A method and system for calculating water vapor budget of an arbitrary area considering surface curvature

Abstract

The application discloses a kind of arbitrary area water vapor balance calculation method and system considering surface curvature, belong to remote sensing science and earth information science field.The method includes: collecting three-dimensional atmospheric data and preprocessing;Calculate the water vapor transport flux of each grid point;Construct the sequence of discrete nodes of regional boundary, calculate the boundary arc length based on the curvature of the earth using spherical distance;Calculate the midpoint normal vector of each arc segment and point to the inside of the region;Using bilinear interpolation to obtain the water vapor transport flux at the midpoint of the arc segment, and project to the inside normal direction;Integrate the boundary arc segment, calculate the regional water vapor balance.This application considers the curvature of the earth in the calculation of boundary length, improves the accuracy of flux by node encryption and bilinear interpolation, and preserves the actual boundary trend, overcomes the defects such as distance calculation deviation, boundary forced approximation and flux representative error of traditional method, significantly improves the accuracy of arbitrary area water vapor balance estimation.

Description

Technical Field

[0001] This invention belongs to the fields of remote sensing science and geoinformation science, and specifically relates to a method and system for calculating water vapor balance in any region that takes into account the curvature of the Earth's surface. Background Technology

[0002] Regional water vapor budget is a crucial indicator for revealing precipitation formation, atmospheric circulation transport characteristics, and the causes of extreme weather. Water vapor budget estimation methods are mainly divided into two categories: water vapor budget calculation methods based on regional divergence integration and water vapor budget calculation methods based on regional boundary flux integration. The former calculates the net water vapor flux within the region through the divergence of water vapor transport flux, but its calculated value is significantly affected by the divergence grid density, making accurate calculation difficult in cases of complex boundaries. The latter projects the water vapor transport flux onto the boundary normal direction and then integrates it, providing a clearer physical meaning and is a commonly used method. However, current methods based on boundary water vapor transport flux have the following problems: First, when calculating regional boundaries, the curvature of the Earth is ignored, and the region is treated as a plane. The distance between two points is calculated as a straight line on the plane instead of a curve, introducing distance calculation errors. Second, when dealing with regional boundaries, to simplify the problem, the boundary line is approximated as north-south and east-west, which differs significantly from the actual shape of the boundary line, introducing significant calculation errors. Third, in actual calculations, the water vapor transport flux at the grid point closest to the boundary line is used, directly replacing the current value with the value at the nearest grid point. This introduces representational errors, especially when the grid intervals are large. To further improve the accuracy of regional water vapor budget estimation, a method is needed that is more rigorous in calculating the regional boundary length, more reasonable in calculating the water vapor transport flux at the boundary, and more flexible in handling the relationship between water vapor transport flux and the boundary line direction. Summary of the Invention

[0003] This invention addresses the problems of existing technologies by providing a method and system for calculating water vapor budget in any region, taking into account the curvature of the Earth's surface. The method considers the Earth's curvature when calculating the length between two points on the boundary of a region. When calculating the water vapor transport flux at the boundary, it does not directly use the value of the nearest neighbor point, but instead uses the midpoint of a small segment of the boundary line as a reference position for interpolation of the water vapor transport flux value to ensure accuracy. When processing the integration of the boundary line and the water vapor transport flux, it does not forcibly approximate the boundary line as east-west or north-south, but retains the actual shape of the boundary line and directly performs the inner product of the water vapor transport flux (vector) with the normal vector of a small segment of the boundary line, avoiding errors caused by approximating the boundary line direction. Through these various measures, the method of this invention is more rigorous in calculating water vapor budget.

[0004] The technical solution is as follows: A method for calculating water vapor deficit in any region that takes into account the curvature of the Earth's surface, comprising the following steps:

[0005] S1. Collect and preprocess three-dimensional atmospheric data of the study area from the ground to the tropopause for a predetermined time period;

[0006] S2. Based on the three-dimensional atmospheric data, combined with the multi-layer atmospheric wind field and humidity field, calculate the water vapor transport flux at each horizontal grid point.

