nutation related to the variation of orientation of the Earth rotation axis, and the polar motion related to the variation of orientation of the Earth with respect to its rotation axis.
  • the predicted values of the other astronomical phenomena related with the rotation of the Earth which are highly compatible with the observed values, can be obtained.
  • the LOD variation data can be obtained through either observation or prediction for a year concerned by using artificial neural network (ANN) with data of LOD variation for 7 to 10 years previous to the year concerned.
  • ANN artificial neural network
  • the predicted LOD variation data on the basis of the above mentioned mathematical model on the rotation of the Earth, the other astronomical phenomena related with the rotation of the Earth for a year can be predicted.
  • FIG. 1 is a flowchart of an EOP predicting apparatus.
  • FIG. 2 is a chart of calculation process of parameters of the rotation of the Earth.
  • FIG. 3 is a chart of the LOD predicting process for a year concerned. Detailed Explanation of the Invention
  • FIG. 1 shows the flow chart of an EOP predicting apparatus according to the present invention.
  • the EOP predicting apparatus comprises a computer 1 loaded with a database, a computer 2 provided with at least a central processing unit (CPU) and a memory loaded with EOP predicting program and a computer 3 loaded with a program for generating EOP prediction data.
  • CPU central processing unit
  • the EOP predicting apparatus is input with data of the LOD variation and the latitude observation.
  • the EOP predicting apparatus outputs the predicted values of the EOP.
  • the database of computer 1 stores the data of the daily variation of LOD in the past years. It is used as input data to predict the LOD for a year concerned.
  • the EOP calculation program loaded into the computer 2 predicts, in a quantitative manner, the various kinds of astronomical phenomena by using the latitude of a place where an observatory locates and either the data stored in the database of computer 1 or the predicted values of LOD variation.
  • the EOP calculation process comprises a process for predicting parameters of the rotation of the Earth, a process for predicting parameters of the precession-nutation related to the variation of orientation of the Earth rotation axis and a process for predicting parameters of the polar motion related to the variation of orientation of the Earth with respect to its rotation axis.
  • the parameters are calculated on the basis of the following mathematical model derived from the above mentioned mathematical model on the rotation of the Earth (1):
  • f M (t) is a moment function of external forces exerted to the Earth containing a random variable K(X), which reflects the non-uniformity of the rotation of the Earth.
  • the parameters of the rotation of the Earth comprises seasonal change, variation of the LOD, irregular and leaping variation of the LOD, non-uniformity of the rotating speed of the Earth within a length of 24 hours, secular reduction of the rotating speed of the Earth, leap second, and the difference between the Universal and the Atomic time scales UT1-TAI, etc..
  • the other kinds of parameters for the rotation of the Earth can be calculated.
  • FIG. 2 shows the process of calculating parameters of the rotation of the Earth.
  • the process for calculating parameters of the rotation of the Earth comprises a step for calculating the distance between the Earth and the Sun, r g ; a step for obtaining random variable K(X) which reflects the non-uniformity of the rotation of the Earth by using r g and the LOD; and a step for calculating the other parameters of the rotation of the Earth except for the LOD variation by solving equation (2) into which the random variable K(X) is input.
  • Random variable K(X) can be determined in a quantitative manner by using the LOD variation and the distance between the Earth and the Sun (r g ) of the day concerned. From the results of harmonic analysis on the seasonal oscillation, the random variable K(X) is identified as being in a range of from not less than 0 to not more than 2. It can be said that the causes of most of astronomical phenomena of the rotation of the Earth are directly related with the ceaseless change of K(X) in the range of 0 to 2.
  • the observation data of the LOD can be used but the availability of observation data is limited up to the current day.
  • the rotation of the Earth is affected by external forces to oscillate on a seasonal basis. At the same time, it is also reflected by a statistical law related with random variables, thus, provided that there are observation data of the LOD in the past years, there is a possibility of predicting the LOD variation in the coming year.
  • the LOD of the year concerned (365 days) can be predicted within the range of relative error not more than 1 percent from the observation data of the LOD variation for 7 to 10 years previous to the year concerned by using artificial neural network (ANN).
  • ANN artificial neural network
  • FIG. 3 shows the process for predicting the LOD for the year concerned.
  • the LOD predicting process for the year concerned comprises: a step for calculating yearly average value of the LOD variation for 7 to 10 years previous to the year concerned; a step for predicting the average value of the LOD variation for the year concerned by using an ANN 1 into which the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned is input; a step for predicting the daily difference from the average value of the LOD variation for the year concerned by using an ANN 2 into which the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned is input; and a step for predicting the LOD and the LOD variation on a daily basis for the year concerned from the average value of the LOD variation and daily difference for the year concerned.
  • the ANN 1 and the ANN 2 comprise the distributed delay network which is suitable to time series prediction. Both of the ANN 1 and the ANN 2 are 3 -layer networks containing a hidden layer.
  • the input of the ANN 1 has 7 to 10 elements which are the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned.
