A method for tropospheric wet delay prediction in a region

Abstract

The present application belongs to the technical field of space geodesy, and particularly relates to a regional troposphere wet delay prediction method. The method first obtains a troposphere wet delay sequence of a previous time period before a to-be-predicted time period, and extrapolates upward to a plane where the highest point in the region is located. After extrapolation, the wet delay space-time increment of adjacent epochs is calculated. Then, the wet delay space-time increment is used to predict the wet delay space-time increment sequence of the to-be-predicted time period. The troposphere wet delay value of the previous epoch is added to the corresponding wet delay space-time increment in the plane where the highest point is located, so as to obtain the troposphere delay prediction value of the plane where the highest point in the region is located. Then, the troposphere delay prediction value of the plane where the highest point in the region is located is extrapolated downward to the ground, so as to obtain the final regional troposphere wet delay prediction result. The wet delay data of the ground is extrapolated upward to the plane where the highest point in the region is located, and then the extrapolated wet delay is used to predict the wet delay space-time increment, so that the prediction accuracy can be improved.

Description

Technical Field

[0001] The invention belongs to the technical field of space geodesy, and in particular relates to a regional tropospheric wet delay prediction method. Background Art

[0002] The troposphere causes propagation delays in space observation technologies that primarily rely on electromagnetic waves, such as the Global Navigation Satellite System, Very Long Baseline Interferometry, Satellite Laser Ranging, and Synthetic Aperture Radar Interferometry. This delay, influenced by meteorological conditions such as temperature, air pressure, and water vapor content, is highly time-varying, changing with geographic location and propagation path. It cannot be eliminated using multi-frequency combined observations, and has become a major bottleneck restricting the accuracy of space geodetic measurements.

[0003] For ease of research, tropospheric delay is typically divided into two components: dry and wet. The dry component exhibits strong regularity and is strongly correlated with the air pressure, elevation, and latitude of the study area, allowing for precise calculation using simple empirical models. The wet delay, on the other hand, is primarily influenced by factors such as water vapor and temperature in the air profile over the study area. These unpredictable factors make accurate determination of the wet delay much more difficult than the dry delay. Therefore, the troposphere's primary constraint on space geodetic technology lies in the wet delay. Acquiring high-precision tropospheric delay information will significantly enhance the service capabilities of space technologies such as GNSS.

[0004] Currently, several methods are commonly used to calculate tropospheric wet delay: hierarchical integration, empirical modeling, estimation, and machine learning. Machine learning holds great potential. Numerous researchers have demonstrated through extensive experiments that machine learning offers unparalleled advantages in complex nonlinear approximation applications, such as meteorological and hydrological analysis and forecasting. When using machine learning for prediction, surface wet delay is often used directly. However, because surface data is affected by multiple factors, such as temperature, air pressure, water vapor content, topography, and vegetation, the spatiotemporal series of wet delay exhibits significant abrupt changes, which in turn weakens the spatiotemporal correlation of the data and hinders the prediction of regional values. Summary of the Invention

[0005] The purpose of the present invention is to provide a regional tropospheric wet delay prediction method to solve the problem of low prediction reliability caused by directly using surface data to predict wet delay.

[0006] To solve the above technical problems, the present invention provides a regional tropospheric wet delay prediction method, comprising the following steps:

[0007] 1) Obtain the tropospheric wet delay sequence of the time period before the time period to be predicted, extend it upward to the plane where the highest elevation point in the region is located, and calculate the spatiotemporal increment of the wet delay of adjacent epochs after extension;

[0008] 2) using the spatiotemporal increments of wet delay obtained in step 1) to predict the spatiotemporal increment sequence of wet delay for the time period to be predicted, adding the tropospheric wet delay value of the previous epoch to the corresponding spatiotemporal increment of wet delay in the plane where the highest point is located, to obtain the tropospheric delay forecast value in the plane where the highest point in the region is located;

[0009] 3) The tropospheric delay forecast value of the plane where the highest point in the region is located is extended downward to the surface to obtain the final regional tropospheric wet delay forecast result.

[0010] Its beneficial effects are as follows: the present invention extends the surface wet delay data upward to the plane where the highest elevation point in the region is located, and then uses the extended wet delay to predict the spatiotemporal increment of the wet delay. This method enhances the spatiotemporal continuity of the regional wet delay by extending the surface wet delay upward, eliminating most spatiotemporal mutation phenomena. Compared with the method of directly using surface data to predict the spatiotemporal increment of wet delay, the method can improve the prediction reliability and obtain forecast results that meet the needs, thereby successfully solving the problem of difficulty or inaccuracy in obtaining real-time tropospheric wet delay information due to untimely updating of meteorological data, and providing effective technical support for research and application in space geodesy fields such as GNSS precise single-point positioning, very long interferometric baseline measurement, and satellite-borne radar interferometry.