[0007] S3. Construct a discrete boundary node sequence based on the boundary line of the study area, and calculate the distance between two adjacent boundary points;

[0008] S4. Calculate the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes;

[0009] S5. Use bilinear interpolation to obtain the water vapor transport flux at the midpoint of each boundary arc segment, and calculate its water vapor transport flux component in the normal direction.

[0010] S6. Calculate the normal water vapor transport flux within each boundary arc segment at each time point, and further obtain the regional water vapor budget for the entire period.

[0011] Furthermore, the aforementioned step S1 includes the following sub-steps:

[0012] S1.1 Collect three-dimensional atmospheric data, including meridional wind, zonal wind, and specific humidity data for each pressure layer;

[0013] S1.2. Conduct quality control on the data, including checking, removing or interpolating missing values ​​and gross errors;

[0014] S1.3. Standardize the data, including spatiotemporal matching of data with different spatiotemporal resolutions and standardizing the format and units of data from different sources.

[0015] Furthermore, the aforementioned step S2 includes the following sub-steps:

[0016] S2.1 At each horizontal grid point, assume the preprocessed data is generated by... It consists of several pressure layers, the first The air pressure of the layer is The wind direction is zonal wind , more wet than , ;

[0017] S2.2, For grid points Calculate the pressure difference between two adjacent pressure layers. The average specific humidity between the two layers Average meridional wind Average zonal wind ;

[0018] S2.3 Calculate the grid points according to the following formulas. The meridional component of water vapor transport flux and latitudinal components :

[0019] ,

[0020] ,

[0021] In the formula, It is the acceleration due to gravity;

[0022] S2.4 Calculate the meridional and zonal components of the water vapor transport flux at all other grid points.

[0023] Furthermore, the aforementioned step S3 includes the following sub-steps:

[0024] S3.1 Constructing a discrete boundary node sequence based on the boundary lines of the study area Calculate the central angle of the great circle between the two boundary points as follows:

[0025] ,

[0026] In the formula, It is the central angle of the great circle between two adjacent boundary nodes on the sphere, that is, the angle between the lines connecting the two points to the center of the sphere. Represents boundary nodes latitude and longitude coordinates Indicates the next adjacent boundary node latitude and longitude coordinates;

[0027] S3.2, Calculation and Length between two adjacent boundary points on the sphere As shown in the following formula:

[0028] ,

[0029] In the formula, The average radius of the Earth;

[0030] S3.3. Set an arc length threshold. When the arc length between two adjacent boundary nodes is greater than the threshold, insert a node between the two adjacent nodes so that the distance between the new node and the original node is less than the threshold, and add the new node to the original boundary node sequence. Then, calculate the arc length distance between all adjacent boundary points segment by segment according to the formulas in steps S3.1 and S3.2.

[0031] Furthermore, the aforementioned step S4 includes the following sub-steps:

[0032] S4.1 Calculate each pair of adjacent nodes The spherical arc segment formed Tangent vector at the midpoint As shown in the following formula:

[0033] ,

[0034] S4.2 Obtain the radial vector from the midpoint of the arc segment to the center of the sphere. :

[0035] ,

[0036] In the formula, O represents the center of the Earth. For arc segment The midpoint;

[0037] S4.3 Calculate the normal vector at the midpoint of the arc segment. for:

[0038] ,

[0039] S4.4, normal vector Convert to a two-dimensional vector in the tangent plane at the midpoint of the arc segment , The two components are the longitudinal and latitudinal directions, respectively. Based on the order of the boundary points and the location of the region center point, the direction of the normal vector is determined. If the normal vector points to the outside of the region, the opposite direction is taken to ensure that all normal vectors point to the inside of the study region.

