A storm surge semi-theoretical and semi-experience prediction and maximum water level increase time prediction method and system

Abstract

The application provides a storm surge semi-theoretical and semi-experience prediction and maximum water level increase time prediction method and system, first verifies and optimizes a typhoon wind field model suitable for the South China Sea, obtains a precise typhoon maximum wind speed radius through a strong wind circle inversion, obtains a semi-theoretical and semi-experience water level increase prediction formula containing air pressure, alongshore wind and onshore wind dynamic mechanism based on a fluid dynamics momentum equation, integrates and simplifies along a vertical shore line direction, and calibrates undetermined coefficients of the formula by using observation data; in combination with a response mechanism of storm surge water level increase to onshore wind stress, a theoretical relationship between maximum water level increase occurrence time and a typhoon path is derived, a statistical prediction method of the maximum water level increase time is established by statistically analyzing a wind direction distribution law at the maximum water level increase time through historical observation data. The scheme of the application considers both a dynamics theory and a measured data characteristic, has small calculation amount, high prediction efficiency, and can simultaneously realize precise prediction of a storm surge water level increase process and the maximum water level increase time.

Description

Technical Field

[0001] This invention relates to the field of marine disaster forecasting technology, specifically to a method and system for semi-theoretical and semi-empirical forecasting of storm surges and prediction of maximum flood time. Background Technology

[0002] Storm surge is an abnormal rise and fall of sea level caused by meteorological factors such as strong winds. It is one of the major marine disasters in my country's coastal areas. As a typhoon-prone area, the South China Sea coast is severely threatened by storm surge disasters, which pose a serious threat to flood control and drainage, marine engineering, and fishery production in coastal cities. Therefore, achieving accurate and efficient storm surge forecasting is of great practical significance.

[0003] Existing storm surge forecasting technologies are mainly divided into three categories: single-station empirical forecasting formulas, numerical forecasting technology, and artificial intelligence forecasting technology. All three types of technologies have significant drawbacks and are difficult to meet the actual needs of storm surge early warning and forecasting along the South China Sea coast.

[0004] Empirical forecasting formulas: These formulas predict storm surge by establishing statistical relationships between the maximum storm surge and factors such as typhoon pressure difference and maximum wind speed. This method is simple to calculate and efficient, but it lacks rigorous dynamic principles. It can only predict the maximum storm surge but not the storm surge process. It also has insufficient ability to predict the timing of the maximum storm surge, usually assuming that the maximum storm surge occurs at the time of lowest air pressure or maximum onshore wind speed, ignoring the lag of the storm surge. Furthermore, the formulas are highly dependent on the accumulation of observational data and are only applicable to coastal sections with abundant observational data, resulting in limited forecast accuracy.

[0005] Since the main driving forces of storm surge are wind and air pressure, the maximum increase in water level during a storm surge is usually expressed in the following form when establishing empirical formulas.

[0006] (1)

[0007] In equation (1), Indicates the maximum increase in water level; This indicates the maximum pressure difference between the forecast station and the typhoon center during the typhoon process; This indicates the maximum wind speed at the forecast station during the typhoon. This represents the angle between the direction of maximum wind speed and the normal direction of the shoreline where the station is located. In reality, it represents the maximum onshore wind speed; a, b, c, and d are undetermined coefficients, obtained through regression analysis of measured data. When establishing the formula, one or more combinations of these coefficients are used.

[0008] Numerical storm surge forecasting technology uses numerical solutions to hydrodynamic equations to predict storm surges. It fully considers the dynamic driving mechanism and the influence of topography and coastline. The model is independent of observational data and can achieve high forecast accuracy when typhoon parameters are accurate, and it can also achieve regional forecasting. However, this method has extremely high computational resource requirements, is computationally intensive, time-consuming, and costly, making it difficult to meet the timeliness requirements of storm surge warnings and forecasts. Furthermore, the numerical model does not incorporate historical observational data, failing to fully utilize the characteristics of measured data to optimize forecast results.