  • the output of the ANN I has one element which is the average value of the LOD variation for the year predicted.
  • the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned are not directly input into the ANN 2.
  • the input data for the ANN 2 are the difference between the yearly average value of the LOD variation for the previous 7 to 10 years and the values of the LOD variation of the same dates in the past as the prediction will occurs.
  • the ANN 2 has 7 to 10 input elements.
  • the output of the ANN 2 is the difference between the average value of the LOD variation for the year to be predicted and the average value of the LOD variation for the day to be predicted.
  • the ANN 2 has 1 output element as well. According to the number of days to be predicted, the output value for the year to be predicted can be obtained on a daily basis by iterating the calculation for the times of the number of days to be predicted (for example, 365 days) by varying input values into the ANN 2.
  • the LOD and the LOD variation for the year concerned can be easily calculated on a daily basis and if necessary, the calculation result can be shown in a table or graphic format.
  • the real time position of the instantaneous pole can be predicted in a quantitative manner against the average pole of the Earth on the basis of the mathematical model on the rotation of the Earth.
  • the polar motion is occurred because the Earth is oscillating against the dynamic rotation axis when the Earth is in a movement of eclipse orbit in the gravitational force field of the Sun.
  • the oscillation energy of the Earth against the rotation axis is the source of energy which causes the polar motion.
  • the angular velocity of polar motion of an instantaneous pole against the average pole on the Earth’s surface is the angular velocity of nutation which is expressed as the angular velocity of the Chandler Wobble. If the latitude variation is observed on the Earth, the position of an instantaneous pole against the average pole can be determined in a quantitative manner.
  • the coordinate of an instantaneous pole against the average pole can be determined independently by using the observation data of latitude obtained from an observatory, on the basis of mathematical model on the rotation of the Earth.
  • both of the observation data of the latitude and LOD variation should be known.
  • the predicted values of LOD variation for a year obtained from the ANN in the process of predicting parameters of the rotation of the Earth or the observed values of LOD variation which are downloaded from the website of IERS can be used as input data of the LOD variation for the determination of polar position.
  • the process for predicting parameters of the polar motion comprises a step for determining a force moment of the Sun exerting to the rotation of the Earth, M sun on the basis of the LOD variation of the predicted day.
  • the force moment of the Sun can be determined according to the following equation:
  • i is an index indicating the predicted day
  • E is the relativistic total energy of the Earth (E ⁇ m Earth C 2 , where m Earth is the mass of the Earth and C is the light velocity); a Moon is a force moment of the Moon exerting to the Earth; r g is the distance between the Earth and the Sun; and K(X) is the random variable indicating the non-uniformity of the rotation of the Earth (the same meaning as the non-uniformity of LOD) which is reflected in the mathematical model on i
  • the process for predicting parameters of the polar motion comprises: a step for calculating the angular velocity of polar motion on the basis of the force moment of the Sun Ms un ; a step for calculating the angle of polar motion oscillating per day by integrating the angular velocity of polar motion; a step for determining the Chandler Period from the angle of polar motion oscillating per day; a step for determining the angle in which an instantaneous pole oscillates from the Greenwich meridian by using the angle of polar motion oscillating per day; a step for calculating the position of an instantaneous pole by using the observation data of latitude and the angle in which an instantaneous pole oscillates from the Greenwich meridian; and a step for transforming the position of an instantaneous pole into a base coordinate system.
  • Table 1 shows the polar motion parameters obtained.
  • the period of polar motion can be determined without observation. If the observation data of latitude is provided, the angular distance between an instantaneous pole and the average pole and the angle in which an instantaneous pole oscillates from the Greenwich meridian can be determined. Thus, the polar coordinates of an instantaneous pole can be determined.
  • the precession and nutation parameters can be calculated on the basis of the following mathematical model.
  • Y is an angular acceleration of precession of the rotation axis of the Earth
  • Q is an angular acceleration of nutation of the rotation axis of the Earth
  • A is an equator inertia moment
  • C is a polar inertia moment
  • w z is an angular velocity of the rotation of the Earth.
  • the process of determining the position of precession within a period of long nutation comprises: a step for calculating an angular distance (linear term) of the rotation axis of the Earth precessing for time t by using the astronomical constants including the equator inertia moment, the polar inertia moment, the angular velocity of the rotation of the Earth and the angular velocity of nutation; a step for adding the variation of angular distance of precession due to the fundamental oscillation of nutation calculated on the basis of the perturbation moment of the Moon, the nutation angle, the angular velocity of nutation and the angular momentum of the rotation of the Earth; a step for adding the variation of angular distance of precession due to harmonics of nutation calculated on the basis of the moment of harmonics, the nutation angle, the angular velocity of nutation, the angular variation of nutation, the angular momentum of the rotation of the Earth and the initial phase of harmonics; and a step for adding the secular variation of pre
  • Dq(t) is a nutation function which shows the real time position of the rotation axis of the Earth from the equilibrium position q 00 .