[0040] Furthermore, the aforementioned step S5 includes the following sub-steps:

[0041] S5.1 Obtaining the arc segment midpoint Grid points around Bilinear interpolation was performed on the meridional and zonal components of the water vapor transport flux, respectively:

[0042] ,

[0043] ,

[0044] In the formula, and These represent the interpolation weights in the longitude and latitude directions, respectively; Representing arc segments midpoint latitude and longitude coordinates;

[0045] S5.2 Calculate the water vapor transport flux vector at the midpoint of the arc segment, as shown in the following formula:

[0046] ,

[0047] S5.3 Project the interpolated water vapor transport flux along the inner normal direction of the arc segment. The normal water vapor transport flux is defined as follows:

[0048] ,

[0049] In the formula, Indicates the first Internal normal water vapor transport flux on each boundary arc segment This indicates that water vapor is transported along the inward normal direction, meaning that water vapor flows from the outside of the region into the inside of the region; This indicates the transport of water vapor in the reverse direction of the interior, meaning that water vapor flows from the interior of the region to the exterior.

[0050] Furthermore, the aforementioned method for calculating water vapor budget in any region that takes into account surface curvature, with interpolation weights in the longitude and latitude directions... and Calculate as follows;

[0051] ,

[0052] ,

[0053] Furthermore, the aforementioned step S6 includes the following sub-steps:

[0054] S6.1 Calculate each time step Normal water vapor transport flux within each boundary arc segment , The time interval between each adjacent moment is ,by Time-centered The regional water vapor balance within the time interval is:

[0055] ,

[0056] In the formula, This represents the length of the i-th arc segment. ;

[0057] Another aspect of the present invention provides a calculation system for a method of calculating water vapor budget in an arbitrary region considering surface curvature, applicable to the aforementioned method of calculating water vapor budget in an arbitrary region considering surface curvature, comprising:

[0058] The data acquisition module is used to collect and preprocess three-dimensional atmospheric data of the study area from the ground to the tropopause for a preset time period.

[0059] The flux calculation module is used to calculate the water vapor transport flux at each horizontal grid point based on three-dimensional atmospheric data and multi-layer atmospheric wind and humidity fields.

[0060] The boundary discretization module is used to construct a sequence of discrete boundary nodes based on the boundary lines of the study area and to calculate the distance between two adjacent boundary points.

[0061] The normal vector calculation module is used to calculate the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes;

[0062] The interpolation component module is used to obtain the water vapor transport flux at the midpoint of each boundary arc segment using the bilinear interpolation method, and to calculate its water vapor transport flux component in the normal direction.

[0063] The income and expenditure calculation module is used to calculate the normal water vapor transport flux within each boundary arc segment at each time point, and further obtain the regional water vapor income and expenditure for the entire period.

[0064] Furthermore, when calculating the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes, the aforementioned normal vector calculation module specifically adopts a surface normal vector solution algorithm based on the Earth ellipsoid model to accurately fit the influence of the surface curvature on the spatial orientation of the boundary arc segment.

[0065] Compared to existing technologies, the beneficial technical effects of the present invention using the above technical solution are as follows: The method of the present invention considers the curvature of the Earth in the calculation of the regional boundary line length, making the calculation of the boundary line length more consistent with the actual geographical geometric characteristics and avoiding distance calculation errors caused by planar approximation; in the processing of the regional boundary line, it does not simply approximate the boundary line as east-west and north-south line segments, but rather preserves the actual boundary orientation as much as possible to reduce the calculation error of the boundary line normal direction; when calculating the water vapor transport flux (IVT) on the boundary, it uses an interpolation method to calculate the IVT instead of using the nearest neighbor method, improving the accuracy of the water vapor transport flux value. This method can be applied to regional water vapor budget analysis, climate diagnostic research, precipitation formation mechanism research, and numerical model water vapor transport assessment, and can be used for quantitative calculation and analysis of water vapor budget at any regional scale. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method of the present invention.