[0009] Artificial intelligence forecasting technology: Based on data such as typhoon paths and parameters, forecasting models are built, which are simple and fast to calculate and have low computational resource requirements. However, this method also lacks the support of dynamic mechanisms, and model training requires a large number of observation samples. The storm surge data accumulated by most marine observation stations cannot meet the sample requirements of more than 300 events, so numerical simulation is needed to supplement the samples, resulting in forecast accuracy that is no higher than that of numerical forecasting. Moreover, static neural network models are prone to the problem of "jumping" in forecast water levels. Although recurrent neural network models can improve this problem, they are still limited by the quantity and quality of samples.

[0010] Currently, the deployment of marine and hydrological stations along the South China Sea coast is becoming increasingly dense, accumulating a large amount of storm surge observation data. There is an urgent need for a method that takes into account both dynamic theory and measured data characteristics, requires less computation, has high forecasting efficiency, and can simultaneously achieve accurate forecasting of storm surge increase process and maximum increase time, thereby solving the respective drawbacks of traditional forecasting techniques. Summary of the Invention

[0011] Based on this, the present invention provides a method and system for semi-theoretical and semi-empirical forecasting of storm surges and prediction of the maximum rise time. It takes into account both the characteristics of fluid dynamics theory and measured data, has low computational load and high forecast efficiency, and can simultaneously achieve accurate forecasting of storm surge rise process and maximum rise time, meeting the timeliness and accuracy requirements of storm surge early warning and forecasting along the South China Sea coast.

[0012] In a first aspect, the present invention provides a method for semi-theoretical and semi-empirical forecasting of storm surges and prediction of the maximum rise time, comprising the following steps:

[0013] 1) Verify and select the typhoon wind field model that is suitable for the target sea area, and use the typhoon gale circle data of the target sea area to invert and obtain the radius of the typhoon's maximum wind speed.

[0014] 2) Based on the y-axis momentum equation of hydrodynamics, the equation is integrated and simplified along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge prediction formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. The undetermined coefficients of the prediction formula are calibrated using storm surge observation data from marine stations in the target sea area.

[0015] 3) Based on the response mechanism of storm surge to onshore wind stress, the theoretical analytical relationship between the time of maximum surge and typhoon path is derived, revealing the influence of typhoon path parameters on the time lag of maximum surge.

[0016] 4) Analyze the wind direction distribution characteristics of the historical storm surge maximum rise time at marine stations in the target sea area, and combine the theoretical analytical relationship in step 3) to establish a statistical forecasting method for the maximum storm surge time in the target sea area.

[0017] 5) Based on the typhoon's maximum wind speed radius obtained in step 1) and the semi-theoretical and semi-empirical storm surge forecasting formula calibrated in step 2), the storm surge process in the target sea area is predicted. Combined with the statistical forecasting method in step 4), the maximum storm surge time in the target sea area is accurately predicted.

[0018] As a further improvement to the technical solution of this invention, step 1) verifies and selects a typhoon wind field model suitable for the target sea area, and uses the typhoon gale circle data of the target sea area to invert and obtain the typhoon's maximum wind speed radius, specifically including:

[0019] The typhoon wind field models of Jelesnianski (1965), Jelesnianski (1966), and Holland (1980) were selected as candidate models to obtain the optimal typhoon path set and wind circle data for the target sea area. The wind circle data includes the radius of wind circles for level 8, level 10, and level 12 winds.

[0020] Based on each candidate model, the maximum wind speed radius of the typhoon is retrieved using wind circle data of different levels. If the maximum wind speed radius corresponding to different levels of wind circles retrieved by the same candidate model is consistent or similar, then the candidate model is determined to be suitable for the target sea area.

[0021] The average value of the maximum wind speed radius corresponding to the wind circles of different levels of gale obtained by the candidate model adapted to the target sea area is taken as the maximum wind speed radius of the typhoon in the target sea area.