  • the process for calculating the position of nutation comprises: a step for calculating the fundamental oscillation term of nutation on the basis of the perturbation moment of the Moon, the angular momentum of the rotation of the Earth, the nutation angle, the average nutation angle and the angular velocity of nutation; a step for adding the term of harmonics of nutation calculated on the basis of the moment of harmonics, the angular momentum of the rotation of the Earth, the angular velocity of nutation, the nutation angle, the angular variation of nutation, the initial phase of harmonics, the perturbation moment of the Moon, the Chandler angular velocity and the equator inertia moment; a step for adding the secular variation of the rotation axis of the Earth calculated on the basis of the moment of harmonics, the angular momentum of the rotation of the Earth, the nutation angle, the angular velocity of nutation, the angular variation of nutation, the initial phase of harmonics, the Chandler angular velocity and the equator inertia moment; and
  • the nutation position of the rotation axis of the Earth is determined by the fundamental oscillation term while the terms of harmonics affect the determination process of nutation position not so much as the fundamental oscillation term.
  • the terms of harmonics of nutation should be applied to the calculation of the precise position of nutation while they are disregarded in the case of rough calculation.
  • the effects of other planets should also be considered.
  • the error between the observed value and the predicted value can be compensated in consideration of relationship of effect among planets.
  • the real time position of the rotation axis of the Earth on the nutation plane is determined by the nutation calculation process on the basis of the mathematical model on the rotation of the Earth.
  • the precession and nutation of the rotation axis of the Earth are determined by the actual rotation law of the Earth.
  • the real time position of the rotation axis of the Earth is totally determined by the calculation process of the precession and the nutation on the basis of the mathematical model on the rotation of the Earth.
  • this program should be synchronized by the observation data at least for once.
  • the observation data can be downloaded from the website of the International Earth Rotation and Reference Systems Service(IERS) which are necessary for the synchronization of the observed value with the calculation value of program.
  • IERS International Earth Rotation and Reference Systems Service
  • the processs for the EOP calculation mentioned above are combined and linked with the Interface to show the prediction result in a table or graphic format.
  • the predicted data for a year and the observation data are comprehensively treated and served.
  • the interface of the service program constitutes 4 modules.
  • a real time service of the EOP is provided.
  • the data to be served are the observed values and predicted values of the EOP for a year including LOD, precession position (v
  • the data for the rotation of the Earth is provided.
  • the data to be served are the LOD variation, the seasonal change, the irregular and leaping change of LOD, the non-uniformity of rotation velocity of the Earth within a length of day, the secular reduction of the rotation velocity of the Earth, the leap seconds, and the difference between the Universal and the Atomic time scales UT1-TAI, etc..
  • the precession and nutation data are provided.
  • the data to be served are the real time position of the rotation axis, the period of long nutation, the period of precession, the nutation eclipse, and several periods of the angular velocity of nutation, etc..
  • the data of polar motion are provided.
  • the data to be served are the position of an instantaneous pole, the periods of polar motion, the latitude change, and the secular change of the average pole, etc..
  • the EOP prediction program is recorded on a computer readable recording media, for example an IC card, a CD-ROM, a DVD-ROM or the like.
  • the program according to the present invention can be distributed in the market.
  • the EOP predicting apparatus shown in the drawings is an embodiment according to the present invention and it should not be interpreted to limit the scope of the invention.

Abstract

The invention relates to a technique for predicting the Earth Orientation Parameters (EOP) by using the observation data for variation of length-of-day (LOD) and latitude observation. The invention provides a method of predicting the EOP in real time with high accuracy by using data of the LOD variation and latitude observation on the basis of a new mathematic model on the rotation of the Earth which can clearly explain the causes of all the astronomical phenomena related with the rotation of the Earth. The invention also provides an EOP predicting apparatus and an EOP predicting program, and a computer readable recording medium recorded with the EOP predicting program.

Description

EOP prediction method, EOP prediction apparatus, EOP prediction program and computer readable recording media recorded with EOP prediction program
Field of the Invention
The present invention relates to a technique for predicting the Earth Orientation Parameters (EOP) by using the observation data for variation of length-of-day (LOD) and latitude observation.
Background and Purpose of the Invention
The rotation of the Earth is closely related with human life, thus it has been studied for a long time.
With the discovery of crystal clock in 1930s and the advent of atomic clock in 1950s, the rapid development and improvement of observation means in recent years have proved that the rotation velocity of the Earth is not uniform contrary to the customary perception of humans that the Earth was rotating at uniform velocity. But the cause of the non-Uniformity of rotation of the Earth has not yet been quantitatively explained. In particular, the Euler’s equation of rotational movement, the Poisson equation and the Euler-Liouville equation have not been able to explain in a quantitative manner the causes for the following astronomical phenomena besides the non-uniformity of rotation of the Earth; the precession-nutation related to the variation of orientation of the Earth rotation axis; and the polar motion related to the variation of orientation of the Earth with respect to its rotation axis.
