CN106324620A - Tropospheric zenith delay method based not on real-time measurement of surface meteorological data - Google Patents

Abstract

The invention provides a tropospheric zenith delay method based not on real-time measurement of surface meteorological data and having comparative precision as the traditional model. The method utilizes a GPT2 model and bilinear interpolation algorithm to obtain the surface meteorological data of a pre-estimated point according to the latitude and longitude and simplified Julian day of the point, and the obtained meteorological data is input into the Hopfield zenith delay model, and finally the tropospheric zenith delay of the point is obtained. In the process of estimating and predicting the tropospheric zenith delay, the method can get rid of the dependence on the surface meteorological equipment while maintaining the comparable accuracy.

Description

A real-time tropospheric zenith delay method independent of surface meteorological data

technical field

The invention relates to related fields such as satellite navigation and tropospheric atmospheric measurement, and in particular to a tropospheric zenith delay method that is accurate and does not depend on real-time measurement of surface meteorological data.

Background technique

With the development of science and technology, Global Navigation Satellite System (GNSS) has been widely used in military and civilian fields, which can provide users with accurate navigation, positioning and timing services.

During the GNSS service process, the inhomogeneity of the troposphere causes the speed of the radio wave used by the GNSS service to slow down and the path to bend. Both the slowed speed and the curved path cause the wave to be delayed in time. In the process of accurately calculating the time delay, the time delay is generally equivalent to the increase of the path. Studies have shown that the delay is about 2.3m in the direction of the tropospheric zenith, and when the incident angle of electromagnetic waves is reduced to about 10°, the magnitude further increases to 20m. Therefore, tropospheric delay must be compensated accordingly during GNSS service. At the same time, in the fields of sky-wave radar target detection, very long baseline interferometry (VLBI), ground-based GPS water vapor retrieval and forecasting, the estimation and prediction of tropospheric delay is also a work of great significance.

At present, the main method for calculating the tropospheric delay is to use a mapping function to map the delay of radio waves in the direction of the tropospheric zenith (hereinafter referred to as the zenith delay) to the direction of the incident angle. The value of the mapping function is generally only related to the position and the incident angle of the radio wave. Therefore, accurate calculation of zenith delay is very important in the estimation and prediction of tropospheric delay. Relevant literature shows that the zenith delay model is mainly established by real-time meteorological data or fitted to multi-year measured zenith delay values. The former is represented by the Hopfield model and the Saastamoinen model, and the latter is represented by the International Global GPS troposphere (IGGtrop) model.

Among them, the establishment of models such as Hopfield and Saastamoinen must obtain meteorological parameters such as surface temperature, air pressure, and water pressure in real time, so the models rely heavily on ground equipment. The IGGtrop model uses a cosine function to fit the measured zenith delay data for 5 years, and finally expresses the zenith delay as a function of time, altitude, and latitude and longitude. The establishment of the IGGtrop model is only a fitting of previous data, and does not study the changing laws of atmospheric refractive index and other factors. In the process of application, although the average error of the IGGtrop model throughout the year is low, the accuracy of estimating the delay at a certain moment is not good, so the time resolution of the model is poor.

It can be seen that the above-mentioned zenith delay models all have corresponding deficiencies: the models established based on real-time surface meteorological data rely heavily on ground equipment; while the time resolution of the model fitted to the measured data is low. Therefore, there is an urgent need to seek a method for estimating tropospheric zenith delays with high accuracy and resolution that does not depend on real-time measurement of surface meteorological data.

Contents of the invention

In order to achieve the above object, the present invention provides a method for estimating tropospheric zenith delay that does not rely on real-time measurement of surface meteorological data and has high time resolution and accuracy.

The present invention does not rely on the tropospheric zenith delay method of real-time measurement of surface meteorological data, comprising the following two steps

Step 1: Get weather data

Determine the latitude and longitude of the receiver's location λ and altitude h ₀ parameters; according to the longitude and latitude, select the four endpoints closest to the receiver in the 1°×1° grid provided by the Global Pressure and Temperature 2 (Global Pressure and Temperature 2, GPT2) model, and use the GPT2 model to provide The model parameters A ₀ , A ₁ , A ₂ , B ₁ , and B ₂ are combined with the following formula to calculate the tropospheric parameters such as air temperature T, air pressure p, and specific humidity Q at the four endpoints

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\\ {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>\end{array}$

In the formula, r(t) represents the meteorological parameters at time t; doy represents the simplified Julian day; when the unit of air pressure p and water vapor pressure e _w0 is mbar, Q is expressed as:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.622</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.378</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}$

According to the obtained meteorological parameters T, p and e _w0 of the four endpoints, combined with the following formula, the meteorological data Z of this point can be obtained by bilinear interpolation Parameter Z Contains information of temperature T ₀ , air pressure P ₀ , water vapor pressure e _w0

In the formula, Z _0,0 , Z _0,1 , Z _1,1 , Z _1,0 represent the meteorological data of each endpoint respectively; λ respectively represent latitude and longitude; parameters Q _0,0 , Q _0,1 , Q _1,1 , Q _1,0 are obtained by the following formula, namely

