CN113378377A - Method for establishing large air density model changing along with space - Google Patents

Method for establishing large air density model changing along with space Download PDF

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CN113378377A
CN113378377A CN202110639475.5A CN202110639475A CN113378377A CN 113378377 A CN113378377 A CN 113378377A CN 202110639475 A CN202110639475 A CN 202110639475A CN 113378377 A CN113378377 A CN 113378377A
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杨玉峰
韩香
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Xian University of Technology
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Abstract

The invention discloses a method for establishing a large air density model changing along with space, which specifically comprises the following steps: step (1): giving out a calculation model T of the change of the earth atmospheric temperature along with time1(ii) a Step (2): giving an atmospheric temperature model T varying with time and latitude2(ii) a And (3): giving out a final atmospheric temperature model T obtained by interpolation of the heights of two adjacent layers; and (4): giving a model P of pressure variation along with height; and (5) obtaining the atmospheric density model rho changing along with the space. The invention discloses a method for establishing a large air density model changing along with space, which solves the problem that an atmospheric density model only changes along with the altitude in the prior art.

Description

Method for establishing large air density model changing along with space
Technical Field
The invention belongs to the technical field of atmospheric research, and particularly relates to a method for establishing a large air density model changing along with air.
Background
In the high-precision autonomous orbit determination of the satellite, because the influence of atmospheric resistance on the orbit needs to be considered, and the star sensor needs to know the atmospheric density when observing the star light passing through the atmosphere, the change rule of the atmospheric density is very complex, and the main factors influencing the atmospheric density are altitude, day and night and season.
The high-altitude atmospheric parameters are influenced by solar radiation factors along with longitude and latitude-seasonal changes. The observation data shows that the main factors of the high-altitude atmospheric density deviation are season and latitude, and the higher the latitude is, the greater the density deviation is, especially in winter. Due to the earth's symmetry about the polar axis, when other conditions are unchanged and only the longitude factor is changed, only a part of trace elements in various gases constituting the atmosphere are slightly changed, and the influence on the total density of the gases is negligible. From a long time scale, longitude, although also having an effect on high altitude atmospheric parameters, has little, negligible effect. The earth rotation makes the atmosphere have day and night changes, the density and wind speed day and night changes are caused by the expansion and contraction of the atmosphere caused by day and night changes of solar heating, and the tide fluctuation characteristics are obvious. The atmospheric density below 200km is less affected by day and night, but the overall effect is negligible. Recent research results rarely consider changes with longitude and latitude, season, day and night when atmospheric density changes are involved. Therefore, in order to consider the particularity of regions and climate, an atmospheric density space-time variation model is established by using an interpolation method, taking the region of Heilongjiang in China as an example, and the accuracy of the model is verified by combining measured data of atmospheric parameters from the actual climate condition.
Disclosure of Invention
The invention aims to provide a method for establishing an atmospheric density model changing along with space, which solves the problem that the atmospheric density model only changes along with the altitude in the prior art.
The invention adopts the technical scheme that a method for establishing a large air density model changing along with space specifically comprises the following steps:
step (1): giving out a calculation model T of the change of the earth atmospheric temperature along with time1；
Step (2): giving an atmospheric temperature model T varying with time and latitude2；
And (3): giving out a final atmospheric temperature model T obtained by interpolation of the heights of two adjacent layers;
