A method for calculating the effective operating distance of a water level station

Abstract

This invention relates to the field of marine surveying data processing technology, and particularly to a method for calculating the effective operating distance of a water level station. The method includes the following steps: acquiring raw tidal observation data from the water level station; recording the changes in the raw tidal observation data according to the tidal level observation time to obtain tidal observation data; performing a Fourier transform on the tidal observation data to convert it into frequency domain data, and calculating the amplitude values ​​of each tidal component to obtain tidal amplitude data; performing time-frequency analysis on the tidal observation data to extract the instantaneous tidal frequency; and determining the angular rate of each tidal component based on the instantaneous frequency to obtain tidal angular rate data. This invention uses a harmonic constant tidal level model to calculate the tidal height difference and employs Taylor series expansion to solve the inverse equation to obtain the effective operating distance of the tide gauge station. It also considers factors such as sea surface curvature, tidal amplitude, and tidal angular rate, making the calculation results more realistic and reliable.

Description

Technical Field

[0001] This invention relates to the field of marine surveying data processing technology, and in particular to a method for calculating the effective range of a water level station. Background Technology

[0002] Currently, underwater topographic surveying generally employs single-beam and multi-beam echo sounder systems, primarily using GNSS positioning and echo sounders to measure water depth. Due to operational needs, it is sometimes necessary to convert the depth measurements of underwater measuring points into specific required elevation values ​​(i.e., water level correction). Water level correction involves the control range of each water level station. Currently, given the uncertainty of water level values, the industry generally lacks a relatively mature and fixed model and formula for the effective distance of water level stations, leading to slight differences in water level correction values. The main reasons for this phenomenon can be attributed to the location of water level stations in the observed water area, sea surface curvature, tidal changes at water level stations, the location of measuring points, and the error accuracy indicators of water level stations. Summary of the Invention

[0003] Therefore, it is necessary to provide a method for calculating the effective operating distance of a water level station to solve at least one of the above-mentioned technical problems.

[0004] To achieve the above objective, a method for calculating the effective operating distance of a water level station is provided, the method comprising the following steps:

[0005] Step S1: Obtain raw tidal observation data from the water level station, record the changes in the raw tidal observation data according to the tidal level observation time, and obtain tidal observation data;

[0006] Step S2: Perform Fourier transform on the tidal observation data to convert it into frequency domain data, and calculate the amplitude value of each tidal component to obtain the tidal amplitude data;

[0007] Step S3: Perform time-frequency analysis on the tidal observation data to extract the instantaneous tidal frequency; determine the angular rate of each tidal component based on the instantaneous frequency to obtain the tidal angular rate data;

[0008] Step S4: Perform phase analysis on the tidal observation data to identify the analytical signal of the tidal observation data; extract phase information from the analytical signal and determine the dedicated lag angle of each tidal component to obtain the dedicated lag angle data of the tidal component;

[0009] Step S5: Obtain the Greenwich astronomical phase angle and extract the distance from the observation point to the tide gauge station from the tidal observation data; construct the tidal characteristic derivation formula based on the tidal amplitude, the tidal angular rate, the tidal angular rate, and the distance from the observation point to the tide gauge station; construct the harmonic constant tidal level model based on the tidal amplitude, tidal angular rate, tidal angular rate, and Greenwich astronomical phase angle.

[0010] Step S6: Calculate the tide level at the measuring point based on the harmonic constant tide level model. Calculate the instantaneous tidal height difference between water level stations using the tidal level value and tidal characteristic derivation formula, and output the relationship between tidal height difference and distance. Perform a mathematical transformation on the relationship between tidal height difference and distance, and perform a Taylor series expansion to obtain the Taylor expanded relationship between tidal height difference and distance. Determine the degree of influence of sea surface curvature in the Taylor expanded relationship between tidal height difference and distance, and output the processed tidal height difference equation. Solve the equation inversely based on the tidal height difference equation to find the effective operating distance of the water level station.

[0011] Preferably, step S2 includes the following steps:

[0012] Step S21: Sort the tidal observation data according to timestamps to form a continuous tidal observation time series;

[0013] Step S22: Denoise the continuous tidal observation time series using wavelet transform, process the tidal data using wavelet basis, and remove high-frequency interference signals to obtain tidal time domain data;

[0014] Step S23: Use Fast Fourier Transform to convert the tidal time domain data into tidal frequency domain data; in the tidal frequency domain data, identify the semi-diurnal tide, diurnal tide and long-period tide components to obtain tidal component data;

[0015] Step S24: Separate the frequency signal of each tidal component data to form a tidal frequency domain data sequence;

[0016] Step S25: Traverse each tidal frequency domain data sequence and calculate the average amplitude, maximum amplitude, and minimum amplitude of each tidal frequency domain data sequence to obtain the tidal amplitude data.

[0017] Preferably, step S3 includes the following steps:

[0018] Step S31: Divide the tidal observation data into time slices to obtain tidal observation time segments;

[0019] Step S32: Pair up the data points in each tidal observation time segment, calculate the phase difference between each pair of data points, and calculate the instantaneous frequency based on the phase difference;

[0020] Step S33: Identify whether there are abrupt changes in the instantaneous frequency within adjacent tidal observation time segments, where abrupt changes are defined as instantaneous frequency changes exceeding a preset threshold; if abrupt changes exist, smooth the abrupt change points to obtain smoothed tidal instantaneous frequencies.

[0021] Step S34: Integrate the instantaneous tidal frequency to obtain tidal phase information;

[0022] Step S35: Calculate the tidal phase information with respect to the time derivative of the tidal observation time segment, and calculate the angular rate of the tidal signal within each tidal observation time segment to obtain the tidal angular rate data.

[0023] Preferably, step S4 includes the following steps:

[0024] Step S41: Perform tidal cycle integrity detection on the observation segments in the tidal observation data, select the observation segments with complete tidal cycles, and record them as tidal complete cycle segments;

[0025] Step S42: Within a complete tidal cycle segment, identify the peak and trough data of the tidal signal by comparing the tidal level change trends of adjacent data points;

[0026] Step S43: For the transition area between peak and trough data, determine the transition point data by calculating the extreme points of the tidal level change rate;

[0027] Step S44: In a complete tidal cycle segment, identify the analytical signal of the tidal observation data based on the peak data, trough data, and transition point data;

[0028] Step S45: For the analytical signal of a complete tidal cycle segment, the phase change time interval is obtained by calculating the time difference between adjacent peaks and troughs;

[0029] Step S46: Calculate the average phase change rate of a complete tidal cycle segment based on the phase change time interval; determine the specific lag angle of each tidal component based on the average phase change rate to obtain the tidal specific lag angle data.

[0030] Preferably, step S5, which involves constructing the tidal characteristic derivation formula based on the tidal amplitude, the tidal lag angle, and the distance from the observation point to the tide gauge station, includes:

[0031]

[0032]

[0033] in, For tidal amplitude, This represents the difference in tidal level between tide gauge station A and measuring point X. This represents the difference in tide level between tide gauge station A and measuring point B; This represents the distance from tide gauge station A to measuring point X. This represents the distance from tide gauge station A to measuring point B; The lag angle is specifically designed for tidal division; This represents the specific tidal lag difference between tide gauge station A and measuring point X; This represents the tide-specific lag difference between tide gauge station A and measuring point B.

[0034] Preferably, the construction of the harmonic constant tidal level model based on tidal amplitude, tidal angular rate, tidal lag angle, and Greenwich astronomical phase angle in step S5 includes:

[0035]

[0036] in, Indicates time The tide level at that moment, Indicates the first The tidal node factor is a parameter related to the tidal cycle. Indicates the first The tidal amplitude of each tidal constituent. Indicates the first The tidal angular velocity of each tidal constituent. Greenwich Mean Time (GMT) astronomical phase angle, representing the fixed astronomical reference phase angle at Greenwich Mean Time (GMT). Indicates local time deviation; Indicates the first A specific late angle for each tide. This indicates the number of tidal constituents, representing the tidal constituent components considered in the model.