[0022] As a further improvement to the technical solution of this invention, the target sea area is the South China Sea, and the suitable typhoon wind field model is the Jelesnianski (1965) model, whose pressure field and wind field calculation formulas are as follows:

[0023]

[0024]

[0025] Where p(r) is the air pressure at the typhoon radius r, p0 is the air pressure at the typhoon center, p∞ is the air pressure on the outer periphery of the typhoon, R is the radius of the typhoon's maximum wind speed, V is the wind speed at the typhoon radius r, and W R This is the maximum wind speed of the typhoon.

[0026] As a further improvement to the technical solution of this invention, in step 2), based on the hydrodynamic y-axis momentum equation, the equation is integrated and simplified along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge prediction formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. Specifically, it includes:

[0027] A right-handed coordinate system is established with the shoreline as the x-axis and the direction perpendicular to the shoreline towards the shore as the y-axis. The y-momentum equation in the two-dimensional full flow equation of fluid dynamics is selected. The convection term and the horizontal friction term are ignored. The integral is performed along the y-axis from the boundary between the continental shelf and the continental slope to the shore.

[0028] By combining the open sea water level and air pressure terms in the integrated results, assuming that the seabed friction force is proportional to the sea surface wind stress, estimating the horizontal flow velocity, and simplifying the Coriolis force integral term, a semi-theoretical and semi-empirical water increase forecasting formula is obtained, which uses the shore-side water increase as the forecast quantity and includes the air pressure response, coastal wind response, and onshore wind response. The formula is in the following form:

[0029]

[0030] Where ηs is the shore-side water level rise, a, b, c are undetermined coefficients, ρ is the seawater density, g is the gravitational acceleration, p∞ is the outer air pressure of the typhoon, ps is the shore-side air pressure, f is the Coriolis force coefficient, u is the average vertical velocity in the x-direction, τay is the wind stress in the y-direction of the sea surface, h is the water depth, ys is the shore-side coordinates, and ye is the coordinates at the boundary between the continental shelf and the continental slope.

[0031] For observation stations that are not suitable for cross-sectional integration along the vertical shoreline, the forecast formula is simplified to include the shoreline pressure difference, easterly wind stress, and northerly wind stress:

[0032] ,

[0033] in, These represent the wind stresses to the east and north of the observation station, respectively.

[0034] As a further improvement to the technical solution of this invention, step 2) involves calibrating the undetermined coefficients of the forecast formula using storm surge observation data from marine stations in the target sea area, specifically including:

[0035] Multiple storm surge observation data from marine stations in the target sea area were selected, and the water level increase data, corresponding typhoon parameters, and wind stress data for each storm surge were extracted.

[0036] By employing both constrained fitting (a=0) and unconstrained fitting (a≠0) methods, and using the least squares method to fit the observed data with the forecast formula, the optimal solution for the undetermined coefficients was obtained through calibration.

[0037] With unbiased fitting as the goal, the coefficient set whose fitting results are evenly distributed on both sides of the perfect fitting line is selected as the final calibration result. If the accuracy of the maximum water increase forecast is the key requirement, the coefficient set of unconstrained fitting is selected.

[0038] As a further improvement to the technical solution of this invention, step 3) derives the theoretical analytical relationship between the time of maximum flood increase and the typhoon path based on the response mechanism of storm surge to onshore wind stress, specifically including:

[0039] Assuming that the maximum increase in water level occurs at the shore when the onshore wind stress perpendicular to the shoreline is the maximum, the Jelesnianski (1965) model is selected to calculate the onshore wind stress outside the radius of the typhoon's maximum wind speed.

[0040] Setting the straight path equation of the typhoon By differentiating the onshore wind stress function and setting the derivative to 0, and combining it with the typhoon path equation, the coordinates of the typhoon's location when the onshore wind stress is maximum can be obtained.