[0011] Furthermore, the formula for upward extension is:

[0012]

[0013] Where ZWD top is the tropospheric wet delay value after upward extension; ZWD surf is the surface wet delay value; ΔH is the difference between the highest point elevation in the area and the elevation of the location to be extended; b i is the coefficient, i=0,1,2, obtained by fitting using historical meteorological data.

[0014] The beneficial effect is that the exponential function coefficients in the extension formula are obtained by fitting historical meteorological data, taking into account the periodic characteristics of the extension parameters in different regions, and can improve the extension accuracy of wet delay to a certain extent.

[0015] Furthermore, the downward extension formula is:

[0016]

[0017] The beneficial effect is that the exponential function coefficients in the extension formula are obtained by fitting historical meteorological data, taking into account the periodic characteristics of the extension parameters in different regions, and can improve the extension accuracy of wet delay to a certain extent.

[0018] Furthermore, in step 2), the spatiotemporal increment of wet delay obtained in step 1) is input into the constructed machine learning model to predict the spatiotemporal increment sequence of wet delay for the time period to be predicted.

[0019] The beneficial effect is that the spatiotemporal increment of wet delay in the time period to be predicted is predicted with high accuracy using a machine learning model.

[0020] Furthermore, the training data for training the machine learning model is obtained in the following manner: historical meteorological data of the target area are collected, and the tropospheric wet delay values ​​of grid points with a certain spatiotemporal resolution in the area are calculated based on the meteorological data, and the correlation index between adjacent epochs is required to be greater than or equal to a preset threshold; and the tropospheric wet delay sequence that meets the requirements is then extended upward to the plane where the highest elevation point in the area is located, and the spatiotemporal increments of the wet delay of adjacent epochs are calculated to obtain training data.

[0021] Its beneficial effect is that the correlation index between adjacent epochs is required to be greater than or equal to a preset threshold, so that the tropospheric wet delay forecast results for a longer time span in the future can be obtained.

[0022] Furthermore, the calculation formula of the correlation index is:

[0023]

[0024] Where r is the correlation index; x i 、y i is the gridded tropospheric wet delay value in the form of a one-dimensional vector between two adjacent epochs; are the average values ​​of the two vectors respectively; n is the sequence length of the one-dimensional vector.

[0025] Furthermore, if the correlation index between any two adjacent epochs is less than a preset threshold, the spatial and temporal resolutions are increased so that the correlation indexes of all adjacent epochs at the new resolution are greater than or equal to the preset threshold.

[0026] The beneficial effect is that model training can reduce the number of cycles while ensuring a certain spatial and temporal resolution.

[0027] Furthermore, the quadratic surface interpolation method is used to increase the spatial resolution, and the equation of the quadratic surface interpolation method is:

[0028] f(B,L)=a0+a1B+a2L+a3B 2 +a4L 2 +a5BL

[0029] Where B and L are the geodetic latitude and geodetic longitude of the discrete point respectively; f() represents the interpolation result; a i Represents the coefficient, i=1,2,…,5.

[0030] Furthermore, a temporal distance weighting method is used to increase the temporal resolution, and the equation of the temporal distance weighting method is:

[0031]

[0032] Where g t (i, j) represents the interpolation result of the (i, j)th grid point at the interpolation time t; D t1 、D t2 is the time difference between time t and the upper and lower adjacent epochs; D is the time difference between the upper and lower epochs adjacent to time t, that is, D = D t1 +D t2 ;g t1 (i,j),g t2 (i, j) represents the tropospheric wet delay value of the (i, j)th grid point in the upper and lower epochs adjacent to time t, respectively.

[0033] Furthermore, the machine learning model is a ConvLSTM network model, and its convolution kernel size is 3×3, the loss function is MSE, the activation function is ReLU, and the optimizer is Adam.