[0037] Preferably, in step S6, the tide level value at the measuring point is calculated based on the harmonic constant tide level model, the instantaneous tidal height difference between water level stations is calculated using the tidal level value and the tidal characteristic derivation formula, and the relationship between tidal height difference and distance is output, including:

[0038]

[0039] in, Indicates time At any given time, the tidal level difference between measuring point X and water level station A; Indicates time At what time, the tide level at measuring point X; Indicates time At what time, the tide level at tide gauge station A; Indicates the first The amplitude of each tidal constituent at tide gauge station A; Indicates the first The difference in tidal amplitude between measuring point X and tide gauge station A; Indicates the first The specific tidal lag difference between tide gauge station A and measuring point X; Indicates the first The specific tidal lag difference of each constituent tide at tide gauge station A; Indicates the first The specific tidal delay angle difference at tide gauge station A for each tidal constituent.

[0040] Preferably, in step S6, the instantaneous tidal height difference relationship is mathematically transformed and subjected to Taylor series expansion to obtain the Taylor expanded tidal height difference versus distance relationship, including:

[0041]

[0042] In the formula:

[0043]

[0044]

[0045] in, , , They are respectively with the first Coefficients of nonlinear terms related to each tidal phase; , , They are respectively with the first Phase angles related to each tidal constituent; Indicates the first The specific tidal lag difference between reference point B and water level station A for each tidal constituent; This represents the distance from measuring point X to water level station A.

[0046] Preferably, in step S6, the degree of influence of sea surface curvature in the Taylor expansion of the tidal height difference versus distance equation is determined, and the processed tidal height difference equation is output, including:

[0047] According to the difference in tidal latitude The influence of the nonlinear term coefficients on sea surface curvature is assessed, and the following is given: Substituting into the approximate expression for tidal difference, we get:

[0048]

[0049] in, This indicates the permissible tidal level difference threshold, used to determine the effective operating distance of the water level station.

[0050] Preferably, in step S6, the effective operating distance of the water level station is determined by inversely solving the equation based on the tidal height difference, including:

[0051] Solve the tidal difference equation to obtain the effective operating distance of the water level station. d；

[0052] Select comprehensive indicators based on the required accuracy of water level station measurements:

[0053] ;

[0054] ;

[0055] in, Indicates time The effective range of the changing water level station Represents all the calculations obtained The minimum value in; express The average value.

[0056] The beneficial effects of this invention are as follows: By acquiring raw tidal observation data from water level stations and recording changes according to the tidal level observation time, tidal observation data is obtained. This process ensures the integrity and temporal continuity of the data, providing high-quality basic data for subsequent accurate analysis and avoiding calculation errors caused by missing data or time discontinuity. The tidal observation data is then subjected to a Fourier transform to convert it into frequency domain data, and the amplitude values ​​of each tidal component are calculated to obtain tidal amplitude data. The Fourier transform can decompose complex tidal signals into tidal components of different frequencies, allowing the amplitude characteristics of each tidal component to be clearly presented, providing crucial frequency domain information for subsequent analysis and contributing to a deeper understanding of the periodic characteristics of tides. Time-frequency analysis is performed on the tidal observation data to extract the instantaneous tidal frequency; based on the instantaneous frequency, the angular rate of each tidal component is determined to obtain tidal angular rate data. Time-frequency analysis captures the dynamic changes of tidal signals in time and frequency, extracts instantaneous frequencies, and further determines the tidal angular rate, providing an important basis for analyzing the dynamic characteristics of tides and making the description of tidal variation patterns more accurate and comprehensive. Phase analysis is performed on tidal observation data to identify the analytical signals; phase information is extracted from the analytical signals, and the specific lag angles of each tidal component are determined, resulting in tidal lag angle data. Phase analysis reveals the phase characteristics of tidal signals, and by extracting specific lag angles, the description of tidal signals is further improved, making the grasp of tidal phase information more accurate and providing key phase parameters for subsequent model construction. The Greenwich astronomical phase angle is obtained, and the distance from the observation point to the tide gauge station in the tidal observation data is extracted; tidal characteristic derivation formulas are constructed based on tidal amplitude, tidal angular rate, tidal lag angle, and the distance from the observation point to the tide gauge station; a harmonic constant tidal level model is constructed based on tidal amplitude, tidal angular rate, tidal lag angle, and Greenwich astronomical phase angle. This process integrates multiple key parameters to construct a harmonic constant tidal level model that accurately reflects the tidal variation pattern. This provides a solid theoretical foundation for subsequent tidal level calculations and the determination of the effective operating distance of water level stations, enabling the model to more accurately simulate tidal phenomena. The process involves calculating the tidal level at the measuring points based on the harmonic constant tidal level model, calculating the instantaneous tidal height difference between water level stations using the tidal level values ​​and tidal characteristic derivations, and outputting the relationship between tidal height difference and distance. This relationship is then mathematically transformed and expanded using Taylor series to obtain the Taylor-expanded relationship between tidal height difference and distance. The influence of sea surface curvature in the Taylor-expanded relationship between tidal height difference and distance is determined, and the processed tidal height difference equation is output. Finally, the effective operating distance of the water level station is calculated by inversely solving the equation based on the tidal height difference equation. This series of operations, through mathematical transformations and Taylor series expansions, conducted a refined analysis of the relationship between tidal height difference and distance, accurately determined the degree of influence of sea surface curvature, and finally solved the effective range of the water level station, realizing the precise quantification of the water level station's range of influence, and providing strong support for the optimization of water level station layout and the improvement of tidal monitoring accuracy. Attached Figure Description

[0057] Figure 1 A flowchart illustrating the steps involved in calculating the effective operating distance of a water level station;

[0058] Figure 2 for Figure 1 A detailed flowchart illustrating the implementation steps of step S4.

[0059] Figure 3 A schematic diagram showing the locations of the water level stations;

[0060] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0061] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0062] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0063] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0064] To achieve the above objectives, please refer to Figures 1 to 3 A method for calculating the effective operating distance of a water level station, the method comprising the following steps:

[0065] Step S1: Obtain raw tidal observation data from the water level station, record the changes in the raw tidal observation data according to the tidal level observation time, and obtain tidal observation data;

[0066] In this embodiment of the invention, a connection is established between a dedicated data acquisition terminal and the water level station via a communication interface. This communication interface adopts the internationally standardized RS232 serial communication protocol, with a baud rate of 9600 bps, 8 data bits, 1 stop bit, and no parity bit. The data acquisition terminal requests the water level station to transmit the raw tidal observation data stored in its internal memory by sending a preset set of instructions. After receiving the instructions, the water level station sends the raw tidal observation data frame by frame to the data acquisition terminal according to a preset data format. Each frame of data includes the tide level value, the observation timestamp, and a data checksum. The tide level value is represented in 16-bit binary floating-point format, the observation timestamp is in UTC time format accurate to the second, and the data checksum is generated using the CRC-16 cyclic redundancy check algorithm. After receiving each frame of data, the data acquisition terminal first verifies the data checksum. If the verification passes, the frame data is stored in the local buffer; if the verification fails, the frame data is discarded and the water level station is requested to retransmit it. After receiving all the data, the data acquisition terminal batches the raw tidal observation data stored in the buffer to the data processing server. The transmission uses the FTP protocol, port 21, and the username and password are preset authorization credentials. On the data processing server, dedicated data parsing software runs. This software, developed in C++, employs a multi-threaded processing mechanism to improve data parsing efficiency. The parsing software first reads the transmitted raw tidal observation data file, parsing the tide level value and observation timestamp for each data point according to the frame structure. It converts the tide level value from 16-bit binary floating-point format to decimal floating-point format in meters, and simultaneously converts the observation timestamp from UTC time format to the local standard time format, accurate to milliseconds. Subsequently, the software sorts the parsed data using the observation timestamp as an index, ensuring the data is arranged in chronological order of observation time. For the sorted data, the software further performs a time series integrity check. If any missing observation time intervals are found, the software estimates the tide level value for the missing time points using a cubic spline interpolation algorithm based on the tide level change trends of adjacent data points. Specifically, the software uses two valid observation points before and after the missing time point as boundaries to calculate the coefficients of the cubic spline interpolation function. Then, it uses this function to solve for the tide level at the missing time point, ensuring the continuity of the tidal observation data over time. After this processing, the resulting tidal observation data is stored in a structured table format in the server's database. The table contains two columns: one for the observation time (hours, minutes, and seconds); and the other for the corresponding tide level (meters), rounded to three decimal places.