[0041] Based on the typhoon's location coordinates, a formula for the relative distance between the typhoon and the observation station at the time of maximum water rise is derived, revealing the shortest distance d from the observation station to the typhoon's path. min The theoretical analytical relationship between the typhoon path slope k and the time lag of maximum water level rise:

[0042]

[0043] Where, d AC θ represents the distance the typhoon travels from its closest point to the location corresponding to the maximum water level rise, and θ is the angle between the shoreline normal and the wind speed direction.

[0044] As a further improvement to the technical solution of the present invention, when the distance between the observation station and the typhoon path is less than the radius of the typhoon's maximum wind speed, it is deduced that the typhoon center moves about 2 hours after passing the observation station, and the distance between the observation station and the typhoon center reaches the radius of the maximum wind speed. At this time, the onshore wind stress is the greatest, and the maximum water level rise occurs on the shore.

[0045] As a further improvement to the technical solution of this invention, step 4) involves statistically analyzing the wind direction distribution characteristics of the historical storm surge maximum rise time at marine stations in the target sea area, and combining this with the theoretical analytical relationship in step 3), to establish a statistical forecasting method for the maximum storm surge time in the target sea area, specifically including:

[0046] Collect wind speed and direction data at the time of maximum storm surge at marine stations in the target sea area, draw wind direction compass diagrams, and obtain the average wind direction D and the root mean square error θ at the time of maximum storm surge.

[0047] Combining the theoretical analysis relationship in step 3), the time corresponding to the wind direction being in the range of D-θ to D+θ during the typhoon is taken as the possible period when the storm surge is at its maximum.

[0048] When the distance between the observation station and the typhoon's path is less than the radius of the typhoon's maximum wind speed, the forecast time for the maximum storm surge is directly taken as 2 hours after the typhoon makes landfall.

[0049] As a further improvement to the technical solution of this invention, step 5) involves forecasting the storm surge increase process in the target sea area, specifically including:

[0050] Obtain real-time typhoon parameters for the target sea area, including typhoon path, central pressure, maximum wind speed, and radius of the strong wind circle;

[0051] Based on the wind field model selected in step 1) and the maximum wind speed radius obtained by inversion, real-time air pressure field and wind stress field data are calculated.

[0052] Substitute the pressure field and wind stress field data into the semi-theoretical and semi-empirical storm surge prediction formula after step 2) to calculate the storm surge data of the target sea area marine station hourly.

[0053] Secondly, the present invention provides a storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction system, comprising:

[0054] The wind field model optimization module is used to verify and optimize the typhoon wind field model that is suitable for the target sea area, and to obtain the maximum wind speed radius of the typhoon by inverting the typhoon wind circle data of the target sea area.

[0055] The forecast formula construction module is based on the hydrodynamic y-direction momentum equation. It integrates and simplifies along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge forecast formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. The undetermined coefficients of the forecast formula are calibrated using storm surge observation data from marine stations in the target sea area.

[0056] The theoretical relationship derivation module, based on the response mechanism of storm surge to onshore wind stress, derives the theoretical analytical relationship between the time of maximum surge and typhoon path, revealing the influence of typhoon path parameters on the time lag of maximum surge.

[0057] The time forecast module statistically analyzes the wind direction distribution characteristics of the maximum storm surge time in the target sea area, and combines theoretical analytical relationships to establish a statistical forecasting method for the maximum storm surge time in the target sea area.