[0034] The beneficial effect is that the ConvLSTM network model with the above parameters can ensure that the tropospheric wet delay forecast results with sufficient accuracy are obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the regional tropospheric wet delay prediction method of the present invention;

[0036] FIG2( a ) is a graph showing the regional zenith tropospheric wet delay value at UTC 00:00 in an embodiment of the method of the present invention;

[0037] FIG2( b ) shows the regional zenith tropospheric wet delay value at UTC 06:00 in an embodiment of the method of the present invention;

[0038] FIG2( c ) is the regional zenith tropospheric wet delay value at UTC 12:00 in an embodiment of the method of the present invention;

[0039] Figure 3 is a correlation index graph of adjacent epochs of tropospheric wet delay in an embodiment of the present invention;

[0040] FIG4( a ) is a schematic diagram of point selection in the middle region in an embodiment of the method of the present invention;

[0041] FIG4( b ) is a schematic diagram of point selection in an edge region in an embodiment of the method of the present invention;

[0042] FIG5( a ) is a frequency distribution diagram of the error interval of the regional zenith tropospheric wet delay prediction in an embodiment of the method of the present invention;

[0043] FIG5( b ) is a regional error diagram of regional zenith tropospheric wet delay prediction by epoch statistics in an embodiment of the method of the present invention;

[0044] FIG5( c ) is a regional ZWD error diagram of the regional zenith tropospheric wet delay forecast at UTC 17:00 on January 25 in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0046] Method Example:

[0047] An embodiment of a regional tropospheric wet delay prediction method of the present invention has the following overall process: Figure 1 The specific implementation process is as follows:

[0048] Step 1: Collect historical meteorological data of the target area and calculate the tropospheric wet delay values ​​of grid points with a certain temporal and spatial resolution in the area based on the historical meteorological data.

[0049] This example uses the Central European region (45°N-55°N, 5°E-25°E) as an example. Hierarchical grid meteorological data with hourly resolution from January 1 to 30, 2021, are collected. The horizontal spatial resolution is 0.25°×0.25°. The spatiotemporal sequence grid values ​​of wet delay in the region are then calculated using the hierarchical integration method. The formula for the hierarchical integration method is:

[0050]

[0051] Where ZWD is the calculated zenith tropospheric delay; surf and trop are the surface elevation and tropopause elevation, respectively; k'2 and k3 are constant coefficients, which are equal to 22.13 K / hPa and 3.739×10 5 K 2 / hPa; p w , T are the water vapor pressure and temperature at each altitude, respectively. Taking January 1, 2021, at 00:00 UTC, 06:00 UTC, and 12:00 UTC as an example, the regional tropospheric wet delay values ​​calculated in this embodiment are shown in Figures 2(a), 2(b), and 2(c), respectively.

[0052] Step 2: Calculate the correlation index of adjacent epochs for the spatiotemporal series of tropospheric wet delay with a certain time resolution a number of days before the predicted date.

[0053] According to the spatiotemporal sequence of tropospheric wet delay obtained in step 1, the correlation index of adjacent epochs is calculated. The correlation index is shown in Figure 3 The calculation formula of the correlation index is:

[0054]

[0055] Where r is the correlation index, unit is %; x i 、y i is the grid tropospheric wet delay value in the form of a one-dimensional vector between two adjacent epochs; n is the sequence length of the one-dimensional vector; are the average values ​​of the two vectors respectively.

[0056] Step 3: Adjust the spatial and temporal resolution: If the correlation index between any two epochs is less than 90%, increase the spatial and temporal resolutions, and then obtain the wet delayed space-time series at the new resolution until all correlation indices are greater than or equal to 90%.

[0057] When increasing the spatial resolution, the quadratic surface interpolation method should be used. The equation for quadratic surface interpolation is:

[0058] f(B,L)=a0+a1B+a2L+a3B 2 +a4L 2 +a5BL

[0059] Where B and L are the geodetic latitude and geodetic longitude of the discrete point respectively; f() represents the interpolation result; a i (i = 1, 2, ..., 5) represents the coefficient of the function to be calculated. Substituting the geodetic latitude and longitude values ​​of six or more grid points surrounding the interpolation point, the coefficient can be calculated using the least squares method. Specifically, 16 surrounding grid points can be selected in the central region, and 9 surrounding grid points can be selected in the edge region. The specific point selection method is shown in Figures 4(a) and 4(b). The hollow circles in Figures 4(a) and 4(b) represent the points selected for calculating the coefficients of the quadratic surface function, while the solid circles represent the points to be interpolated.