[0067] Step S2: Perform Fourier transform on the tidal observation data to convert it into frequency domain data, and calculate the amplitude value of each tidal component to obtain the tidal amplitude data;

[0068] In this embodiment of the invention, tidal observation data generated in step S1 is read from the database. This data includes tidal level observations arranged in a time series and their corresponding observation times. To convert the tidal observation data from the time domain to the frequency domain, a Fast Fourier Transform (FFT) algorithm is used for processing. The FFT algorithm is implemented based on a numerical computing library. Its input is the tidal level value sequence of the tidal observation data, with a length of N, where N is a power of 2 to ensure the efficiency of the FFT algorithm. If the original length of the tidal observation data does not meet this condition, it is extended to the nearest power of 2 length by padding with zeros. During the FFT processing, the sampling frequency is set to 1 / Δt, where Δt is the time interval of the tidal observation data in seconds. The FFT algorithm converts the tidal level value sequence into complex frequency domain data, and the output contains N frequency components, each corresponding to a frequency value and its corresponding complex amplitude. The formula for calculating the frequency value is f=k / (NΔt), where k is the index of the frequency component, ranging from 0 to N-1. Subsequently, the frequency domain data was analyzed to extract the amplitude values ​​of each tidal component. Based on tidal theory, the theoretical frequencies of the major tidal components are known; for example, the frequency of the M2 tidal component is approximately 1.9323 times / day, and the frequency of the S2 tidal component is approximately 2.0 times / day. The amplitude value of each frequency component is obtained by calculating the modulus of its complex amplitude. Specifically, for each complex component A(k) in the frequency domain data, the amplitude value is calculated using the formula |A(k)|=sqrt(Re[A(k)]²+Im[A(k)]²), where Re[A(k)] and Im[A(k)] are the real and imaginary parts of the complex component A(k), respectively. Finally, the extracted amplitude values ​​of each tidal component are stored as tidal amplitude data. The data format includes the tidal component identifier (e.g., M2, S2, etc.), the corresponding frequency value, and the amplitude value. The tidal amplitude data is stored in tabular form, with the frequency value in units of times / day and the amplitude value in units of meters.

[0069] Step S3: Perform time-frequency analysis on the tidal observation data to extract the instantaneous tidal frequency; determine the angular rate of each tidal component based on the instantaneous frequency to obtain the tidal angular rate data;

[0070] In this embodiment of the invention, tidal observation data generated in step S1 is read from the storage system. This data is a sequence of tidal levels changing over time, with a time interval of Δt in seconds. Wavelet transform technology is used to perform time-frequency analysis on the tidal observation data. The Morlet wavelet is selected as the mother wavelet, with its parameter ω0 fixed at 6 to balance time and frequency resolution. The scale range of the wavelet transform is set from 2 to 128, divided into 128 scale steps to cover different frequency components in the tidal signal. The tidal observation data is analyzed point-by-point by the wavelet transform processing module. At each time point, the wavelet coefficients of the tidal observation data at different scales are calculated. The wavelet transform module outputs a wavelet coefficient matrix, where the horizontal axis represents time and the vertical axis represents scale. Subsequently, modulus maxima analysis is performed on the wavelet coefficient matrix. At each time point, modulus maxima points are found along the scale direction; these points correspond to local frequency components of the signal. The modulus maxima analysis module determines the location of the modulus maxima points by comparing the wavelet coefficients of adjacent scales. Instantaneous frequency information is extracted based on the location of the modulus maxima points. Instantaneous frequency extraction is based on the relationship between scale and frequency in wavelet transform, achieved by converting the scale corresponding to the modulus maxima into frequency values. The unit of instantaneous frequency is Hertz (Hz). The instantaneous angular rate of the tidal signal is obtained by converting the Hertz unit to angular rate units (radians per second). The specific conversion formula is to multiply the Hertz value by 2π to obtain the instantaneous angular rate sequence. To determine the angular rate of each tidal component, the extracted instantaneous angular rate sequence is matched with the known theoretical frequencies of the tidal components. According to tidal theory, the theoretical frequency of the M2 tidal component is approximately 1.9323 times / day, and the theoretical frequency of the S2 tidal component is approximately 2.0 times / day. By comparing the instantaneous angular rate sequence with these theoretical frequencies, the angular rate corresponding to each tidal component is identified. For each tidal component, its angular rate value at different time points is recorded. Finally, the angular rate data of each tidal component is stored as tidal angular rate data, with the data format including the tidal component identifier, time series, and corresponding angular rate value in radians per second. Tidal angular rate data are stored in a structured tabular format in the database, providing accurate frequency characteristic information for subsequent calculations of the effective operating distance of water level stations.

[0071] Step S4: Perform phase analysis on the tidal observation data to identify the analytical signal of the tidal observation data; extract phase information from the analytical signal and determine the dedicated lag angle of each tidal component to obtain the dedicated lag angle data of the tidal component;

[0072] In this embodiment of the invention, in step S4, tidal observation data is first read from the storage system. This data is a sequence of tide levels changing over time, with a time interval of Δt in seconds. For phase analysis, a Hilbert transform is applied to the tidal observation data. The Hilbert transform multiplies the tidal observation data by a specific filter function (1 / πt), where t is the time variable, through a convolution operation. This convolution operation generates an analytical signal of the tidal observation data. The real part of the analytical signal is the original tidal observation data, and the imaginary part is the signal after the Hilbert transform. The amplitude and phase information of the analytical signal can be extracted as follows: the amplitude is the modulus of the analytical signal, i.e., the square root of the sum of the squares of the real and imaginary parts; the phase is the argument of the analytical signal, i.e., the arctangent of the imaginary and real parts. By calculating the argument of the analytical signal, the instantaneous phase sequence of the tidal observation data is obtained, in radians. To determine the specific lag angle of each tidal component, the extracted instantaneous phase sequence needs to be compared with the known theoretical phases of the tidal components. According to tidal theory, the theoretical phase relationships of the major tidal components (such as M2, S2, etc.) are known. By fitting the instantaneous phase sequence to these theoretical phases, the difference between the actual observed phase and the theoretical phase is calculated, thus obtaining the specific lag angle of each tidal component. The specific lag angle reflects the phase delay of the tidal signal during propagation, and its unit is radians. Finally, the specific lag angle data of each tidal component are compiled into tidal specific lag angle data, the data format of which includes the tidal component identifier, time series, and corresponding specific lag angle value. The tidal specific lag angle data is stored in tabular form, providing accurate phase characteristic information for subsequent calculation of the effective operating distance of water level stations.

[0073] Step S5: Obtain the Greenwich astronomical phase angle and extract the distance from the observation point to the tide gauge station from the tidal observation data; construct the tidal characteristic derivation formula based on the tidal amplitude, the tidal angular rate, the tidal angular rate, and the distance from the observation point to the tide gauge station; construct the harmonic constant tidal level model based on the tidal amplitude, tidal angular rate, tidal angular rate, and Greenwich astronomical phase angle.