[0067] Figure 2 This is a comparison chart of the hourly average water vapor balance in Yunnan region in July and August 2025 calculated by the example and the results calculated by the conventional method. Detailed Implementation

[0068] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0069] In this invention, various aspects of the invention are described with reference to the accompanying drawings, in which numerous illustrative embodiments are shown. Embodiments of the invention are not limited to those depicted in the drawings. It should be understood that the invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0070] This invention proposes a method for calculating water vapor budget in any region that takes into account surface curvature. This method addresses issues such as neglecting Earth's curvature, simplifying boundary line direction, and representative errors in water vapor transport flux when calculating regional water vapor budget, thereby improving the accuracy of regional water vapor budget estimation. To verify the effectiveness of this invention, three-dimensional atmospheric data from Yunnan Province in July and August 2025 were used as an example to implement the method, with reference to... Figure 1 The specific steps are as follows:

[0071] Step S1: Data Preparation and Preprocessing

[0072] This study collects three-dimensional atmospheric vector files of the study area from the ground to the tropopause over a specific time period, including meridional wind, zonal wind, and specific humidity data for each pressure layer, to calculate the integrated water vapor transport flux (IVT). A specific time period refers to a day, month, year, or any duration, determined according to the specific problem. Data sources can include meteorological reanalysis data, such as the ERA5 product from the European Centre for Medium-Range Weather Forecasts (ECMWF), reanalysis products from the National Center for Environmental Prediction (NCEP) in the United States, or actual three-dimensional atmospheric data from radiosondes and other observations.

[0073] Step S2: Calculate the water vapor transport flux. Based on the multi-layer atmospheric wind field and humidity field, calculate the water vapor transport flux at each horizontal grid point. Specifically, at each horizontal grid point, the preprocessed data is... It consists of several pressure layers, the first The air pressure of the layer is The wind direction is zonal wind , more wet than , For a specific grid point Calculate the pressure difference between two adjacent pressure layers. The average specific humidity between the two layers Average meridional wind Average zonal wind Then, the meridional component of the water vapor transport flux at that grid point is calculated using the following formula. and latitudinal components :

[0074] ,

[0075] ,

[0076] In the formula, This is the acceleration due to gravity.

[0077] Then calculate all other grid points in the same way. Meridian component and latitudinal component.

[0078] Step S3: Discretization and length calculation of the region boundary line

[0079] Construct a discrete boundary node sequence based on the boundary line of the study area in a counter-clockwise direction. Calculate the boundary points of two adjacent points. and When calculating the distance between two boundary points, since the Earth's surface is curved, the distance is calculated as a spherical distance, i.e., the arc length between adjacent nodes is calculated based on the great circle path on the sphere. The central angle of the great circle between the two boundary points is also considered. Calculated using the Haversine formula:

[0080] ,

[0081] In the formula, It is the central angle of the great circle between two adjacent boundary nodes on the sphere, that is, the angle between the lines connecting the two points to the center of the sphere. Represents boundary nodes latitude and longitude coordinates Indicates the next adjacent boundary node Latitude and longitude coordinates.

[0082] and Length between two adjacent boundary points on the sphere for:

[0083] ,

[0084] In the formula, This is the average radius of the Earth.

[0085] To improve the precision of boundary description, an arc length threshold is set. When the arc length between two adjacent boundary nodes exceeds this threshold, an interpolation is performed between the two adjacent nodes to make the distance between the new node and the original node less than the threshold, and the new node is added to the original boundary node sequence. In the middle, the arc length distance between all adjacent boundary points is calculated segment by segment.

[0086] Step S4: Discretization and length calculation of the region boundary line

[0087] Calculate each pair of adjacent nodes The spherical arc segment formed midpoint The normal vector at that location.

[0088] arc Tangent vector at the midpoint for:

[0089] ,

[0090] The radial vector from the midpoint of the arc segment to the center of the sphere for:

[0091] ,

[0092] In the formula, O represents the center of the Earth. For arc segment The midpoint.

[0093] Then the normal vector at the midpoint of the arc segment for:

[0094] ,

[0095] normal vector Convert to a two-dimensional vector in the tangent plane at the midpoint of the arc segment , The two components of the normal vector have directions of longitude and latitude, respectively. To ensure the consistency of the normal vector direction, the direction of the normal vector is determined based on the order of the boundary points and the position of the region center point. If the normal vector points outward from the region, it is reversed, thus ensuring that all normal vectors point inward from the study region.

[0096] Step S5: Interpolation of water vapor transport flux and calculation of normal flux

[0097] The midpoints of each boundary arc segment are obtained using bilinear interpolation. And calculate its water vapor transport flux component in the normal direction.