[0060] When increasing the temporal resolution, the temporal distance weighting method should be used. The temporal distance weighting equation is:

[0061]

[0062] Where g t (i, j) represents the interpolation result of the (i, j)th grid point at the interpolation time t; D t1 、D t2 is the time difference between time t and the upper and lower adjacent epochs; D is the time difference between the upper and lower epochs adjacent to time t, that is, D = D t1 +D t2 ;gt1 (i,j),g t2 (i, j) represents the tropospheric wet delay value of the (i, j)th grid point in the upper and lower epochs adjacent to time t, respectively.

[0063] Combine Figure 3 It can be seen that all correlation indexes in this embodiment are greater than or equal to 90%, so no adjustment is required.

[0064] Step 4: Extend the tropospheric wet delay sequence that meets the requirements upward to the plane where the highest elevation point in the area is located, and calculate the spatiotemporal increments of wet delays in adjacent epochs.

[0065] 1) Use the following formula to extend the wet delay of the area that meets the requirements upward to the plane where the highest point in the area is located:

[0066]

[0067] Where ZWD top ZWD is the tropospheric wet delay value extended to the plane of the highest point on the surface; surf is the surface wet delay value; ΔH is the difference between the highest point elevation in the area and the elevation of the location to be extended; b i (i=0,1,2) is the coefficient to be determined, which can be obtained by fitting the vertical profile ZWD of each grid point based on the historical annual average meteorological data.

[0068] 2) Subtract the tropospheric wet delays of adjacent epochs after extension to obtain the spatiotemporal increment of the wet delay.

[0069] Step 5: Use the ConvLSTM machine learning model to take the spatiotemporal increment of wet delay as the input sequence to predict the incremental sequence value for a period of time in the future. Add the absolute value of the wet delay of the previous epoch to the incremental value to obtain the tropospheric wet delay forecast value at the highest point plane in the area.

[0070] Substitute the spatiotemporal increment information obtained in the previous step into the ConvLSTM machine learning model to obtain the predicted value of the wet delay after extension. In this embodiment, the basic settings of the ConvLSTM network are shown in Table 1. The first two dimensions of the input and output matrices are related to the spatial resolution and regional size of the tropospheric wet delay. When the regional size is 45°N~55°N, 5°E~25°E, and the horizontal spatial resolution is 0.25°×0.25°, it is 41×81; the third dimension of the matrix is ​​related to the step size of the historical data to be learned. The larger the third dimension of the input matrix, the higher the prediction accuracy, but the model training takes more time and consumes more computer memory; the larger the third dimension of the output matrix, the larger the span of the predicted future sequence, but the prediction accuracy will decrease. Each parameter in the network will affect the accuracy or efficiency of the forecast to a certain extent, so it needs to be set as appropriate when training the model.

[0071] To obtain tropospheric wet delay forecasts with a longer time span, the time resolution can be reduced in the input sequence, and then steps 2 to 4 can be repeated, but the correlation index of adjacent epochs must be ensured to be always greater than 90%, and the final calculation accuracy must meet the requirements.

[0072] Table 1. Basic parameters of ConvLSTM network

[0073] ConvLSTM parameters Setting situation Remark Input matrix size 41×81×7 The first two dimensions are the ZWD grid size, and the third dimension is the historical step size. Output matrix size 41×81×7 The first two dimensions are the ZWD grid size, and the third dimension is the prediction step size. Training data samples 480 BC Test data sample 240 epochs later Convolution kernel size 3×3 Activation Function ReLU Optimizer Adam Loss Function MSE Number of circuit training sessions 50

[0074] Step 6: Extend the obtained forecast value downward to the surface to obtain the final regional tropospheric wet delay forecast result.

[0075] The forecast value obtained in step 5 is extended downward to the surface to obtain the final regional tropospheric wet delay forecast result. In this embodiment, the model prediction accuracy is shown in Figure 5(a) to Figure 5(c) Figure 5(a) shows the frequency distribution of the error intervals, Figure 5(b) shows the regional error statistics by epoch, including the mean absolute error (MAE), mean error (Mean), and standard deviation (STD), and Figure 5(c) shows the regional ZWD error at 17:00 UTC on January 25.

[0076] In summary, this method can obtain accurate tropospheric wet delay results for the study area based on historical meteorological data forecasts. First, by extending the surface wet delay upward, the spatiotemporal continuity of the regional wet delay is enhanced, eliminating most spatiotemporal mutations and improving the reliability of the prediction. Second, the exponential function coefficients in the extension formula are fitted based on historical meteorological data, taking into account the periodic characteristics of the extension parameters in different regions, which can improve the wet delay extension accuracy to a certain extent. Furthermore, by setting appropriate ConvLSTM network parameters and the spatiotemporal resolution of the input data, a forecast result that meets the requirements is obtained. This method can successfully solve the problem of difficulty or inaccuracy in obtaining real-time tropospheric wet delay information caused by untimely meteorological data updates, and can provide effective technical support for research and application in space geodesy fields such as GNSS precise single-point positioning, very long interferometric baseline measurement, and spaceborne radar interferometry.