The astronomers discovered and proved, on the basis of modem observation means, various kinds of astronomical phenomena related to the rotation of the Earth. They discovered the Chandler Wobble in polar motion through analyzing the observation data related to the latitude variation, several periodic phenomena in the polar motion identified as 14 months-period, annual period, semiannual period and 1 month-period and the secular variation in the mean pole motion.
Because all the astronomical phenomena with respect to the rotation of the Earth have been discovered at the different time and have their own peculiar characteristic, they have been analyzed independently and the astronomers have tried to find out the causes of these kinds of the astronomical phenomena in various ways for a long time.
It is very important and of great significance to clearly identify the causes of and predict in a quantitative manner these astronomical phenomena because tremendous amounts of fund and effort are required in research and observation of these astronomical phenomena.
There are many research conducted to predict the EOP, but because of the complexity of data processing, the method and technique of predicting the EOP in real time are still under way of development.
The present invention provides a method of predicting the EOP in real time with high accuracy by using data of the LOD variation and latitude observation on the basis of a new mathematical model which can clearly explain the causes of all the astronomical phenomena related with the rotation of the Earth.
The present invention also provides an EOP predicting apparatus and an EOP predicting program, and a computer readable recording medium recorded with the EOP predicting program.
Brief Explanation of the Invention
All the astronomical phenomena related with the rotation of the Earth can be explained theoretically and manifested as physical phenomena by a certain mathematic model on the rotation of the Earth.
The rotation of the Earth can be modeled as follows on the basis of the relativistic movement law.
Figure imgf000003_0001
where
Figure imgf000003_0002
is a moment caused by the gravitational force of the Sun, is a perturbation moment caused by the gravitational force of the Moon; and
Figure imgf000003_0003
is a perturbation moment caused by the gravitational force of a planet. K(X) and
Figure imgf000003_0004
rg((p) are main elements affecting the non-uniformity of the rotation of the Earth, where K(X), as a random variable reflecting the non-uniformity of the rotation of the Earth, is a main element of semiannual oscillation, rg((p), as the distance between the Earth and the Sun according to the latitude, is a main element of annual oscillation.
The present invention, based on the above mentioned mathematical model, provides a method and program which analyze and predict, in a quantitative manner, various kinds of astronomical phenomena including the non-uniformity of the rotation of the Earth, the precession-nutation related to the variation of orientation of the Earth rotation axis, and the polar motion related to the variation of orientation of the Earth with respect to its rotation axis.
According to the invention, provided that the data of the LOD variation and latitude observation are given, the predicted values of the other astronomical phenomena related with the rotation of the Earth, which are highly compatible with the observed values, can be obtained.
The LOD variation data can be obtained through either observation or prediction for a year concerned by using artificial neural network (ANN) with data of LOD variation for 7 to 10 years previous to the year concerned. In the case of using the predicted LOD variation data, on the basis of the above mentioned mathematical model on the rotation of the Earth, the other astronomical phenomena related with the rotation of the Earth for a year can be predicted.
The invention is explained in a greater detail with reference to the drawings appended.
Explanation of the Drawings
FIG. 1 is a flowchart of an EOP predicting apparatus.
FIG. 2 is a chart of calculation process of parameters of the rotation of the Earth.
FIG. 3 is a chart of the LOD predicting process for a year concerned. Detailed Explanation of the Invention
FIG. 1 shows the flow chart of an EOP predicting apparatus according to the present invention. The EOP predicting apparatus comprises a computer 1 loaded with a database, a computer 2 provided with at least a central processing unit (CPU) and a memory loaded with EOP predicting program and a computer 3 loaded with a program for generating EOP prediction data.
The EOP predicting apparatus is input with data of the LOD variation and the latitude observation. The EOP predicting apparatus outputs the predicted values of the EOP.
The database of computer 1 stores the data of the daily variation of LOD in the past years. It is used as input data to predict the LOD for a year concerned.
On the basis of the above mentioned mathematical model on the rotation of the Earth, the EOP calculation program loaded into the computer 2 predicts, in a quantitative manner, the various kinds of astronomical phenomena by using the latitude of a place where an observatory locates and either the data stored in the database of computer 1 or the predicted values of LOD variation.
The EOP calculation process comprises a process for predicting parameters of the rotation of the Earth, a process for predicting parameters of the precession-nutation related to the variation of orientation of the Earth rotation axis and a process for predicting parameters of the polar motion related to the variation of orientation of the Earth with respect to its rotation axis.
In the process for predicting parameters of the rotation of the Earth, the parameters are calculated on the basis of the following mathematical model derived from the above mentioned mathematical model on the rotation of the Earth (1):
Figure imgf000004_0001
where fM(t) is a moment function of external forces exerted to the Earth containing a random variable K(X), which reflects the non-uniformity of the rotation of the Earth.