[0098] Obtaining arcs midpoint Grid points around Bilinear interpolation was performed on the meridional and zonal components of the water vapor transport flux:

[0099] ,

[0100] ,

[0101] In the formula, and These represent the interpolation weights in the longitude and latitude directions, respectively. Representing arc segments midpoint latitude and longitude coordinates;

[0102] The water vapor transport flux vector at the midpoint of the arc segment is obtained as follows:

[0103] ,

[0104] The interpolated water vapor transport flux is projected along the inward normal direction of the arc segment. Arc segment The normal water vapor transport flux is defined as:

[0105] ,

[0106] In the formula, Indicates the first Inward normal water vapor transport flux on each boundary arc segment. This indicates that water vapor is transported along the inward normal direction, that is, water vapor flows from the outside of the region into the inside of the region (input). This indicates the transport of water vapor in the reverse direction of the interior, meaning that water vapor flows from the interior of the region to the exterior (output).

[0107] and These represent the interpolation weights in the longitude and latitude directions, respectively.

[0108] ,

[0109] ,

[0110] Step S6: Calculation of Regional Water Vapor Budget

[0111] Calculate each time point Normal water vapor transport flux within each boundary arc segment , The time interval between each adjacent moment is Then Time-centered The regional water vapor balance within the time interval is:

[0112] ,

[0113] In the formula, This represents the length of the i-th arc segment. .

[0114] Regional water vapor balance over the entire period for:

[0115] ,

[0116] when When, it indicates that the region receives net water vapor input from the outside, and the region is a water vapor sink; when When the region outputs water vapor to the outside, it indicates that the region is a net water vapor source.

[0117] In this embodiment, three-dimensional atmospheric data from Yunnan Province in July and August 2025 were selected to calculate the regional water vapor budget. The data underwent preprocessing, quality control, and standardization. The hourly water vapor transport flux (IVT) for the Yunnan region was then calculated. In step S4, the arc length threshold was set to 25 km. The regional boundary line was discretized, and the length of the boundary arc segments was calculated. The normal vector at the midpoint of each boundary arc segment was calculated, and the consistency of the normal vector direction was determined. Bilinear interpolation was used to obtain the normal vector at the midpoint of each boundary arc segment. The water vapor transport flux component in the normal direction was calculated. Flux integration over the regional boundary yielded a water vapor input of 1.85 * 10^22 m ... 14 kg, water vapor output is 1.36*10 13 kg, the regional water vapor budget is 1.71*10 14 kg, thus obtaining the average hourly water vapor balance of Yunnan Province over two months as 1.15*10 kg. 11 kg.

[0118] The average hourly water vapor balance calculated using the method of this invention (averaging the same hours for each day) is as follows: Figure 2 As shown by the blue curve, for comparison, the same calculation was performed using conventional methods (boundary line spacing calculated as planar distance, nearest neighbor value used instead when calculating water vapor transport flux at the boundary, and boundary lines forced to approximate an east-west or north-south orientation), and the results are as follows. Figure 2 As shown by the orange curve in the middle, the calculated balance of water vapor is greater than that calculated by conventional methods. This is because conventional methods calculate the boundary line distance as a straight line in a plane, while the actual ground is curved, resulting in a smaller calculated distance than the true value, leading to an underestimation of the water vapor balance. In contrast, the method of this invention uses the spherical distance between two points, which is closer to the actual situation.

[0119] Another aspect of the present invention provides a calculation system for a method of calculating water vapor budget in an arbitrary region considering surface curvature, applicable to the aforementioned method of calculating water vapor budget in an arbitrary region considering surface curvature, comprising:

[0120] The data acquisition module is used to collect and preprocess three-dimensional atmospheric data of the study area from the ground to the tropopause for a preset time period.

[0121] The flux calculation module is used to calculate the water vapor transport flux at each horizontal grid point based on three-dimensional atmospheric data and multi-layer atmospheric wind and humidity fields.

[0122] The boundary discretization module is used to construct a sequence of discrete boundary nodes based on the boundary lines of the study area and to calculate the distance between two adjacent boundary points.