and (4): giving a model P of pressure variation along with height;
and (5) obtaining the atmospheric density model rho changing along with the space.
The present invention is also characterized in that,
the step (1) is implemented according to the following steps:
the statistical characteristics of the earth atmospheric parameters changing along with the altitude at any time and place are completed based on the global operation analysis data of the NCEP FNL, and a calculation model of the earth atmospheric temperature changing along with the time is provided in a form of carrying out standard expansion on the atmospheric parameters, and the method specifically comprises the following steps:
Figure BDA0003106660700000021
in the formula, T1Is an atmospheric temperature model changing along with time, t is given time, t is 1-365, w is a model period,
Figure BDA0003106660700000022
T0when the measured time and temperature data of the NCEP is substituted into equation (1) 365, the coefficient a is obtained by least square fitting0、aiAnd biFor different areas a0、aiAnd biThe value of (c) is different.
The step (2) is implemented according to the following steps:
linear interpolation with 10 degrees of latitude interval is carried out on the formula (1) to obtain the change relation of the atmospheric temperature along with time and latitude, and the change relation is as follows:
Figure BDA0003106660700000031
in the formula, TmAnd Tm-1Is a latitude value of
Figure BDA0003106660700000032
And
Figure BDA0003106660700000033
the corresponding temperature as a function of time,
Figure BDA0003106660700000034
T2for an atmospheric temperature model over time and latitude,
Figure BDA0003106660700000035
is the latitude value of a certain area input by the formula (2).
The step (3) is specifically implemented according to the following steps:
fitting the change relation of the temperature along with the latitude and the time by using a formula (2); for model T1And model T2Linear interpolation is carried out in the range of the heights of two adjacent layers, so that the change relation of the atmospheric temperature in the range of the heights of two adjacent layers along with time and latitude can be obtained, and the method specifically comprises the following steps:
Figure BDA0003106660700000036
in the formula, hnAnd hn-1The model is a final atmospheric temperature model obtained by interpolation of two adjacent layers of heights, wherein h is the interpolation height and T is the interpolation height of the two adjacent layers of heights.
The step (4) is specifically implemented according to the following steps:
the atmospheric pressure decreases with increasing altitude and the degree of decrease slows down, so according to this law of variation, it can be assumed that the pressure variation with altitude complies with:
P＝aebh (4)
wherein a and b are coefficients to be obtained by fitting, the numerical value of the atmospheric pressure P corresponding to the height h in the range of 10-50 km is obtained from NCEP FNL data by using a nctolbox, and the numerical values are respectively substituted into the formula (4) to obtain the coefficient a which is 1.273 × 105、b＝-0.1633。
The step (5) is specifically implemented according to the following steps:
and (5): the density, the pressure and the temperature satisfy the relation by the equation of state of the ideal gas
Figure BDA0003106660700000037
Wherein R is a gas constant, taking value 287, and substituting formula (3) and formula (4)
Figure BDA0003106660700000041
Obtaining a model of the atmospheric density rho changing along with time and space within the range of 10-50 km:
Figure BDA0003106660700000042
the invention has the beneficial effects that: the invention relates to a method for establishing a large air density model changing along with space, which is characterized in that the established atmospheric density model considers the influence along with space-time change, and the new model is more accurate than the atmospheric density model changing along with height.
Drawings
FIG. 1 is the atmospheric density chart of Heilongjiang in the example.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a method for establishing a large air density model changing along with space, which is implemented according to the following steps:
step (1): the statistical characteristics of the earth atmospheric parameters changing with the altitude at any time (day) and place (longitude and latitude) are completed based on the global operation analysis data of the FNL (national center for weather and environmental forecasting) of the NCEP (national center for meteorological environment), a calculation model of the earth atmospheric temperature changing with the time is provided in a form of carrying out standard expansion on the atmospheric parameters, and the atmospheric temperature changing rule with the time can be expanded in a Fourier standard form, and the method specifically comprises the following steps:
Figure BDA0003106660700000043
in the formula, T1Is an atmospheric temperature model changing along with time, t is given time (day), t is 1-365, w is a model period,
Figure BDA0003106660700000044
T0when the measured time and temperature data of the NCEP is substituted into equation (1) 365, the coefficient a is obtained by least square fitting0、aiAnd biFor different areas a0、aiAnd biAre different in value;
step (2): in the process of constructing the global atmospheric parameter model, a linear interpolation method is used, the formula (1) is used for fitting the change of the corresponding atmospheric density along with time under different latitudes, and the linear interpolation with 10-degree latitude interval is carried out on the formula (1) to obtain the change relation of the atmospheric temperature along with time and latitude, which is concretely as follows:
Figure BDA0003106660700000051
in the formula, TmAnd Tm-1Is a latitude value of
Figure BDA0003106660700000052
And
Figure BDA0003106660700000053
the corresponding temperature as a function of time,
Figure BDA0003106660700000054
T2for an atmospheric temperature model over time and latitude,
Figure BDA0003106660700000055
the latitude value of a certain area is input by the formula (2);
step (3) the NCEP FNL data is to divide the height 10-50 km into 31 layers from 1000 mbar to 10 mbar at 26 mandatory (and other pressure) levels, and for each layer of height, fitting the temperature variation with latitude and time using equation (2); for model T1And model T2Linear interpolation is carried out in the range of the heights of two adjacent layers, and the change relation of the atmospheric temperature along with time and latitude in the range of the heights of two adjacent layers can be obtained:
Figure BDA0003106660700000056
in the formula, hnAnd hn-1Two adjacent layers of height values are obtained, h is the interpolation height, and T is the final atmospheric temperature model obtained by interpolation of the two adjacent layers of height;
and (4): the atmospheric pressure decreases with increasing altitude and the degree of decrease slows down, so according to this law of variation, it can be assumed that the pressure variation with altitude complies with:
P＝aebh (4)
wherein a and b are coefficients to be obtained by fitting, the numerical value of the atmospheric pressure P corresponding to the height h in the range of 10-50 km is obtained from NCEP FNL data by using a nctolbox, and the numerical values are respectively substituted into the formula (4) to obtain the coefficient a which is 1.273 × 105、b＝-0.1633；
And (5): the density, the pressure and the temperature satisfy the relation by the equation of state of the ideal gas
Figure BDA0003106660700000061
Wherein R is a gas constant, taking value 287, and substituting formula (3) and formula (4)
Figure BDA0003106660700000062
Obtaining a model of the atmospheric density rho changing along with time and space within the range of 10-50 km:
Figure BDA0003106660700000063
examples
Taking the example of Heilongjiang (53 degrees 33 'north latitude and 135 degrees 05' east longitude), the atmospheric temperature changes only with time and altitude since it is fixed for the latitude of this area. Fitting by utilizing an atmospheric temperature time-varying model to obtain a coefficient a with the height of 10-50 km0＝218.1514、a1＝0.2145、a2＝0.4172、a3＝-0.2068、a4＝0.0947、b1＝0.3385、b2＝0.8757、b3＝-0.1757、b40.0947, i.e. the atmospheric temperature model is:
Figure BDA0003106660700000064
the function of the annual atmospheric temperature along with the altitude in the Heilongjiang area obtained by interpolation is as follows:
Figure BDA0003106660700000065
the atmospheric pressure model is:
P＝1.273×105e-0.1633h (8)
substituting the formula (7) and the formula (8) into the formula (5) can obtain an atmospheric density space-time variation model:
Figure BDA0003106660700000071
the factors influencing the atmospheric density change, which are considered by the established new atmospheric density change-over-time model, are more, compared with the prior atmospheric density change-over-height model, the calculation result is more accurate, and the results of the atmospheric density change-over-time model of Heilongjiang are shown in figure 1.