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; q</span>}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}\end{array}\right.$

In the formula, p=(λ-λ ₀₀ )/(λ ₁₁ -λ ₀₀ ); The parameters λ ₀₀ , Indicates the latitude and longitude of the endpoint in the lower left corner of the grid; the parameters λ ₁₁ , Indicates the latitude and longitude of the upper right corner in the grid;

Step 2: Input the obtained meteorological parameters into the Hopfield model, and calculate the zenith delay, as follows:

Put the surface temperature T ₀ obtained in step 1 into the following formula to calculate the top height h _d and h _w of the dry and wet atmosphere

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 40136</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 148.72</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 273.16</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 11000</span>}\end{array}\right.$

Put the temperature T ₀ , air pressure P ₀ , and water vapor pressure e _w0 at the surface obtained in step 1 into the following formula to calculate the initial refractive index N _d0 and N _w0 of the dry and wet atmosphere

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 77.6</span>}\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\\ {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.73</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right.$

Combine the N _d0 , N _w0 , h _d , h _w obtained in the above steps with the following formula to calculate the dry and wet refractive indices N _dh , N _wh at any height h in the troposphere

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right.$

In the formula, h ₀ represents the local altitude; use the dry and wet refractive index N _dh , N _wh and the layer top height h _d , h _w of the dry and wet atmosphere in combination with the following formula to estimate the dry and wet delay of the tropospheric zenith

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}\end{array}\right.$

according to Calculate the zenith total delay D ^S .

Through the above calculation process, the present invention can obtain the zenith delay at any time at any latitude and longitude, and does not depend on ground meteorological measuring equipment.

Description of drawings

Fig. 1 shows the principle diagram of the tropospheric zenith delay method that does not rely on surface meteorological data real-time measurement of the present invention;

Figure 2 shows a schematic diagram of bilinear interpolation;

Fig. 3 shows the meteorological data error map of some observation stations in my country in 2012 using the GPT2 model bilinear interpolation;

Fig. 4 shows that the method of the present invention and the Hopfield model calculate the zenith delay error comparison chart of some stations in my country in 2012;

Fig. 5 shows the result map of forecasting a certain point in the year of 2016 by the method of the present invention in terms of meteorological parameters and zenith delay results.

In the figure: BJFS is Beijing Fangshan Station; TWTF is Taiwan Taoyuan Station; WUHN is Hubei Wuhan Station; XIAN is Shaanxi Xi’an Station.

detailed description

The specific implementation steps of the present invention will be described in detail below in conjunction with the accompanying drawings.

Fig. 1 shows a schematic diagram of the tropospheric zenith delay method for real-time measurement independent of surface meteorological data according to the present invention. It can be seen from Fig. 1 that the present invention uses a bilinear interpolation algorithm combined with the GPT2 model to obtain the meteorological parameters required by the Hopfield model, and finally obtains the zenith delay according to the Hopfield model, including two steps.

Step 1: Get Weather Data

Determine the latitude and longitude of the receiver's location λ and altitude h ₀ and other parameters; select the four endpoints closest to the receiver in the 1°×1° grid provided by the GPT2 model according to the latitude and longitude, and use the model parameters A ₀ , A ₁ , A ₂ , B ₁ , B ₂ (taken from the GPT2 model database), combined with the following formula to calculate the tropospheric parameters such as temperature T, air pressure p, and specific humidity Q of the four endpoints.

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\\ {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>\end{array}$

In the formula, r(t) represents the meteorological parameters at time t; doy represents the simplified Julian day. When the unit of air pressure p and water vapor pressure e _w0 is mbar, Q can be expressed as:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.622</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.378</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}$

According to the obtained four-terminal meteorological parameters T, p and e _w0 combined with the following formula bilinear interpolation to get the meteorological data Z of this point Parameter Z Contains information of temperature T ₀ , air pressure P ₀ , and water vapor pressure e _w0 .

In the formula, Z _0,0 , Z _0,1 , Z _1,1 , Z _1,0 represent the meteorological data of each endpoint respectively; λ represents latitude and longitude respectively. Parameters Q _0,0 , Q _0,1 , Q _1,1 , Q _1,0 can be obtained by the following formula, namely

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; q</span>}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}\end{array}\right.$

In the formula, p=(λ-λ ₀₀ )/(λ ₁₁ -λ ₀₀ ); The parameters λ ₀₀ , Indicates the latitude and longitude of the lower left corner endpoint (endpoint 1 in Figure 2) in the grid; the parameters λ ₁₁ , Indicates the latitude and longitude of the upper right corner in the grid (endpoint 3 in Figure 2).

Figure 3 shows the bilinear interpolation of the meteorological data errors of some stations in my country in 2012 using the GPT2 model. It can be seen from Figure 3 that the accuracy of the meteorological data acquisition method in the four stations in my country meets the requirements.

Step 2: Input the acquired meteorological parameters into the Hopfield model to calculate the zenith delay. details as follows:

Put the surface temperature T ₀ obtained in step 1 into the following formula to calculate the top height h _d and h _w of the dry and wet atmosphere.