[0123] The normal vector calculation module is used to calculate the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes;

[0124] The interpolation component module is used to obtain the water vapor transport flux at the midpoint of each boundary arc segment using the bilinear interpolation method, and to calculate its water vapor transport flux component in the normal direction.

[0125] The income and expenditure calculation module is used to calculate the normal water vapor transport flux within each boundary arc segment at each time point, and further obtain the regional water vapor income and expenditure for the entire period.

[0126] As a preferred embodiment, when calculating the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes, the normal vector calculation module specifically adopts a surface normal vector solution algorithm based on the Earth ellipsoid model to accurately fit the influence of the surface curvature on the spatial orientation of the boundary arc segment.

[0127] While the present invention has been described above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for calculating water vapor deficit in any region considering surface curvature, characterized in that, The steps are as follows: S1. Collect and preprocess three-dimensional atmospheric data of the study area from the ground to the tropopause for a predetermined time period; Includes the following sub-steps: S1.1 Collect three-dimensional atmospheric data, including meridional wind, zonal wind, and specific humidity data for each pressure layer; S1.

2. Conduct quality control on the data, including checking, removing or interpolating missing values ​​and gross errors; S1.

3. Standardize the data, including spatiotemporal matching of data with different spatiotemporal resolutions and standardization of formats and units for data from different sources. S2. Based on the three-dimensional atmospheric data, combined with the multi-layer atmospheric wind field and humidity field, calculate the water vapor transport flux at each horizontal grid point. S3. Construct a discrete boundary node sequence based on the boundary line of the study area, and calculate the arc distance between two adjacent boundary points; S4. Calculate the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes; S5. Use bilinear interpolation to obtain the water vapor transport flux at the midpoint of each boundary arc segment, and calculate its water vapor transport flux component in the normal direction. S6. Calculate the normal water vapor transport flux within each boundary arc segment at each time point, and further obtain the regional water vapor budget for the entire period.

2. The method for calculating water vapor deficit in any region considering surface curvature according to claim 1, characterized in that, Step S2 includes the following sub-steps: S2.1 At each horizontal grid point, assume the preprocessed data is generated by... It consists of several pressure layers, the first The air pressure of the layer is The wind direction is Zonal winds are , more wet than , ; S2.2, For grid points Calculate the pressure difference between two adjacent pressure layers. The average specific humidity between the two layers Average meridional wind Average zonal wind ; S2.3 Calculate the grid points according to the following formulas. The meridional component of water vapor transport flux and latitudinal components : ， ， In the formula, It is the acceleration due to gravity; S2.4 Calculate the meridional and zonal components of the water vapor transport flux at all other grid points.

3. The method for calculating water vapor deficit in any region considering surface curvature according to claim 2, characterized in that, Step S3 includes the following sub-steps: S3.1 Constructing a discrete boundary node sequence based on the boundary lines of the study area Calculate the central angle of the great circle between two adjacent boundary nodes on the sphere. As shown in the following formula: ， In the formula, It is the central angle of the great circle between two adjacent boundary nodes on the sphere, that is, the angle between the lines connecting the two points to the center of the sphere. Represents boundary nodes latitude and longitude coordinates Indicates the next adjacent boundary node latitude and longitude coordinates; S3.2, Calculation and Length between two adjacent boundary points on the sphere As shown in the following formula: ， In the formula, The average radius of the Earth; S3.

3. Set an arc length threshold. When the arc length between two adjacent boundary nodes is greater than the threshold, insert a node between the two adjacent nodes so that the distance between the new node and the original node is less than the threshold, and add the new node to the original boundary node sequence. Then, calculate the arc length distance between all adjacent boundary points segment by segment according to the formulas in steps S3.1 and S3.

2.