[0058] The integrated forecasting module, based on the typhoon's maximum wind speed radius and a calibrated semi-theoretical and semi-empirical storm surge forecasting formula, forecasts the storm surge process in the target sea area. Combined with the statistical forecasting method for the maximum storm surge time, it achieves accurate prediction of the maximum storm surge time in the target sea area.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] This invention lays a reliable foundation for typhoon dynamic parameters in forecasting by optimizing a typhoon wind field model adapted to the target sea area and retrieving the accurate radius of the typhoon's maximum wind speed. Based on the fluid dynamics momentum equation, it constructs a semi-theoretical, semi-empirical flooding forecasting formula that integrates the core dynamic mechanisms of pressure gradient force, Coriolis force, and wind stress. This formula balances the support of dynamic theory with the characteristics of measured data, overcoming the shortcomings of traditional empirical formulas lacking theoretical basis. Furthermore, it significantly reduces the computational load through equation simplification and calibration of measured coefficients, solving the problems of high computational resource requirements and long processing times in numerical forecasting. Simultaneously, it derives the relationship between the maximum flooding time and the typhoon path by combining the response mechanism of storm flooding to onshore wind stress. This method, which analyzes the theoretical relationships and integrates the statistical characteristics of wind direction distribution from historical observation data, establishes a method for predicting the maximum storm surge time. This method overcomes the technical limitations of traditional methods, such as the inability to accurately predict the maximum storm surge time and the neglect of storm surge lag. It can also flexibly adjust the formula to suit the terrain features of different observation stations, and requires far fewer observation samples than machine learning methods. The method has a small overall computational load, high forecasting efficiency, and does not require high-end computing resources. It can simultaneously achieve accurate forecasting of storm surge processes and maximum storm surge times, making full use of the dense marine station observation data along the target sea area. It meets the dual requirements of timeliness and accuracy for storm surge warning and forecasting, and has a wide range of applications and strong practicality. Attached Figure Description

[0061] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0062] Figure 1a A schematic diagram of the typhoon radius (level 8 vs. level 10) inverted by the Jelesnianski (1965) model;

[0063] Figure 1b The typhoon radius (Category 8 vs. Category 12) was inverted using the Jelesnianski (1965) model.

[0064] Figure 1c A schematic diagram showing the typhoon radius (Category 10 vs. Category 12) inverted using the Jelesnianski (1965) model;

[0065] Figure 2 This is a schematic diagram showing the wind speed and water level increase at Shanwei Station during Typhoon No. 1713 in 2017.

[0066] Figure 3 This is a schematic diagram showing the wind speed and water level increase at Guangzhou Station during Typhoon No. 1713 in 2017.

[0067] Figure 4 This is a schematic diagram of the coordinate system;

[0068] Figure 5 This is a schematic diagram showing the wind speed, water level process, and water level increase mechanism at the Shanwei station during Typhoon No. 1822 in 2018.

[0069] Figure 6 A schematic diagram of the station locations and integral cross-section distribution for a semi-theoretical, semi-empirical formula.

[0070] Figure 7 This is a schematic diagram of the fitting results of the unconstrained empirical formula (a≠0) for the Zhapo Station.

[0071] Figure 8 For the constraint empirical formula of Zhapo Station ( Schematic diagram of the fitting results;

[0072] Figure 9a A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 0312);

[0073] Figure 9b A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 8402);

[0074] Figure 9c A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 8702);

[0075] Figure 9d A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon 9309);

[0076] Figure 9e A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 0307);

[0077] Figure 9f A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 1311);

[0078] Figure 10a A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 8908);

[0079] Figure 10b A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon 9302);

[0080] Figure 10c A schematic diagram for verifying the empirical formula at Zhapo Station (storm surge during Typhoon No. 1822);

[0081] Figure 11 This is a schematic diagram of the typhoon's path and maximum onshore wind speed.

[0082] Figure 12 for A graph showing the relationship between the slope and the path.

[0083] Figure 13 This is a schematic diagram showing the variation of maximum onshore wind stress with the landfall angle; (the angle is defined as the angle between the typhoon's path and the x-axis).

[0084] Figure 14 This is a schematic diagram showing the relationship between the maximum onshore wind speed and the location of the typhoon center. (The circle "o" in the diagram represents the position of the typhoon across the y-axis. The intersection of the typhoon path passing through the circle and the corresponding curve is the location of the typhoon center when the maximum onshore wind occurs at the origin (0,0).