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 40136</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 148.72</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 273.16</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 11000</span>}\end{array}\right.$

Put the surface temperature T ₀ , air pressure P ₀ , and water vapor pressure e _w0 obtained in step 1 into the following formula to calculate the initial refractive index N _d0 and N _w0 of the dry and wet atmosphere.

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 77.6</span>}\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\\ {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.73</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right.$

Combine N _d0 , N _w0 , h _d , h _w obtained in the above steps with the following formula to calculate the dry and wet refractive indices N _dh , N _wh at any height h in the troposphere.

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right.$

In the formula, h ₀ represents the local altitude. Using the dry and wet refractive indices N _dh , N _wh and h _d , h _w combined with the following formula to estimate the dry and wet delays of the tropospheric zenith

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}\end{array}\right.$

according to Calculate the zenith total delay D ^S .

Fig. 4 shows that the above-mentioned zenith delay calculation method and the Hopfield model calculate the zenith delay error comparison of some stations in my country in 2012. As can be seen from Fig. 4, the real-time measurement model independent of surface meteorological data proposed by the present invention and the traditional Hopfield The model has considerable accuracy. Therefore, in the global navigation satellite system including the Beidou satellite navigation system, this combined model has a broad application prospect.

An application example of the present invention is as follows:

Use GPS satellites to provide time service to ground user equipment, and the time service receiver is located at 0# (34.28°N, 109.03°E), with an altitude of 390m. The zenith delay prediction process for the whole year of 2016 in this case is as follows:

First, perform grid query in the GPT2 model according to the latitude and longitude of 0#. At this time, the coordinates of the four endpoints corresponding to the bilinear interpolation process are 1# (33.5N, 108.5E); 2# (34.5N, 108.5 E); 3#(34.5N, 109.5E); 4#(33.5N, 109.5E); Then, according to the parameters such as A ₀ , A ₁ , A ₂ , B ₁ , B ₂ provided by the GPT2 model combined with doy prediction four The air pressure, temperature, and water vapor pressure of the endpoint in 2016, and use the obtained meteorological parameters to perform bilinear interpolation on 0#; finally, input the interpolated meteorological data into the Hopfield model to predict the annual zenith delay, Figure 5 reflects the forecasted meteorological data and the zenith delay results.

Claims (1)

1. A tropospheric zenith delay method that does not rely on real-time measurement of surface meteorological data, including the following two steps Step 1: Get weather data Determine the latitude and longitude of the receiver's location λ and altitude h ₀ parameters; select the four endpoints nearest to the receiver in the 1°×1° grid provided by the global pressure temperature 2GPT2 model according to latitude and longitude, and use the model parameters A ₀ , A ₁ , A provided by the GPT2 model ₂ , B ₁ , B ₂ , combined with the following formula to calculate the tropospheric parameters such as temperature T, air pressure p, and specific humidity Q at the four endpoints $\begin{array}{c}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; +</span>}\\ {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; 365.25</span>}}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>\end{array}$ In the formula, r(t) represents the meteorological parameters at time t; doy represents the simplified Julian day; when the unit of air pressure p and water vapor pressure e _w0 is mbar, Q is expressed as: $\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.622</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.378</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}$ According to the obtained meteorological parameters T, p and e _w0 of the four endpoints, combined with the following formula, the meteorological data of this point can be obtained by bilinear interpolation parameter Contains information of temperature T ₀ , air pressure P ₀ , water vapor pressure e _w0 In the formula, Z _0,0 , Z _0,1 , Z _1,1 , Z _1,0 represent the meteorological data of each endpoint respectively; λ respectively represent latitude and longitude; parameters Q _0,0 , Q _0,1 , Q _1,1 , Q _1,0 are obtained by the following formula, namely $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; q</span>}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}\end{array}\right.$ In the formula, p=(λ-λ ₀₀ )/(λ ₁₁ -λ ₀₀ ); The parameters λ ₀₀ , Indicates the latitude and longitude of the endpoint in the lower left corner of the grid; the parameters λ ₁₁ , Indicates the latitude and longitude of the upper right corner in the grid; Step 2: Input the obtained meteorological parameters into the Hopfield model to calculate the zenith delay, as follows: Put the surface temperature T ₀ obtained in step 1 into the following formula to calculate the top height h _d and h _w of the dry and wet atmosphere $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 40136</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 148.72</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 273.16</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 11000</span>}\end{array}\right.$ Put the temperature T ₀ , air pressure P ₀ , and water vapor pressure e _w0 at the surface obtained in step 1 into the following formula to calculate the initial refractive index N _d0 and N _w0 of the dry and wet atmosphere $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 77.6</span>}\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\\ {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3.73</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right.$ Combine the N _d0 , N _w0 , h _d , h _w obtained in the above steps with the following formula to calculate the dry and wet refractive indices N _dh , N _wh at any height h in the troposphere $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right.$ In the formula, h ₀ represents the local altitude; use the dry and wet refractive index N _dh , N _wh and the layer top height h _d , h _w of the dry and wet atmosphere in combination with the following formula to estimate the dry and wet delay of the tropospheric zenith $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; h</span>}\end{array}\right.$ according to Calculate the zenith total delay D ^S .