The parameters of the rotation of the Earth comprises seasonal change, variation of the LOD, irregular and leaping variation of the LOD, non-uniformity of the rotating speed of the Earth within a length of 24 hours, secular reduction of the rotating speed of the Earth, leap second, and the difference between the Universal and the Atomic time scales UT1-TAI, etc..
In the process for predicting parameters of the rotation of the Earth, on the basis of either the observation data of the LOD variation for 7 to 10 years previous to the year concerned or the prediction data of the LOD variation in the year concerned, the other kinds of parameters for the rotation of the Earth can be calculated.
FIG. 2 shows the process of calculating parameters of the rotation of the Earth. The process for calculating parameters of the rotation of the Earth comprises a step for calculating the distance between the Earth and the Sun, rg; a step for obtaining random variable K(X) which reflects the non-uniformity of the rotation of the Earth by using rg and the LOD; and a step for calculating the other parameters of the rotation of the Earth except for the LOD variation by solving equation (2) into which the random variable K(X) is input.
Random variable K(X) can be determined in a quantitative manner by using the LOD variation and the distance between the Earth and the Sun (rg) of the day concerned. From the results of harmonic analysis on the seasonal oscillation, the random variable K(X) is identified as being in a range of from not less than 0 to not more than 2. It can be said that the causes of most of astronomical phenomena of the rotation of the Earth are directly related with the ceaseless change of K(X) in the range of 0 to 2.
The observation data of the LOD can be used but the availability of observation data is limited up to the current day. The rotation of the Earth is affected by external forces to oscillate on a seasonal basis. At the same time, it is also reflected by a statistical law related with random variables, thus, provided that there are observation data of the LOD in the past years, there is a possibility of predicting the LOD variation in the coming year.
In the present invention, the LOD of the year concerned (365 days) can be predicted within the range of relative error not more than 1 percent from the observation data of the LOD variation for 7 to 10 years previous to the year concerned by using artificial neural network (ANN). Once the LOD for the year concerned is predicted, the other parameters for the rotation of the Earth can be predicted according to the process shown in FIG. 2.
FIG. 3 shows the process for predicting the LOD for the year concerned. The LOD predicting process for the year concerned comprises: a step for calculating yearly average value of the LOD variation for 7 to 10 years previous to the year concerned; a step for predicting the average value of the LOD variation for the year concerned by using an ANN 1 into which the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned is input; a step for predicting the daily difference from the average value of the LOD variation for the year concerned by using an ANN 2 into which the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned is input; and a step for predicting the LOD and the LOD variation on a daily basis for the year concerned from the average value of the LOD variation and daily difference for the year concerned. The ANN 1 and the ANN 2 comprise the distributed delay network which is suitable to time series prediction. Both of the ANN 1 and the ANN 2 are 3 -layer networks containing a hidden layer.
As mentioned above, the input of the ANN 1 has 7 to 10 elements which are the yearly average value of the LOD variation for 7 to 10 years previous to the year concerned. The output of the ANN I has one element which is the average value of the LOD variation for the year predicted.
The yearly average value of the LOD variation for 7 to 10 years previous to the year concerned are not directly input into the ANN 2. The input data for the ANN 2 are the difference between the yearly average value of the LOD variation for the previous 7 to 10 years and the values of the LOD variation of the same dates in the past as the prediction will occurs. Thus, the ANN 2 has 7 to 10 input elements. The output of the ANN 2 is the difference between the average value of the LOD variation for the year to be predicted and the average value of the LOD variation for the day to be predicted. Thus, the ANN 2 has 1 output element as well. According to the number of days to be predicted, the output value for the year to be predicted can be obtained on a daily basis by iterating the calculation for the times of the number of days to be predicted (for example, 365 days) by varying input values into the ANN 2.
Based on the output value of the ANN 1 and ANN 2, the LOD and the LOD variation for the year concerned can be easily calculated on a daily basis and if necessary, the calculation result can be shown in a table or graphic format.
In the process for predicting the parameters of polar motion, the real time position of the instantaneous pole can be predicted in a quantitative manner against the average pole of the Earth on the basis of the mathematical model on the rotation of the Earth. The polar motion is occurred because the Earth is oscillating against the dynamic rotation axis when the Earth is in a movement of eclipse orbit in the gravitational force field of the Sun. The oscillation energy of the Earth against the rotation axis is the source of energy which causes the polar motion. Thus, the angular velocity of polar motion of an instantaneous pole against the average pole on the Earth’s surface is the angular velocity of nutation which is expressed as the angular velocity of the Chandler Wobble. If the latitude variation is observed on the Earth, the position of an instantaneous pole against the average pole can be determined in a quantitative manner.
In the present invention, provided that the angular velocity of polar motion of an instantaneous pole against the average pole is given, the coordinate of an instantaneous pole against the average pole can be determined independently by using the observation data of latitude obtained from an observatory, on the basis of mathematical model on the rotation of the Earth.