[0085] Figure 15 A schematic diagram showing the typhoon wind speed distribution during the maximum water level rise at the marine station;

[0086] Figure 16 This is an exemplary flowchart of a method for semi-theoretical and semi-empirical forecasting of storm surges and prediction of maximum flood time according to the present invention.

[0087] Figure 17 This is a schematic diagram of the structure of a storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction system of the present invention. Detailed Implementation

[0088] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0089] The present invention will be further described in detail below with reference to the accompanying drawings.

[0090] Reference Figure 16 In a first aspect, the present invention provides a method for semi-theoretical and semi-empirical forecasting of storm surges and prediction of the maximum rise time, comprising the following steps:

[0091] 1) Verify and select the typhoon wind field model that is suitable for the target sea area, and use the typhoon gale circle data of the target sea area to invert and obtain the radius of the typhoon's maximum wind speed.

[0092] 2) Based on the y-axis momentum equation of hydrodynamics, the equation is integrated and simplified along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge prediction formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. The undetermined coefficients of the prediction formula are calibrated using storm surge observation data from marine stations in the target sea area.

[0093] 3) Based on the response mechanism of storm surge to onshore wind stress, the theoretical analytical relationship between the time of maximum surge and typhoon path is derived, revealing the influence of typhoon path parameters on the time lag of maximum surge.

[0094] 4) Analyze the wind direction distribution characteristics of the historical storm surge maximum rise time at marine stations in the target sea area, and combine the theoretical analytical relationship in step 3) to establish a statistical forecasting method for the maximum storm surge time in the target sea area.

[0095] 5) Based on the typhoon's maximum wind speed radius obtained in step 1) and the semi-theoretical and semi-empirical storm surge forecasting formula calibrated in step 2), the storm surge process in the target sea area is predicted. Combined with the statistical forecasting method in step 4), the maximum storm surge time in the target sea area is accurately predicted.

[0096] This invention provides a precise foundation of typhoon dynamic parameters for storm surge forecasting by optimizing and adapting a typhoon wind field model to the target sea area and inverting the typhoon's maximum wind speed radius. Based on the fluid dynamics momentum equation, it constructs a semi-theoretical, semi-empirical storm surge forecasting formula that integrates the core dynamic mechanism, balancing theoretical support with the characteristics of measured data. This overcomes the shortcomings of traditional empirical formulas lacking theoretical basis and reduces computational load through equation simplification and coefficient calibration, addressing the high computational resource requirements of numerical forecasting. Combining the dynamic mechanism to derive the theoretical relationship between the maximum storm surge time and the typhoon path, and integrating historical observation statistical characteristics to establish a time forecasting method, it overcomes the limitation of traditional methods in accurately predicting the maximum storm surge time. The overall method can simultaneously achieve accurate forecasting of both the storm surge process and the maximum storm surge time, with low computational load, high forecasting efficiency, and low requirement for observational samples. It can fully utilize marine station observation data in the target sea area, meeting the timeliness and accuracy requirements of storm surge warning and forecasting.

[0097] In some embodiments, step 1) verifies and selects a typhoon wind field model suitable for the target sea area, and uses typhoon gale circle data of the target sea area to invert and obtain the typhoon's maximum wind speed radius, specifically including:

[0098] The typhoon wind field models of Jelesnianski (1965), Jelesnianski (1966), and Holland (1980) were selected as candidate models to obtain the optimal typhoon path set and wind circle data for the target sea area. The wind circle data includes the radius of wind circles for level 8, level 10, and level 12 winds.

[0099] Based on each candidate model, the maximum wind speed radius of the typhoon is retrieved using wind circle data of different levels. If the maximum wind speed radius corresponding to different levels of wind circles retrieved by the same candidate model is consistent or similar, then the candidate model is determined to be suitable for the target sea area.