[0074] In this embodiment of the invention, the Greenwich Mean Time (GMTA) is first obtained through an astronomical data service interface. This data service provides real-time astronomical phase angle information with an accuracy down to the second level, measured in degrees. The Greenwich Mean Time is calculated based on the Earth's rotation and celestial motion, and is used to describe the Earth's position relative to a reference celestial body (such as the Moon or the Sun). Next, the distance information from the observation point to the tide gauge station is extracted from the tidal observation data. Using Geographic Information System (GIS) technology, combined with the geographic coordinates (longitude and latitude) of the observation point and the tide gauge station, the great circle distance between them is calculated. Specifically, the longitude and latitude coordinates of the observation point and the tide gauge station are input into the GIS software, and the spherical distance calculation tool is used to output the distance value between them, measured in kilometers. Subsequently, based on the tidal amplitude data obtained in step S2, the tidal angular rate data obtained in step S3, and the tidal lag angle data obtained in step S4, a tidal characteristic derivation formula is constructed. The specific operation is as follows: The tidal amplitude is used as the amplitude component of the tidal signal; the tidal angular rate multiplied by a time variable (in seconds) is used as the phase change component; and the tidal lag angle is used as the phase shift component. For each tidal component (such as M2, S2, etc.), these parameters are combined into a tidal characteristic expression to describe the dynamic changes of the tidal signal. Furthermore, a harmonic constant tidal level model is constructed by combining the Greenwich Mean Time (GMT) astronomical phase angle. Specifically, the GMT astronomical phase angle is used as the astronomical phase reference, multiplied by the tidal angular rate to obtain the astronomical phase change component, and then added to the tidal lag angle to form a complete phase expression. For each tidal component, the tidal amplitude, tidal angular rate, tidal lag angle, and GMT astronomical phase angle are combined to generate the parameters of the harmonic constant tidal level model. These parameters can predict tidal level changes based on a given time point and astronomical phase angle. After completing the above operations, the parameters of the harmonic constant tidal level model (including tidal amplitude, tidal angular rate, tidal lag angle, and Greenwich astronomical phase angle) are organized into a structured data format and stored in the database. These parameters will provide a complete tidal characteristic description for subsequent calculations of the effective operating distance of water level stations.

[0075] Step S6: Calculate the tide level at the measuring point based on the harmonic constant tide level model. Calculate the instantaneous tidal height difference between water level stations using the tidal level value and tidal characteristic derivation formula, and output the relationship between tidal height difference and distance. Perform a mathematical transformation on the relationship between tidal height difference and distance, and perform a Taylor series expansion to obtain the Taylor expanded relationship between tidal height difference and distance. Determine the degree of influence of sea surface curvature in the Taylor expanded relationship between tidal height difference and distance, and output the processed tidal height difference equation. Solve the equation inversely based on the tidal height difference equation to find the effective operating distance of the water level station.

[0076] In this embodiment of the invention, the tidal level at the measuring point is first calculated using the harmonic constant tidal level model. Based on the harmonic constant tidal level model constructed in step S5, the current time point and Greenwich astronomical phase angle are input, and the tidal amplitude, tidal angular rate, and tidal lag angle are combined to calculate the tidal level at the measuring point. This calculation is performed using numerical calculation tools to ensure millimeter-level accuracy. Next, the instantaneous tidal height difference between water level stations is calculated using the calculated tidal level values ​​at the measuring point. Specifically, two water level stations are selected as the calculation objects, and their tidal level values ​​at the same time point are calculated respectively. Then, the difference between the two is obtained to obtain the instantaneous tidal height difference. This tidal height difference is calculated using difference operations to ensure time synchronization. Subsequently, the instantaneous tidal height difference is correlated with the distance between water level stations, and the relationship between tidal height difference and distance is output. Using data fitting techniques, the tidal height difference is used as the dependent variable, and the distance between water level stations is used as the independent variable to fit the relationship curve between the two. The least squares method is used to fit this curve to ensure fitting accuracy. Next, the relationship between tidal height difference and distance is mathematically transformed and expanded using a Taylor series. Specifically, the Taylor series expansion is performed on the relationship at a specific point (e.g., when the distance is zero), yielding the expanded Taylor series. The order of the Taylor series expansion is determined based on practical needs, typically to the third or fourth order to ensure accuracy. The influence of sea surface curvature on the tidal height difference is then determined within the expanded Taylor series. By analyzing the coefficients of higher-order terms in the Taylor expansion, the influence of sea surface curvature on the tidal height difference is identified. Specifically, the coefficients of higher-order terms in the Taylor expansion are compared with known sea surface curvature parameters to determine the degree of influence. Finally, the effective range of the water level station is calculated by inversely solving the equation based on the processed tidal height difference equation. Specifically, the processed tidal height difference equation is set to zero, and the equation is solved using numerical methods (such as Newton's iteration method) to obtain the effective range of the water level station. The calculated distance, in kilometers, is stored in a database to provide a basis for subsequent optimization of the water level station layout.

[0077] Of particular importance, step S1 includes the following steps:

[0078] Step S11: Obtain raw tidal observation data from the water level station and detect the rate of tidal level change in the raw tidal observation data;

[0079] Step S12: By comparing the tidal level change rates of adjacent data points, identify abrupt change points and mark them as outliers;

[0080] Step S13: Perform linear interpolation correction on the marked outliers, and smooth the corrected data with a preset time window to obtain smoothed tidal observation data;

[0081] Step S14: Identify the turning points of tidal rise and fall in the tidal observation smoothing data and record them as the boundary points of the tidal observation sub-data segments;

[0082] Step S15: Divide the smoothed tidal observation data into tidal observation sub-data segments based on the boundary points, calculate the average, maximum and minimum values ​​of the tide level respectively, and record the duration of each tidal observation sub-data segment to obtain the tidal observation data.

[0083] In this embodiment of the invention, in step S11, raw tidal observation data is obtained from the water level station. This data includes tidal level values ​​and their corresponding timestamps, with a time interval of Δt in seconds. The rate of change of tidal level is calculated using numerical differentiation techniques, which is the difference between tidal level values ​​at adjacent time points divided by the time interval Δt. Specifically, for each time point t_i, the rate of change of tidal level ΔH_i = (H_{i+1} - H_{i}) / Δt is calculated, where H_{i} and H_{i+1} are the tidal level values ​​at time points t_i and t_{i+1}, respectively. In step S12, abrupt changes are identified by comparing the rate of change of tidal level of adjacent data points. A threshold ΔH_th is set to determine whether the rate of change of tidal level is abnormal. Specifically, for each time point t_i, if |ΔH_i - ΔH_{i-1}| > ΔH_th, then the point is marked as an outlier. The threshold ΔH_th is determined empirically based on historical data, with units of meters per second. In step S13, linear interpolation correction is performed on the marked outliers. For each outlier point t_i, linear interpolation is performed using its adjacent normal data points. Specifically, if t_i is an outlier, the corrected tide level H'_i = H_{i-1} + (H_{i+1} - H_{i-1}) × (t_i - t_{i-1}) / (t_{i+1} - t_{i-1}). Subsequently, the corrected data is smoothed using a moving average method, with a time window of W in seconds. Specifically, for each time point t_i, the average tide level within the time window W is calculated as H_{smooth,i} = (1 / W) × Σ_{j=iW / 2}^{i+W / 2}H'_j, where H'_j is the corrected tide level. In step S14, the tidal rise and fall inflection points of the smoothed tidal observation data are identified. Inflection points are identified by calculating the sign change of the tidal level change rate between adjacent time points. Specifically, for each time point t_i, if ΔH_{i}×ΔH_{i+1}<0, then t_i is marked as an inflection point and recorded as the boundary point of the tidal observation sub-data segment. In step S15, the smoothed tidal observation data is divided into tidal observation sub-data segments based on the boundary points. For each sub-data segment, the average, maximum, and minimum tidal levels are calculated. Specifically, for each sub-data segment, the average tidal level H_{avg}=(1 / N)×Σ_{i=1}^{N}H_{smooth,i}, the maximum tidal level H_{max}=max(H_{smooth,i}), and the minimum tidal level H_{min}=min(H_{smooth,i}), where N is the length of the sub-data segment. At the same time, the duration of each sub-data segment is recorded as T=N×Δt, in seconds.The final tidal observation data includes the average tidal level, maximum tidal level, minimum tidal level, and duration of each sub-data segment, which are stored in the database to provide basic data support for subsequent analysis.

[0084] Preferably, step S2 includes the following steps:

[0085] Step S21: Sort the tidal observation data according to timestamps to form a continuous tidal observation time series;

[0086] Step S22: Denoise the continuous tidal observation time series using wavelet transform, process the tidal data using wavelet basis, and remove high-frequency interference signals to obtain tidal time domain data;

[0087] Step S23: Use Fast Fourier Transform to convert the tidal time domain data into tidal frequency domain data; in the tidal frequency domain data, identify the semi-diurnal tide, diurnal tide and long-period tide components to obtain tidal component data;

[0088] Step S24: Separate the frequency signal of each tidal component data to form a tidal frequency domain data sequence;

[0089] Step S25: Traverse each tidal frequency domain data sequence and calculate the average amplitude, maximum amplitude, and minimum amplitude of each tidal frequency domain data sequence to obtain the tidal amplitude data.