In order to determine the polar position according to the present invention, both of the observation data of the latitude and LOD variation should be known. The predicted values of LOD variation for a year obtained from the ANN in the process of predicting parameters of the rotation of the Earth or the observed values of LOD variation which are downloaded from the website of IERS can be used as input data of the LOD variation for the determination of polar position.
The process for predicting parameters of the polar motion comprises a step for determining a force moment of the Sun exerting to the rotation of the Earth, Msun on the basis of the LOD variation of the predicted day. The force moment of the Sun can be determined according to the following equation:
Figure imgf000006_0001
Where i is an index indicating the predicted day; E is the relativistic total energy of the Earth (E≃ mEarthC2, where mEarth is the mass of the Earth and C is the light velocity); aMoon is a force moment of the Moon exerting to the Earth; rg is the distance between the Earth and the Sun; and K(X) is the random variable indicating the non-uniformity of the rotation of the Earth (the same meaning as the non-uniformity of LOD) which is reflected in the mathematical model on i
the rotation of the Earth.
The process for predicting parameters of the polar motion comprises: a step for calculating the angular velocity of polar motion on the basis of the force moment of the Sun Msun; a step for calculating the angle of polar motion oscillating per day by integrating the angular velocity of polar motion; a step for determining the Chandler Period from the angle of polar motion oscillating per day; a step for determining the angle in which an instantaneous pole oscillates from the Greenwich meridian by using the angle of polar motion oscillating per day; a step for calculating the position of an instantaneous pole by using the observation data of latitude and the angle in which an instantaneous pole oscillates from the Greenwich meridian; and a step for transforming the position of an instantaneous pole into a base coordinate system. Table 1 shows the polar motion parameters obtained.
Table 1
Figure imgf000007_0003
As shown in the process for predicting parameters of the polar motion, provided that the LOD variation is given, the period of polar motion can be determined without observation. If the observation data of latitude is provided, the angular distance between an instantaneous pole and the average pole and the angle in which an instantaneous pole oscillates from the Greenwich meridian can be determined. Thus, the polar coordinates of an instantaneous pole can be determined.
In the process for predicting parameters of the precession-nutation related to the variation of the orientation of the Earth rotation axis, the precession and nutation parameters can be calculated on the basis of the following mathematical model.
Figure imgf000007_0001
where Y is an angular acceleration of precession of the rotation axis of the Earth; Q is an angular acceleration of nutation of the rotation axis of the Earth; A is an equator inertia moment; C is a polar inertia moment; and wz is an angular velocity of the rotation of the Earth.
In the formula (3), when considering harmonics of the Earth due to the gravitational force of the Moon, the precession position of the rotation axis of the Earth can be expressed on a real time basis as follows:
Figure imgf000007_0002
The process of determining the position of precession within a period of long nutation comprises: a step for calculating an angular distance (linear term) of the rotation axis of the Earth precessing for time t by using the astronomical constants including the equator inertia moment, the polar inertia moment, the angular velocity of the rotation of the Earth and the angular velocity of nutation; a step for adding the variation of angular distance of precession due to the fundamental oscillation of nutation calculated on the basis of the perturbation moment of the Moon, the nutation angle, the angular velocity of nutation and the angular momentum of the rotation of the Earth; a step for adding the variation of angular distance of precession due to harmonics of nutation calculated on the basis of the moment of harmonics, the nutation angle, the angular velocity of nutation, the angular variation of nutation, the angular momentum of the rotation of the Earth and the initial phase of harmonics; and a step for adding the secular variation of precession calculated on the basis of the moment of harmonics, the nutation angle, the angular velocity of nutation, the angular variation of nutation, the angular momentum of the rotation of the Earth and the initial phase of harmonics. On the basis of it, the angular distance of precession in which the rotation axis of the Earth precesses within a period of long nutation [0, T] can be calculated by the following equation
Figure imgf000008_0001
The real time position of the rotation axis of the Earth q(t) on the nutation plane in which nutation occurs can be expressed as follows:
q(t) = 0oo + Dq(t) (5)
where Dq(t) is a nutation function which shows the real time position of the rotation axis of the Earth from the equilibrium position q00.
The process for calculating the position of nutation comprises: a step for calculating the fundamental oscillation term of nutation on the basis of the perturbation moment of the Moon, the angular momentum of the rotation of the Earth, the nutation angle, the average nutation angle and the angular velocity of nutation; a step for adding the term of harmonics of nutation calculated on the basis of the moment of harmonics, the angular momentum of the rotation of the Earth, the angular velocity of nutation, the nutation angle, the angular variation of nutation, the initial phase of harmonics, the perturbation moment of the Moon, the Chandler angular velocity and the equator inertia moment; a step for adding the secular variation of the rotation axis of the Earth calculated on the basis of the moment of harmonics, the angular momentum of the rotation of the Earth, the nutation angle, the angular velocity of nutation, the angular variation of nutation, the initial phase of harmonics, the Chandler angular velocity and the equator inertia moment; and a step for adding the variation of position of nutation due to the Chandler Wobble.