[0100] The average value of the maximum wind speed radius corresponding to the wind circles of different levels of gale obtained by the candidate model adapted to the target sea area is taken as the maximum wind speed radius of the typhoon in the target sea area.

[0101] This invention selects typical typhoon wind field models as candidate models and conducts model validation by combining the optimal typhoon path set and multi-level gale wind circle data for the target sea area. The consistency of the maximum wind speed radius retrieved from wind circles of different levels of gale is used as the criterion for model adaptability. This allows for the accurate selection of wind field models that match the typhoon characteristics of the target sea area. At the same time, the maximum wind speed radius corresponding to the multi-level gale wind circles retrieved by the adapted model is averaged, resulting in a typhoon maximum wind speed radius that is closer to the measured situation. This solves the problem of large deviations from the measured situation caused by fitting the maximum wind speed radius to the central pressure in traditional methods. This provides more reliable typhoon parameter support for subsequent storm surge forecasting and improves the accuracy of the basic data of the overall forecasting method.

[0102] In some embodiments, the target sea area is the South China Sea, and the adapted typhoon wind field model is the Jelesnianski (1965) model, whose pressure field and wind field calculation formulas are as follows:

[0103]

[0104]

[0105] Where p(r) is the air pressure at the typhoon radius r, p0 is the air pressure at the typhoon center, p∞ is the air pressure on the outer periphery of the typhoon, R is the radius of the typhoon's maximum wind speed, V is the wind speed at the typhoon radius r, and W R This is the maximum wind speed of the typhoon.

[0106] It should be noted that the Jelesnianski (1965) model, which has the best adaptability for the South China Sea, was determined, and its specific calculation formulas for pressure and wind fields were clarified. The maximum wind speed radius of typhoons inverted by this model in the South China Sea has no systematic deviation, and it can more reasonably describe the structural characteristics of typhoons in the South China Sea. It avoids the problems of excessively rapid attenuation of the outer wind field and small maximum wind speed radius that occur when other models are applied in the South China Sea. By directly calculating the pressure and wind speed at different radii of the typhoon through clear formulas, the pressure and wind field data of typhoons in the South China Sea can be obtained quickly and accurately, which improves the calculation efficiency and accuracy of typhoon dynamic parameters and provides key model and formula support for the accuracy of storm surge forecasting in the South China Sea.

[0107] In some embodiments, step 2) involves integrating and simplifying the hydrodynamic momentum equation along the shelf direction perpendicular to the coastline to construct a semi-theoretical, semi-empirical storm surge prediction formula that incorporates pressure gradient force, Coriolis force, and wind stress dynamics. Specifically, this includes:

[0108] A right-handed coordinate system is established with the shoreline as the x-axis and the direction perpendicular to the shoreline towards the shore as the y-axis. The y-momentum equation in the two-dimensional full flow equation of fluid dynamics is selected. The convection term and the horizontal friction term are ignored. The integral is performed along the y-axis from the boundary between the continental shelf and the continental slope to the shore.

[0109] By combining the open sea water level and air pressure terms in the integrated results, assuming that the seabed friction force is proportional to the sea surface wind stress, estimating the horizontal flow velocity, and simplifying the Coriolis force integral term, a semi-theoretical and semi-empirical water increase forecasting formula is obtained, which uses the shore-side water increase as the forecast quantity and includes the air pressure response, coastal wind response, and onshore wind response. The formula is in the following form:

[0110]

[0111] Where ηs is the shore-side water level rise, a, b, c are undetermined coefficients, ρ is the seawater density, g is the gravitational acceleration, p∞ is the outer air pressure of the typhoon, ps is the shore-side air pressure, f is the Coriolis force coefficient, u is the average vertical velocity in the x-direction, τay is the wind stress in the y-direction of the sea surface, h is the water depth, ys is the shore-side coordinates, and ye is the coordinates at the boundary between the continental shelf and the continental slope.