[0090] In this embodiment of the invention, tidal observation data is obtained from a water level station. This data includes tidal levels and their corresponding timestamps. These data are sorted in ascending order of timestamps to form a continuous tidal observation time series. Specifically, each line of a data file is read, the timestamp field is extracted, and all records are sorted according to the chronological order of the timestamps to ensure that the tidal levels are arranged in chronological order, thus obtaining a continuous tidal observation time series. In step S22, the continuous tidal observation time series is denoised. Wavelet transform technology is used, and the Morlet wavelet is selected as the wavelet basis. The scale range of the wavelet transform is set from 2 to 128, divided into 128 scale steps. Specifically, the sorted tidal time series is subjected to wavelet transform, decomposing the signal into wavelet coefficients of different scales. By analyzing the distribution of the wavelet coefficients, high-frequency interference signals are identified and removed. High-frequency interference signals usually correspond to abrupt changes in the high-frequency bands of the wavelet coefficients. By setting these high-frequency wavelet coefficients to zero, denoising of the original signal is achieved. Finally, the denoised signal is reconstructed into tidal time-domain data using inverse wavelet transform. In step S23, the denoised tidal time-domain data is converted into frequency-domain data. Fast Fourier Transform (FFT) is used to convert the time-domain data into frequency-domain data. Specifically, the denoised tidal time series is input into the FFT algorithm, and the sampling frequency is set to 1 / Δt, where Δt is the time interval of the time series in seconds. The FFT algorithm outputs frequency-domain data, including frequency components and their corresponding amplitude values. In the frequency-domain data, based on the known frequency ranges of the tidal constituents, semi-diurnal, diurnal, and long-period tides are identified. For example, the frequency range of a semi-diurnal tide is approximately 1.9323 times / day, the frequency range of a diurnal tide is approximately 1.0 times / day, and the frequency range of a long-period tide is typically below 0.1 times / day. By filtering the data within these frequency ranges, the tidal constituent data is obtained. In step S24, the frequency signal of each tidal constituent data is separated to form a tidal frequency-domain data sequence. The specific operation is as follows: For each identified tidal component, its corresponding frequency signal is extracted. Based on the frequency values, the tidal component data are stored as independent frequency domain data sequences, each sequence containing the frequency component and its amplitude value. For example, the frequency signals of the semi-diurnal tide are stored as one sequence, the frequency signals of the diurnal tide as another sequence, and so on. In step S25, each tidal frequency domain data sequence is traversed, and the average amplitude, maximum amplitude, and minimum amplitude of each sequence are calculated. Specifically, for each tidal frequency domain data sequence, the sum of all amplitude values ​​in the sequence is calculated and divided by the number of data points to obtain the average amplitude. The maximum and minimum amplitude values ​​are found in the sequence and recorded as the maximum amplitude and minimum amplitude, respectively. In this way, the amplitude data of each tidal component, including the average amplitude, maximum amplitude, and minimum amplitude, are obtained.

[0091] Of particular importance, step S25 includes the following steps:

[0092] Step S251: For each tidal frequency domain data sequence, identify the trend change points in the sequence by comparing the differences between adjacent data points;

[0093] Step S252: At the identified trend change points, calculate the average amplitude, maximum amplitude, and minimum amplitude of the previous sequence segment respectively;

[0094] Step S253: Repeat step S252 in the sequence after the trend change point until the entire tidal frequency domain data sequence has been processed;

[0095] Step S254: For each tidal frequency domain data sequence, determine a weighting factor based on the calculated average amplitude, maximum amplitude, and minimum amplitude, wherein the weighting factor is based on the degree of amplitude variation in each segment of the sequence;

[0096] Step S255: Use a weighting factor to perform a weighted average of the amplitude data of each segment to obtain the final tidal amplitude data;

[0097] Step S256: Compare the final tidal amplitude data with the preset amplitude threshold to identify abnormal amplitude data;

[0098] Step S257: For the identified abnormal amplitude data, repeat steps S251 to S255 until the amplitude data of all tidal frequency domain data sequences are within the preset amplitude threshold range.

[0099] In this embodiment of the invention, in step S251, for each tidal frequency domain data sequence, the difference between adjacent data points is calculated sequentially. Specifically, starting from the first data point in the sequence, the difference between the current data point and the previous data point is calculated one by one. If the sign of the difference changes, i.e., from positive to negative or from negative to positive, the current data point is marked as a trend change point, and its position is recorded. In step S252, for a segment of the sequence before the identified trend change point, the average amplitude, maximum amplitude, and minimum amplitude of that segment are calculated. Specifically, the range of the data segment before the trend change point is determined, and statistical analysis is performed on that segment. The average amplitude is calculated as the sum of all amplitude values ​​in that segment divided by the number of data points; the maximum amplitude is the maximum amplitude value in that segment; and the minimum amplitude is the minimum amplitude value in that segment. In step S253, starting from the sequence after the trend change point, the operation of step S252 is repeated. The process continues to identify new trend change points, and calculates the average amplitude, maximum amplitude, and minimum amplitude for the sequence segment preceding each newly identified trend change point. This process continues until the entire tidal frequency domain data sequence is processed, and the amplitude statistics for each segment are recorded. In step S254, for each tidal frequency domain data sequence, a weighting factor is determined based on the degree of amplitude change in each segment. Specifically, the amplitude change range of each sequence segment is calculated, i.e., the difference between the maximum and minimum amplitudes. The weighting factor is assigned according to the size of the amplitude change range; the larger the amplitude change range, the smaller the corresponding weighting factor. For example, if the amplitude change range is large, a smaller weighting factor is used; if the amplitude change range is small, a larger weighting factor is used. In step S255, the amplitude data of each segment is weighted and averaged using the weighting factor. Specifically, for each sequence segment, the weighted average amplitude is calculated, i.e., the average amplitude of that segment is multiplied by the corresponding weighting factor. The weighted average amplitudes of all segments are summed to obtain the final tidal amplitude data. In step S256, the final tidal amplitude data is compared with a preset amplitude threshold. Specifically, an amplitude threshold range is set, and each tidal amplitude data point is compared to see if it falls within this range. If the amplitude data exceeds the threshold range, it is identified as abnormal amplitude data. In step S257, for the identified abnormal amplitude data, steps S251 to S255 are repeated. Specifically, starting from the location of the abnormal amplitude data, the process of identifying trend change points, calculating amplitude statistics, determining weighting factors, and performing weighted averaging is repeated until the amplitude data of all tidal frequency domain data sequences are within the preset amplitude threshold range. The final tidal amplitude data meets the preset amplitude threshold requirements, providing accurate amplitude information for subsequent analysis.

[0100] Preferably, step S3 includes the following steps:

[0101] Step S31: Divide the tidal observation data into time slices to obtain tidal observation time segments;

[0102] Step S32: Pair up the data points in each tidal observation time segment, calculate the phase difference between each pair of data points, and calculate the instantaneous frequency based on the phase difference;

[0103] Step S33: Identify whether there are abrupt changes in the instantaneous frequency within adjacent tidal observation time segments, where abrupt changes are defined as instantaneous frequency changes exceeding a preset threshold; if abrupt changes exist, smooth the abrupt change points to obtain smoothed tidal instantaneous frequencies.

[0104] Step S34: Integrate the instantaneous tidal frequency to obtain tidal phase information;

[0105] Step S35: Calculate the tidal phase information with respect to the time derivative of the tidal observation time segment, and calculate the angular rate of the tidal signal within each tidal observation time segment to obtain the tidal angular rate data.