Generally, the nutation position of the rotation axis of the Earth is determined by the fundamental oscillation term while the terms of harmonics affect the determination process of nutation position not so much as the fundamental oscillation term. Thus, the terms of harmonics of nutation should be applied to the calculation of the precise position of nutation while they are disregarded in the case of rough calculation.
What is noted in the process of nutation calculation is the term of secular movement of the rotation axis of the Earth. The effect of this term shows that the rotation axis of the Earth is in a secular movement with the speed of 22. "55 per 100 years against the ecliptic axis.
The effects of other planets should also be considered. The error between the observed value and the predicted value can be compensated in consideration of relationship of effect among planets.
The real time position of the rotation axis of the Earth on the nutation plane is determined by the nutation calculation process on the basis of the mathematical model on the rotation of the Earth.
The precession and nutation of the rotation axis of the Earth are determined by the actual rotation law of the Earth. Thus, the real time position of the rotation axis of the Earth is totally determined by the calculation process of the precession and the nutation on the basis of the mathematical model on the rotation of the Earth. As there are integral constants included in the calculation process, this program should be synchronized by the observation data at least for once. The observation data can be downloaded from the website of the International Earth Rotation and Reference Systems Service(IERS) which are necessary for the synchronization of the observed value with the calculation value of program. Once the program is synchronized with the observed value, the program can be used in the prediction of the real time position of the rotation axis of the Earth.
In the service program of the EOP prediction data loaded into the computer 3, the processs for the EOP calculation mentioned above are combined and linked with the Interface to show the prediction result in a table or graphic format. Thus, the predicted data for a year and the observation data are comprehensively treated and served.
The interface of the service program constitutes 4 modules.
In the first module, a real time service of the EOP is provided. The data to be served are the observed values and predicted values of the EOP for a year including LOD, precession position (v|/(t)), nutation position (0(t)), and the coordinates of polar motion(X, Y).
In the second module, the data for the rotation of the Earth is provided. The data to be served are the LOD variation, the seasonal change, the irregular and leaping change of LOD, the non-uniformity of rotation velocity of the Earth within a length of day, the secular reduction of the rotation velocity of the Earth, the leap seconds, and the difference between the Universal and the Atomic time scales UT1-TAI, etc..
In the third module, the precession and nutation data are provided. The data to be served are the real time position of the rotation axis, the period of long nutation, the period of precession, the nutation eclipse, and several periods of the angular velocity of nutation, etc..
In the fourth module, the data of polar motion are provided. The data to be served are the position of an instantaneous pole, the periods of polar motion, the latitude change, and the secular change of the average pole, etc..
The EOP prediction program is recorded on a computer readable recording media, for example an IC card, a CD-ROM, a DVD-ROM or the like.
The program according to the present invention can be distributed in the market.
The EOP predicting apparatus shown in the drawings is an embodiment according to the present invention and it should not be interpreted to limit the scope of the invention.

Claims

Claims
1. A EOP predicting method comprising a process for predicting parameters of the rotation of the Earth, a process for predicting parameters of polar motion related to the variation of orientation of the Earth with respect to its rotation axis, a process for predicting parameters of the precession-nutation related to the variation of orientation of the Earth rotation axis and a process for serving the said predicted parameters on the basis of model on the rotation of the Earth.
2. A EOP predicting method according to claim 1 , a process for predicting parameters of the rotation of the Earth comprises:
a step for calculating a distance between the Earth and the Sun;
a step for obtaining a random variable which reflects non-uniformity of the rotation of the Earth by using the said distance between the Earth and the Sun and a observed value or predicted value ofLOD; and
a step for calculating parameters of the rotation of the Earth by solving a mathematic model on the rotation of the Earth into which the said random variable is input.
3. A EOP predicting method according to claim 1, a process for predicting parameters of polar motion related to the variation of orientation of the Earth with respect to its rotation axis comprises:
a step for determining a force moment of the Sun exerting to the rotation of the Earth on the basis ofLOD variation of a predicted day;
a step for calculating an angular velocity of polar motion on the basis of the said force moment of the Sun exerting to the rotation of the Earth;
a step for calculating an angle of polar motion oscillating per day by integrating the said angular velocity of polar motion;
a step for determining a Chandler Period from the said angle of polar motion oscillating per day;
a step for determining an angle in which an instantaneous pole oscillates from the Greenwich meridian by using the said angle of polar motion oscillating per day;
a step for calculating a position of an instantaneous pole by using an observation data of latitude and the said angle in which an instantaneous pole oscillates from the Greenwich meridian; and
a step for transforming the said position of an instantaneous pole into a base coordinate system.