Claims (6)

1. A method for establishing a large air density model changing along with space is characterized by comprising the following steps:
step (1): giving out a calculation model T of the change of the earth atmospheric temperature along with time1；
Step (2): giving an atmospheric temperature model T varying with time and latitude2；
And (3): giving out a final atmospheric temperature model T obtained by interpolation of the heights of two adjacent layers;
and (4): giving a model P of pressure variation along with height;
and (5) obtaining the atmospheric density model rho changing along with the space.
2. The method for building the space-time-varying atmospheric density model according to claim 1, wherein the step (1) is implemented by the following steps:
the statistical characteristics of the earth atmospheric parameters changing along with the altitude at any time and place are completed based on the global operation analysis data of the NCEP FNL, and a calculation model of the earth atmospheric temperature changing along with the time is provided in a form of carrying out standard expansion on the atmospheric parameters, and the method specifically comprises the following steps:
Figure FDA0003106660690000011
in the formula, T1Is an atmospheric temperature model changing along with time, t is given time, t is 1-365, w is a model period,
Figure FDA0003106660690000012
T0when the measured time and temperature data of the NCEP is substituted into equation (1) 365, the coefficient a is obtained by least square fitting0、aiAnd biFor different areas a0、aiAnd biThe value of (c) is different.
3. The method for creating the space-time-varying atmospheric density model according to claim 2, wherein the step (2) is implemented by the following steps:
linear interpolation with 10 degrees of latitude interval is carried out on the formula (1) to obtain the change relation of the atmospheric temperature along with time and latitude, and the change relation is as follows:
Figure FDA0003106660690000021
in the formula, TmAnd Tm-1Is a latitude value of
Figure FDA0003106660690000022
And
Figure FDA0003106660690000023
the corresponding temperature as a function of time,
Figure FDA0003106660690000024
T2as a function of time and latitudeThe model of the temperature of the atmosphere,
Figure FDA0003106660690000025
is the latitude value of a certain area input by the formula (2).
4. A method for creating a space-time varying atmospheric density model according to claim 3, wherein step (3) is specifically performed according to the following steps:
fitting the change relation of the temperature along with the latitude and the time by using a formula (2); for model T1And model T2Linear interpolation is carried out in the range of the heights of two adjacent layers, so that the change relation of the atmospheric temperature in the range of the heights of two adjacent layers along with time and latitude can be obtained, and the method specifically comprises the following steps:
Figure FDA0003106660690000026
in the formula, hnAnd hn-1The model is a final atmospheric temperature model obtained by interpolation of two adjacent layers of heights, wherein h is the interpolation height and T is the interpolation height of the two adjacent layers of heights.
5. The method for creating the space-time-varying atmospheric density model according to claim 4, wherein the step (4) is implemented by the following steps:
the atmospheric pressure decreases with increasing altitude and the degree of decrease slows down, so according to this law of variation, it can be assumed that the pressure variation with altitude complies with:
P＝aebh (4)
wherein a and b are coefficients to be obtained by fitting, the numerical value of the atmospheric pressure P corresponding to the height h in the range of 10-50 km is obtained from NCEP FNL data by using a nctolbox, and the numerical values are respectively substituted into the formula (4) to obtain the coefficient a which is 1.273 × 105、b＝-0.1633。
6. The method for creating a space-time varying atmospheric density model according to claim 5, wherein the step (5) is implemented by the following steps:
and (5): the density, the pressure and the temperature satisfy the relation by the equation of state of the ideal gas
Figure FDA0003106660690000031
Wherein R is a gas constant, taking value 287, and substituting formula (3) and formula (4)
Figure FDA0003106660690000032
Obtaining a model of the atmospheric density rho changing along with time and space within the range of 10-50 km:
Figure FDA0003106660690000033
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Publication number Priority date Publication date Assignee Title
CN101004453A (en) * 2006-12-20 2007-07-25 西安理工大学 Method for mensurating parameter of weather and atmospheric environment
US20190310392A1 (en) * 2016-12-29 2019-10-10 Landmark Graphics Corporation Global surface paleo-temperature modeling tool
CN111914467A (en) * 2020-06-05 2020-11-10 西安理工大学 Method for establishing starlight atmospheric refraction model based on GA algorithm
CN112632760A (en) * 2020-12-15 2021-04-09 西安理工大学 Method for establishing refraction angle model by reference area atmospheric parameters
CN112668166A (en) * 2020-12-21 2021-04-16 西安理工大学 Method for establishing space-time variation atmospheric temperature model

Non-Patent Citations (1)

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Title
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