[0106] In this embodiment of the invention, in step S31, the tidal observation data is processed by time segmentation. Based on the timestamps of the tidal observation data, the entire data sequence is divided into multiple time segments. The length of each time segment is set to ΔT, in seconds. Specifically, starting from the beginning time of the data sequence, a segment of data is extracted every ΔT time interval to form a tidal observation time segment. For example, if ΔT is set to 3600 seconds (1 hour), each data segment contains all tidal level observation data points within that hour. In step S32, the data points within each tidal observation time segment are paired. Specifically, within each time segment, two adjacent data points are selected sequentially, and the phase difference between them is calculated. The phase difference is calculated based on the phase information of the data points, using the phase difference formula. Subsequently, the instantaneous frequency is calculated based on the phase difference. The instantaneous frequency is calculated by dividing the phase difference by the time interval; that is, the instantaneous frequency equals the phase difference divided by the time difference Δt between the two data points, in Hertz. In step S33, it is identified whether there are abrupt changes in the instantaneous frequency within adjacent tidal observation time segments. The specific operation is as follows: Compare the changes in instantaneous frequency within adjacent time segments. Set a frequency change threshold Δf_th, in Hertz. If the change in instantaneous frequency within adjacent time segments exceeds this threshold, i.e., |Δf|>Δf_th, a sudden change is identified. For the identified sudden change points, smoothing is performed. The smoothing process uses a moving average method, taking several data points before and after the sudden change point as the center and averaging them to obtain the smoothed instantaneous frequency value. In step S34, the smoothed tidal instantaneous frequency is integrated to obtain tidal phase information. The specific operation is as follows: Integrate the instantaneous frequency value within each time segment. The integration process uses a numerical integration method, such as the trapezoidal integral method. Using each time point within the time segment as the integration interval, multiply the instantaneous frequency value by the time interval Δt and sum them to obtain the tidal phase change within that time segment. Accumulate the phase changes of all time segments to obtain complete tidal phase information. In step S35, perform time derivative calculation on the tidal phase information with respect to the tidal observation time segment. The specific operation is as follows: Differential calculations are performed on the tidal phase information within each time segment to calculate the phase difference between adjacent time points. This difference is then divided by the time interval Δt to obtain the angular rate of the tidal signal within that time segment. The unit of angular rate is radians per second. The angular rate values ​​within each time segment are recorded to form tidal angular rate data.

[0107] Preferably, step S4 includes the following steps:

[0108] Step S41: Perform tidal cycle integrity detection on the observation segments in the tidal observation data, select the observation segments with complete tidal cycles, and record them as tidal complete cycle segments;

[0109] Step S42: Within a complete tidal cycle segment, identify the peak and trough data of the tidal signal by comparing the tidal level change trends of adjacent data points;

[0110] Step S43: For the transition area between peak and trough data, determine the transition point data by calculating the extreme points of the tidal level change rate;

[0111] Step S44: In a complete tidal cycle segment, identify the analytical signal of the tidal observation data based on the peak data, trough data, and transition point data;

[0112] Step S45: For the analytical signal of a complete tidal cycle segment, the phase change time interval is obtained by calculating the time difference between adjacent peaks and troughs;

[0113] Step S46: Calculate the average phase change rate of a complete tidal cycle segment based on the phase change time interval; determine the specific lag angle of each tidal component based on the average phase change rate to obtain tidal specific lag angle data.

[0114] In this embodiment of the invention, in step S41, tidal cycle integrity detection is performed on the observation segments in the tidal observation data. Specifically, the time range of the tidal observation data is first determined, and then the duration of each observation segment is calculated. A tidal cycle integrity threshold, such as 24 hours, is set to determine whether an observation segment contains a complete tidal cycle. If the duration of an observation segment is greater than or equal to the threshold, the segment is considered to have a complete tidal cycle and is recorded as a complete tidal cycle segment. In step S42, within the complete tidal cycle segment, the peak and trough data of the tidal signal are identified by comparing the tidal level change trends of adjacent data points. Specifically, the data points within each complete tidal cycle segment are analyzed point by point, and the tidal level change trend between adjacent data points is calculated. When the tidal level changes from rising to falling, the point is marked as peak data; when the tidal level changes from falling to rising, the point is marked as trough data. In step S43, for the transition region between peak and trough data, the transition point data is determined by calculating the extreme points of the tidal level change rate. The specific operation is as follows: Within the data segment between the crest and trough, calculate the tidal level change rate for each data point, which is the difference in tidal level between adjacent data points divided by the time interval. Find the points corresponding to the maximum and minimum values ​​of the tidal level change rate, and use them as transition point data from crest to trough and from trough to crest, respectively. In step S44, within the complete tidal cycle segment, identify the analytical signal of the tidal observation data based on the crest data, trough data, and transition point data. Specifically, use the crest data, trough data, and transition point data as key feature points, and reconstruct the analytical signal of the tidal signal by combining the tidal level change trend between these points. The analytical signal reflects the complete periodic characteristics of the tidal signal, including the rise and fall of the tidal level and the positions of the crests and troughs. In step S45, for the analytical signal of the complete tidal cycle segment, obtain the phase change time interval by calculating the time difference between adjacent crests and troughs. Specifically, within each complete tidal cycle segment, calculate the time difference between adjacent crests and troughs sequentially, i.e., the time interval from crest to trough and the time interval from trough to crest. These time intervals reflect the phase change period of the tidal signal. In step S46, the average phase change rate of a complete tidal cycle segment is calculated based on the phase change time intervals. Specifically, the average phase change time interval is obtained by averaging all phase change time intervals within each complete tidal cycle segment. Then, the average phase change rate is obtained by dividing 2π by the average phase change time interval, in radians per second. Based on the average phase change rate and combined with the known theoretical phase change rates of the tidal components, the specific lag angle for each tidal component is determined. The specific lag angle is the difference between the actual phase change rate and the theoretical phase change rate, thus obtaining the tidal specific lag angle data.

[0115] Preferably, step S5, which involves constructing the tidal characteristic derivation formula based on the tidal amplitude, the tidal lag angle, and the distance from the observation point to the tide gauge station, includes:

[0116]

[0117]

[0118] in, For tidal amplitude, This represents the difference in tidal level between tide gauge station A and measuring point X. This represents the difference in tide level between tide gauge station A and measuring point B; This represents the distance from tide gauge station A to measuring point X. This represents the distance from tide gauge station A to measuring point B; The lag angle is specifically designed for tidal division; This represents the specific tidal lag difference between tide gauge station A and measuring point X; This represents the tide-specific lag difference between tide gauge station A and measuring point B.

[0119] In this embodiment of the invention, tidal amplitude data, tidal angular rate data, and tidal lag angle data are first extracted from the database. These data are obtained by steps S2, S3, and S4, respectively, and are correlated with each tidal component (such as M2, S2, etc.). Simultaneously, the actual geographical distance between tide gauge station A and measuring point X is collected. And the actual geographical distance between tide gauge station A and reference point B. These distance data are calculated using Geographic Information System (GIS) technology, utilizing latitude and longitude coordinates to ensure consistency in distance units, such as using kilometers. This is achieved using formulas. Calculate the tidal level difference between tide gauge station A and measuring point X. ,here, This is the tidal level difference between tide gauge station A and reference point B, a value obtained from historical tidal data. Next, the formula is used... Calculate the tide-specific lag difference from tide gauge station A to measuring point X. ,here This is the difference in tidal lag between tide gauge station A and reference point B, a value also obtained from historical data. Then, a harmonic constant tide level model is constructed based on the tidal amplitude, tidal angular rate, tidal lag, and Greenwich Mean Time (GMTA). Specifically, the GMTA is first converted to a timescale matching the tidal angular rate, and then multiplied by the tidal angular rate to obtain the astronomical phase change. Next, the obtained astronomical phase change is added to the tidal lag to form a complete phase expression. Finally, combined with the tidal amplitude, the parameters of the harmonic constant tide level model are generated. These parameters include the tidal amplitude, tidal angular rate, tidal lag, and the converted GMTA value. These parameters are then organized into a structured data format and stored in a database.

[0120] Preferably, the construction of the harmonic constant tidal level model based on tidal amplitude, tidal angular rate, tidal lag angle, and Greenwich astronomical phase angle in step S5 includes:

[0121]

[0122] in, Indicates time The tide level at that moment, Indicates the first The tidal node factor is a parameter related to the tidal cycle. Indicates the first The tidal amplitude of each tidal constituent. Indicates the first The tidal angular velocity of each tidal constituent. Greenwich Mean Time (GMT) astronomical phase angle, representing the fixed astronomical reference phase angle at Greenwich Mean Time (GMT). Indicates local time deviation; Indicates the first A specific late angle for each tide. This indicates the number of tidal constituents, representing the tidal constituent components considered in the model.