4. A EOP predicting method according to any one of claims 1 ~ 3, a process predicting LOD for the year concerned comprises:
a step for calculating yearly average value of LOD variation for 7 to 10 years previous to the year concerned;
a step for predicting average value of the LOD variation for the year concerned by using an ANN 1 into which the said yearly average value of the LOD variation for 7 to 10 years previous to the year concerned is input; a step for predicting daily difference from the said average value of the LOD variation for the year concerned by using an ANN 2 into which the said yearly average value of the LOD variation for 7 to 10 years previous to the year concerned is input; and
a step for predicting the LOD and the LOD variation on a daily basis for the year concerned from the said average value of the LOD variation and the said daily difference for the year concerned.
5. A EOP predicting method according to claim 1, a process of determining position of precession within a period of long nutation in the process for predicting parameters of the precession-nutation related to the variation of orientation of the Earth rotation axis comprises: a step for calculating an angular distance of the rotation axis of the Earth precessing for time t by using equator inertia moment, polar inertia moment, angular velocity of the rotation of the Earth and angular velocity of nutation;
a step for adding a variation of angular distance of precession due to fundamental oscillation of nutation calculated on the basis of perturbation moment of the Moon, nutation angle, angular velocity of nutation and angular momentum of the rotation of the Earth;
a step for adding a variation of angular distance of precession due to harmonics of nutation calculated on the basis of moment of harmonics, nutation angle, angular velocity of nutation, angular variation of nutation, angular momentum of the rotation of the Earth and initial phase of harmonics;
a step for adding a secular variation of precession calculated on the basis of moment of harmonics, nutation angle, angular velocity of nutation, angular variation of nutation, angular momentum of the rotation of the Earth and initial phase of harmonics; and
a step for calculating an angular distance of precession in which the rotation axis of the Earth precesses within a period of long nutation.
6. A EOP predicting method according to claim 1, a process for calculating position of nutation in the process for predicting parameters of precession-nutation related to the variation of orientation of the Earth rotation axis comprises:
a step for calculating a fundamental oscillation term of nutation on the basis of perturbation moment of the Moon, angular momentum of the rotation of the Earth, nutation angle, average nutation angle and angular velocity of nutation;
a step for adding a term of harmonics of nutation calculated on the basis of moment of harmonics, angular momentum of the rotation of the Earth, angular velocity of nutation, nutation angle, angular variation of nutation, initial phase of harmonics, perturbation moment of the Moon, Chandler angular velocity and equator inertia moment;
a step for adding a secular variation of the rotation axis of the Earth calculated on the basis of moment of harmonics, angular momentum of the rotation of the Earth, nutation angle, angular velocity of nutation, angular variation of nutation, initial phase of harmonics, Chandler angular velocity and equator inertia moment; and
a step for adding a variation of position of nutation due to Chandler Wobble.
7. A EOP predicting method according to claim 1, a process for serving predicted values comprises.
a step for serving EOP for a year;
a step for serving data of the rotation of the Earth;
a step for serving data of the precession-nutation related to the variation of orientation of the Earth rotation axis; and
a step for serving data of polar motion related to the variation of orientation of the Earth with respect to its rotation axis.
Wherein the EOP to be served is LOD, precession position, nutation position and coordinates of polar motion; the data of the rotation of the Earth to be served are LOD variation, seasonal change, irregular and leaping change of LOD, non-uniformity of rotation velocity of the Earth within a length of day, secular reduction of the rotation velocity of the Earth, leap seconds and the difference between the Universal and the Atomic time scales UT1-TAI; the data of precession and nutation to be served are real time position of the rotation axis of the Earth, period of long nutation, period of precession, nutation eclipse and several periods of the angular velocity of nutation, the data of polar motion to be served are position of an instantaneous pole, periods of polar motion, latitude change and secular change of an average pole.
8. A EOP prediction apparatus comprising:
a database stored with data of the daily variation of LOD in the past years;
a processor predicting parameters of the rotation of the Earth, parameters of polar motion related to the variation of orientation of the Earth with respect to its rotation axis and parameters of the precession-nutation related to the variation of orientation of the Earth rotation axis on the basis of model on the rotation of the Earth; and
a processor for serving the said predicted parameters
9. A EOP prediction program for realizing on a computer, it comprises:
a function for predicting parameters of the rotation of the Earth;
a function for predicting parameters of precession-nutation related to the variation of orientation of the Earth rotation axis;
a function for predicting parameters of polar motion related to the variation of orientation of the Earth with respect to its rotation axis; and
a function for serving the said predicted parameters.
10. A computer readable recording media recorded with EOP prediction program for realizing on a computer, it comprises:
a function for predicting parameters of the rotation of the Earth;
a function for predicting parameters of the precession-nutation related to the variation of orientation of the Earth rotation axis;
a function for predicting the parameters of polar motion related to the variation of orientation of the Earth with respect to its rotation axis; and
a function for serving the said predicted parameters.
PCT/KP2019/000049 2019-04-25 2019-07-22 Εορ prediction method, εορ prediction apparatus, eop prediction program and computer readable recording media recorded with eop prediction program WO2020218626A2 (en)

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