Claims

1. A regional tropospheric wet delay prediction method, characterized in that: The steps include: 1) Obtain the tropospheric wet delay sequence of the time period before the time period to be predicted, extend it upward to the plane where the highest elevation point in the region is located, and calculate the spatiotemporal increment of the wet delay of adjacent epochs after extension; 2) using the spatiotemporal increments of wet delay obtained in step 1) to predict the spatiotemporal increment sequence of wet delay for the time period to be predicted, adding the tropospheric wet delay value of the previous epoch to the corresponding spatiotemporal increment of wet delay in the plane where the highest point is located, to obtain the tropospheric delay forecast value in the plane where the highest point in the region is located; 3) The tropospheric delay forecast value of the plane where the highest point in the region is located is extended downward to the surface to obtain the final regional tropospheric wet delay forecast result.

2. The regional tropospheric wet delay prediction method according to claim 1, characterized in that: The formula for upward continuation is: Where ZWD top is the tropospheric wet delay value after upward extension; ZWD surf is the surface wet delay value; ΔH is the difference between the highest point elevation in the area and the elevation of the location to be extended; b i are coefficients, i = 0, 1, 2, obtained by fitting using historical meteorological data.

3. The regional tropospheric wet delay prediction method according to claim 1, characterized in that: The formula for downward continuation is:

4. The regional tropospheric wet delay prediction method according to any one of claims 1 to 3, characterized in that: In step 2), the wet delay spatiotemporal increment obtained in step 1) is input into the constructed machine learning model to predict the wet delay spatiotemporal increment sequence for the time period to be predicted.

5. The regional tropospheric wet delay prediction method according to claim 4, characterized in that: The training data for training the machine learning model is obtained in the following manner: historical meteorological data of the target area are collected, and the tropospheric wet delay values ​​of grid points with a certain spatiotemporal resolution in the area are calculated based on the meteorological data, and the correlation index between adjacent epochs is required to be greater than or equal to a preset threshold; the tropospheric wet delay sequence that meets the requirements is then extended upward to the plane where the highest elevation point in the area is located, and the spatiotemporal increments of wet delays of adjacent epochs are calculated to obtain training data.

6. The regional tropospheric wet delay prediction method according to claim 5, characterized in that: The calculation formula of the correlation index is: Where r is the correlation index; x i 、y i is the gridded tropospheric wet delay value in the form of a one-dimensional vector between two adjacent epochs; are the average values ​​of the two vectors respectively; n is the sequence length of the one-dimensional vector.

7. The regional tropospheric wet delay prediction method according to claim 5, characterized in that: If the correlation index between any two adjacent epochs is less than a preset threshold, the spatial and temporal resolutions are increased so that the correlation index of all adjacent epochs at the new resolution is greater than or equal to the preset threshold.

8. The regional tropospheric wet delay prediction method according to claim 7, characterized in that: The quadratic surface interpolation method is used to increase the spatial resolution, and the equation of the quadratic surface interpolation method is: f(B,L)=a0+a1B+a2L+a3B 2 +a4L 2 +a5BL Where B and L are the geodetic latitude and geodetic longitude of the discrete point respectively; f() represents the interpolation result; a i Represents the coefficient, i=1,2,…,5.

9. The regional tropospheric wet delay prediction method according to claim 7, characterized in that: The temporal distance weighting method is used to increase the temporal resolution, and the equation of the temporal distance weighting method is: Where g t (i, j) represents the interpolation result of the (i, j)th grid point at the interpolation time t; D t1 、D t2 is the time difference between time t and the upper and lower adjacent epochs; D is the time difference between the upper and lower epochs adjacent to time t, that is, D = D t1 +D t2 ;g t1 (i,j),g t2 (i, j) represents the tropospheric wet delay value of the (i, j)th grid point in the upper and lower epochs adjacent to time t, respectively.

10. The regional tropospheric wet delay prediction method according to claim 4, characterized in that: The machine learning model is a ConvLSTM network model, and its convolution kernel size is 3×3, the loss function is MSE, the activation function is ReLU, and the optimizer is Adam.

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