[0123] In this embodiment of the invention, firstly, for each tidal component, its corresponding tidal amplitude is extracted from the database. tidal angular rate and the special tidal angle Then, based on the current time and the preset Greenwich astronomical phase angle... Calculate the phase of each tidal component at that moment; this step involves converting the Greenwich astronomical phase angle and dealing with local time deviations. The adjustments were then made. Subsequently, using the extracted tidal parameters and the calculated phase, the timing of each tidal component at a specific time was calculated using the formula described above. The tidal level contribution. This calculation process requires performing it separately for each tidal constituent and summing the tidal level contributions of all tidal constituents to obtain the total tidal level value. .

[0124] Preferably, in step S6, the tide level value at the measuring point is calculated based on the harmonic constant tide level model, the instantaneous tidal height difference between water level stations is calculated using the tidal level value and the tidal characteristic derivation formula, and the relationship between tidal height difference and distance is output, including:

[0125]

[0126] in, Indicates time At any given time, the tidal level difference between measuring point X and water level station A; Indicates time At what time, the tide level at measuring point X; Indicates time At what time, the tide level at tide gauge station A; Indicates the first The amplitude of each tidal constituent at tide gauge station A; Indicates the first The difference in tidal amplitude between measuring point X and tide gauge station A; Indicates the first The specific tidal lag difference between tide gauge station A and measuring point X; Indicates the first The specific tidal lag difference of each constituent tide at tide gauge station A; Indicates the first The specific tidal delay angle difference at tide gauge station A for each tidal constituent.

[0127] In this embodiment of the invention, the tide level at the measuring point is first calculated based on the harmonic constant tide level model. Using the harmonic constant tide level model parameters obtained in step S5, the tidal amplitude is... tidal angular rate and the special tidal angle and Greenwich astronomical phase angle Calculate in time At time tidal difference between measuring point X and water level station A The specific operation is as follows: For each tidal component, calculate its time... The tidal contribution, and then according to the formula Calculate the tidal range, where Indicates time At what time, the tide level at measuring point X; Indicates time The tide level at tide gauge station A is recorded at a specific time. Next, the instantaneous tidal height difference between the stations is calculated using the tide level values. Specifically, two stations are selected as the calculation objects, their tide levels at the same time are calculated, and the difference between them is obtained to get the instantaneous tidal height difference. This tidal height difference is calculated using difference operations to ensure time synchronization. Then, the relationship between the tidal height difference and distance is mathematically transformed and expanded using a Taylor series to obtain the Taylor expanded relationship between the tidal height difference and distance. Specifically, the Taylor series expansion is performed on the tidal height difference and distance relationship at a specific point (e.g., the distance is zero) to obtain the Taylor expanded relationship between the tidal height difference and distance. The order of the Taylor series expansion is determined according to actual needs, usually expanding to the third or fourth order to ensure accuracy. The influence of sea surface curvature in the Taylor expanded relationship between the tidal height difference and distance is determined, and the processed tidal height difference equation is output. Specifically, the influence of sea surface curvature on the tidal height difference is identified by analyzing the coefficients of higher-order terms in the Taylor expansion. The specific steps are as follows: The coefficients of higher-order terms in the Taylor expansion are compared with known sea surface curvature parameters to determine the degree of influence of sea surface curvature. Finally, the effective range of the water level station is calculated by inversely solving the tidal difference equation. Specifically, the processed tidal difference equation is set to zero, and the equation is solved using numerical methods (such as Newton's iteration method) to obtain the effective range of the water level station. The calculated range is in kilometers and stored in a database.

[0128] Preferably, in step S6, the instantaneous tidal height difference relationship is mathematically transformed and subjected to Taylor series expansion to obtain the Taylor expanded tidal height difference versus distance relationship, including:

[0129]

[0130] In the formula:

[0131]

[0132]

[0133] in, , , They are respectively with the first Coefficients of nonlinear terms related to each tidal phase; , , They are respectively with the first Phase angles related to each tidal constituent; Indicates the first The specific tidal lag difference between reference point B and water level station A for each tidal constituent; This represents the distance from measuring point X to water level station A.

[0134] In this embodiment of the invention, the coefficients of the nonlinear term are calculated:

[0135] For each tidal component Calculate the first-order coefficients :

[0136] Calculate the second-order coefficients :

[0137] Calculate the third-order coefficients :

[0138] Calculate the phase angle:

[0139] Calculate the first-order phase angle :

[0140] Calculate the second-order phase angle :

[0141] Calculate the second-order phase angle :

[0142] Taylor expansion calculation:

[0143] For each tidal component Calculate the first-order terms:

[0144] First-order term =

[0145] Calculate the second-order term:

[0146] Second-order term =

[0147] Calculate the third-order terms:

[0148] Third-order term =

[0149] The total tidal range is obtained by summing the first, second, and third-order terms of all tidal components. = .

[0150] Preferably, in step S6, the degree of influence of sea surface curvature in the Taylor expansion of the tidal height difference versus distance equation is determined, and the processed tidal height difference equation is output, including:

[0151] According to the difference in tidal latitude The influence of the nonlinear term coefficients on sea surface curvature is assessed, and the following is given: Substituting into the approximate expression for tidal difference, we get:

[0152]

[0153] in, This indicates the permissible tidal level difference threshold, used to determine the effective operating distance of the water level station.

[0154] Preferably, in step S6, the effective operating distance of the water level station is determined by inversely solving the equation based on the tidal height difference, including:

[0155] Solve the tidal difference equation to obtain the effective operating distance of the water level station. d；

[0156] Select comprehensive indicators based on the required accuracy of water level station measurements:

[0157] ;

[0158] ;

[0159] in, Indicates time The effective range of the changing water level station Represents all the calculations obtained The minimum value in; express The average value.

[0160] In this embodiment of the invention, the effective operating distance of the water level station is first calculated by solving the tidal difference equation inversely. The specific operation includes: setting the tidal difference equation obtained in step S5 to zero, that is... Substituting this into the Taylor expansion formula for the relationship between tidal height difference and distance, and using numerical methods such as Newton's iteration method, the tidal height difference threshold can be calculated. Below, the distance between measuring point X and water level station A. Next, a comprehensive index is selected based on the required accuracy of the water level station measurements. The specific procedure is as follows: calculate all the calculated... minimum value ,as well as average .in, Represents all the calculations obtained The minimum value in, express Average. These calculations involve the average value. Statistical analysis of the dataset, including the calculation of minimum and average values, can determine the effective range of the water level station.

[0161] Example Calculation and Analysis: Calculations were performed using some tide gauge stations in a certain sea area. A schematic diagram of the station locations is shown below. Figure 3 As shown. Harmonic constants for each station. , The effective range of the tide gauge station was calculated using the least squares tidal analysis method based on one month's water level observation data. Then, the effective range of the tide gauge station was calculated using the direct adjustment and constant model estimation method described in this paper. The results are shown in Table 1. From the table, it can be seen that when determining the effective range of station A using stations A and B, the frequency value is 0.971. This indicates that in one month, there are 720 x 0.971 = 699 hours (29 days) of effective range for station A. With a constraint of 20cm, the entire survey area between the two stations can be controlled. This means that in this Within a certain distance, when using water level data from station A for water level correction, the following conditions are always met: The accuracy requirement is 20cm. As can be seen from Table 2, with... A decrease in the value indicates an increase in the required precision. Its effective operating distance... The relevant values ​​also decreased accordingly.

[0162] Table 1 Calculation results of effective operating distance of water level stations

[0163]

[0164] Table 2 Calculation results of effective operating distance of water level stations

[0165]

[0166] Therefore, the embodiments should be considered as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the application are intended to be included within the invention.