4. The method for calculating water vapor deficit in any region considering surface curvature according to claim 3, characterized in that, Step S4 includes the following sub-steps: S4.1 Calculate each pair of adjacent nodes The spherical arc segment formed Tangent vector at the midpoint As shown in the following formula: ， S4.2 Obtain the radial vector from the midpoint of the arc segment to the center of the sphere. : ， In the formula, O represents the center of the Earth. For arc segment The midpoint; S4.3 Calculate the normal vector at the midpoint of the arc segment. for: ， S4.4, normal vector Convert to a two-dimensional vector in the tangent plane at the midpoint of the arc segment , The two components are the longitudinal and latitudinal directions, respectively. Based on the order of the boundary points and the location of the region center point, the direction of the normal vector is determined. If the normal vector points to the outside of the region, the opposite direction is taken to ensure that all normal vectors point to the inside of the study region.

5. The method for calculating water vapor deficit in any region considering surface curvature according to claim 4, characterized in that, Step S5 includes the following sub-steps: S5.1 Obtaining the arc segment midpoint Grid points around Bilinear interpolation is performed on the meridional and zonal components of the water vapor transport flux, respectively, as shown in the following equation: ， ， In the formula, and These represent the interpolation weights in the longitude and latitude directions, respectively; Representing arc segments midpoint latitude and longitude coordinates; S5.2 Calculate the water vapor transport flux vector at the midpoint of the arc segment. As shown in the following formula: ， S5.3 Project the interpolated water vapor transport flux along the inner normal direction of the arc segment. Internal normal water vapor transport flux Defined as follows: ， In the formula, Indicates the first Internal normal water vapor transport flux on each boundary arc segment This indicates that water vapor is transported along the inward normal direction, meaning that water vapor flows from the outside of the region into the inside of the region; This indicates the transport of water vapor in the reverse direction of the interior, meaning that water vapor flows from the interior of the region to the exterior.

6. The method for calculating water vapor deficit in any region considering surface curvature according to claim 5, characterized in that, Interpolation weights in longitude and latitude directions and Calculate as follows; ， 。 7. The method for calculating water vapor budget in any region considering surface curvature according to claim 6, characterized in that, Step S6 includes the following sub-steps: S6.1 Calculate each time step Normal water vapor transport flux within each boundary arc segment , The time interval between each adjacent moment is ,by Time-centered Regional water vapor balance within the time interval for: ， In the formula, This represents the length of the i-th arc segment. .

8. A calculation system for a method of calculating water vapor budget in an arbitrary region considering surface curvature, applied to the method of calculating water vapor budget in an arbitrary region considering surface curvature as described in any one of claims 1-7, characterized in that, include: The data acquisition module is used to collect and preprocess three-dimensional atmospheric data of the study area from the ground to the tropopause over a preset time period; the configuration executes the following steps: S1.1 Collect three-dimensional atmospheric data, including meridional wind, zonal wind, and specific humidity data for each pressure layer; S1.

2. Conduct quality control on the data, including checking, removing or interpolating missing values ​​and gross errors; S1.

3. Standardize the data, including spatiotemporal matching of data with different spatiotemporal resolutions and standardization of formats and units for data from different sources. The flux calculation module is used to calculate the water vapor transport flux at each horizontal grid point based on three-dimensional atmospheric data and multi-layer atmospheric wind and humidity fields. The boundary discretization module is used to construct a sequence of discrete boundary nodes based on the boundary lines of the study area and to calculate the distance between two adjacent boundary points. The normal vector calculation module is used to calculate the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes; The interpolation component module is used to obtain the water vapor transport flux at the midpoint of each boundary arc segment using the bilinear interpolation method, and to calculate its water vapor transport flux component in the normal direction. The income and expenditure calculation module is used to calculate the normal water vapor transport flux within each boundary arc segment at each time point, and further obtain the regional water vapor income and expenditure for the entire period.

9. The calculation system of the method for calculating water vapor budget in any region considering surface curvature according to claim 8, applied to the method for calculating water vapor budget in any region considering surface curvature according to any one of claims 1-7, characterized in that, When calculating the normal vector at the midpoint of the spherical arc segment formed by each pair of adjacent nodes, the normal vector calculation module specifically adopts a surface normal vector solution algorithm based on the Earth ellipsoid model to accurately fit the influence of the surface curvature on the spatial orientation of the boundary arc segment.

Images