[0167] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A method for calculating the effective operating distance of a water level station, characterized in that, Includes the following steps: Step S1: Obtain raw tidal observation data from the water level station, record the changes in the raw tidal observation data according to the tidal level observation time, and obtain tidal observation data; Step S2: Perform Fourier transform on the tidal observation data to convert it into frequency domain data, and calculate the amplitude value of each tidal component to obtain the tidal amplitude data; Step S3: Perform time-frequency analysis on the tidal observation data to extract the instantaneous tidal frequency; determine the angular rate of each tidal component based on the instantaneous frequency to obtain the tidal angular rate data; Step S4: Perform phase analysis on the tidal observation data to identify the analytical signal of the tidal observation data; extract phase information from the analytical signal and determine the dedicated lag angle of each tidal component to obtain the dedicated lag angle data of the tidal component; Step S5: Obtain the Greenwich astronomical phase angle and extract the distance from the observation point to the tide gauge station from the tidal observation data; construct the tidal characteristic derivation formula based on the tidal amplitude, the tidal angular rate, the tidal angular rate, and the distance from the observation point to the tide gauge station; construct the harmonic constant tidal level model based on the tidal amplitude, tidal angular rate, tidal angular rate, and Greenwich astronomical phase angle. Step S6: Calculate the tide level at the measuring point based on the harmonic constant tide level model. Calculate the instantaneous tidal height difference between water level stations using the tidal level value and tidal characteristic derivation formula, and output the relationship between tidal height difference and distance. Perform a mathematical transformation on the relationship between tidal height difference and distance, and perform a Taylor series expansion to obtain the Taylor expanded relationship between tidal height difference and distance. Determine the degree of influence of sea surface curvature in the Taylor expanded relationship between tidal height difference and distance, and output the processed tidal height difference equation. Solve the equation inversely based on the tidal height difference equation to find the effective operating distance of the water level station.

2. The method for calculating the effective operating distance of a water level station according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Sort the tidal observation data according to timestamps to form a continuous tidal observation time series; Step S22: Denoise the continuous tidal observation time series using wavelet transform, process the tidal data using wavelet basis, and remove high-frequency interference signals to obtain tidal time domain data; Step S23: Use Fast Fourier Transform to convert the tidal time domain data into tidal frequency domain data; in the tidal frequency domain data, identify the semi-diurnal tide, diurnal tide and long-period tide components to obtain tidal component data; Step S24: Separate the frequency signal of each tidal component data to form a tidal frequency domain data sequence; Step S25: Traverse each tidal frequency domain data sequence and calculate the average amplitude, maximum amplitude, and minimum amplitude of each tidal frequency domain data sequence to obtain the tidal amplitude data.

3. The method for calculating the effective operating distance of a water level station according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Divide the tidal observation data into time slices to obtain tidal observation time segments; Step S32: Pair up the data points in each tidal observation time segment, calculate the phase difference between each pair of data points, and calculate the instantaneous frequency based on the phase difference; Step S33: Identify whether there are abrupt changes in the instantaneous frequency within adjacent tidal observation time segments, where abrupt changes are defined as instantaneous frequency changes exceeding a preset threshold; if abrupt changes exist, smooth the abrupt change points to obtain smoothed tidal instantaneous frequencies. Step S34: Integrate the instantaneous tidal frequency to obtain tidal phase information; Step S35: Calculate the tidal phase information with respect to the time derivative of the tidal observation time segment, and calculate the angular rate of the tidal signal within each tidal observation time segment to obtain the tidal angular rate data.

4. The method for calculating the effective operating distance of a water level station according to claim 1, characterized in that, Step S4 includes the following steps: Step S41: Perform tidal cycle integrity detection on the observation segments in the tidal observation data, select the observation segments with complete tidal cycles, and record them as tidal complete cycle segments; Step S42: Within a complete tidal cycle segment, identify the peak and trough data of the tidal signal by comparing the tidal level change trends of adjacent data points; Step S43: For the transition area between peak and trough data, determine the transition point data by calculating the extreme points of the tidal level change rate; Step S44: In a complete tidal cycle segment, identify the analytical signal of the tidal observation data based on the peak data, trough data, and transition point data; Step S45: For the analytical signal of a complete tidal cycle segment, the phase change time interval is obtained by calculating the time difference between adjacent peaks and troughs; Step S46: Calculate the average phase change rate of a complete tidal cycle segment based on the phase change time interval; determine the specific lag angle of each tidal component based on the average phase change rate to obtain the tidal specific lag angle data.

5. The method for calculating the effective operating distance of a water level station according to claim 1, characterized in that, Step S5 involves constructing the tidal characteristic derivation formula based on the tidal amplitude, the tidal lag angle, and the distance from the observation point to the tide gauge station. This includes: in, For tidal amplitude, This represents the difference in tidal level between tide gauge station A and measuring point X. This represents the difference in tide level between tide gauge station A and measuring point B; This represents the distance from tide gauge station A to measuring point X. This represents the distance from tide gauge station A to measuring point B; The lag angle is specifically designed for tidal division; This represents the specific tidal lag difference between tide gauge station A and measuring point X; This represents the tide-specific lag difference between tide gauge station A and measuring point B.

6. The method for calculating the effective operating distance of a water level station according to claim 1, characterized in that, Step S5, which involves constructing a harmonic constant tidal level model based on tidal amplitude, tidal angular rate, tidal lag angle, and Greenwich astronomical phase angle, includes: in, Indicates time The tide level at that moment, Indicates the first The tidal node factor is a parameter related to the tidal cycle. Indicates the first The tidal amplitude of each tidal constituent. Indicates the first The tidal angular velocity of each tidal constituent. Greenwich Mean Time (GMT) astronomical phase angle, representing the fixed astronomical reference phase angle at Greenwich Mean Time (GMT). Indicates local time deviation; Indicates the first A specific late angle for each tide. This indicates the number of tidal constituents, representing the tidal constituents considered in the model.

7. The method for calculating the effective operating distance of a water level station according to claim 6, characterized in that, In step S6, the tide level value at the measuring point is calculated based on the harmonic constant tide level model. The instantaneous tidal height difference between water level stations is calculated using the tidal level value and the tidal characteristic derivation formula, and the relationship between tidal height difference and distance is output, including: in, Indicates time At any given time, the tidal level difference between measuring point X and water level station A; Indicates time At what time, the tide level at measuring point X; Indicates time At what time, the tide level at tide gauge station A; Indicates the first The amplitude of each tidal constituent at tide gauge station A; Indicates the first The difference in tidal amplitude between measuring point X and tide gauge station A; Indicates the first The specific tidal lag difference between tide gauge station A and measuring point X; Indicates the first The specific tidal lag difference of each constituent tide at tide gauge station A; Indicates the first The specific tidal delay angle difference at tide gauge station A for each tidal constituent.

8. The method for calculating the effective operating distance of a water level station according to claim 7, characterized in that, In step S6, the instantaneous tidal height difference relationship is mathematically transformed and expanded using Taylor series to obtain the Taylor expanded tidal height difference versus distance relationship, which includes: In the formula: in, , , They are respectively with the first Coefficients of nonlinear terms related to each tidal phase; , , They are respectively with the first Phase angles related to each tidal constituent; Indicates the first The specific tidal lag difference between reference point B and water level station A for each tidal constituent; This represents the distance from measuring point X to water level station A.

9. The method for calculating the effective operating distance of a water level station according to claim 8, characterized in that, Step S6 determines the influence of sea surface curvature in the Taylor expansion equation for the relationship between tidal height difference and distance, and outputs the processed tidal height difference equation, including: According to the difference in tidal latitude The influence of the nonlinear term coefficients on sea surface curvature is assessed, and the following is given: Substituting into the approximate expression for tidal difference, we get: in, This indicates the permissible tidal level difference threshold, used to determine the effective operating distance of the water level station.

10. The method for calculating the effective operating distance of a water level station according to claim 1, characterized in that, In step S6, the effective operating distance of the water level station is determined by inversely solving the equation based on the tidal height difference, including: Solve the tidal difference equation to obtain the effective operating distance of the water level station. d； Select comprehensive indicators based on the required accuracy of water level station measurements: ； ； in, Indicates time The effective range of the changing water level station Represents all the calculations obtained The minimum value in; express The average value.

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