[0112] For observation stations that are not suitable for cross-sectional integration along the vertical shoreline, the forecast formula is simplified to include the shoreline pressure difference, easterly wind stress, and northerly wind stress:

[0113] ,

[0114] in, These represent the wind stresses to the east and north of the observation station, respectively.

[0115] This invention establishes a standardized coordinate system and performs targeted integration and simplification of the y-axis momentum equation in hydrodynamics, preserving the core dynamic mechanisms of storm surge, such as pressure gradient force, Coriolis force, and wind stress. This gives the constructed semi-theoretical, semi-empirical storm surge forecast formula a solid foundation in hydrodynamics, enabling it to accurately reflect the intrinsic dynamic laws of storm surge. Furthermore, for observation stations unsuitable for vertical shoreline cross-sectional integration, a simplified forecast formula is provided, balancing theoretical validity with practical applicability. The formula's form can be flexibly adjusted according to the topographic features of different observation stations, significantly expanding its applicability to various marine stations in the target sea area and solving the problem of a single formula being difficult to adapt to complex terrain.

[0116] In some embodiments, step 2) involves calibrating the undetermined coefficients of the forecast formula using storm surge observation data from marine stations in the target sea area, specifically including:

[0117] Multiple storm surge observation data from marine stations in the target sea area were selected, and the water level increase data, corresponding typhoon parameters, and wind stress data for each storm surge were extracted.

[0118] By employing both constrained fitting (a=0) and unconstrained fitting (a≠0) methods, and using the least squares method to fit the observed data with the forecast formula, the optimal solution for the undetermined coefficients was obtained through calibration.

[0119] With unbiased fitting as the goal, the coefficient set whose fitting results are evenly distributed on both sides of the perfect fitting line is selected as the final calibration result. If the accuracy of the maximum water increase forecast is the key requirement, the coefficient set of unconstrained fitting is selected.

[0120] This invention calibrates the undetermined coefficients of the forecast formula by selecting storm surge observation data from multiple marine stations in the target sea area, ensuring the matching of the coefficients with the actual characteristics of storm surges in the target sea area. Simultaneously, it employs both constrained and unconstrained fitting methods, selecting the optimal coefficient set based on the fitting effect and actual forecast requirements. This achieves unbiased fitting, ensuring the fitting results are evenly distributed on both sides of the perfect fit line, improving the forecast accuracy of conventional storm surge events. Furthermore, it selects unconstrained fitting coefficients to address the critical needs of maximum storm surge forecasting, guaranteeing the accuracy of forecasting high-risk storm surge peaks. Through scientific coefficient calibration methods, the semi-theoretical, semi-empirical forecast formula closely matches the measured data of the target sea area, further improving the forecast accuracy of storm surge events.

[0121] In some embodiments, step 3) derives the theoretical analytical relationship between the time of maximum flooding and the typhoon path based on the response mechanism of storm surge to onshore wind stress, specifically including:

[0122] Assuming that the maximum increase in water level occurs at the shore when the onshore wind stress perpendicular to the shoreline is the maximum, the Jelesnianski (1965) model is selected to calculate the onshore wind stress outside the radius of the typhoon's maximum wind speed.

[0123] Setting the straight path equation of the typhoon By differentiating the onshore wind stress function and setting the derivative to 0, and combining it with the typhoon path equation, the coordinates of the typhoon's location when the onshore wind stress is maximum can be obtained.

[0124] Based on the typhoon's location coordinates, a formula for the relative distance between the typhoon and the observation station at the time of maximum water rise is derived, revealing the shortest distance d from the observation station to the typhoon's path. min The theoretical analytical relationship between the typhoon path slope k and the time lag of maximum water level rise:

[0125]

[0126] Where, d AC θ represents the distance the typhoon travels from its closest point to the location corresponding to the maximum water level rise, and θ is the angle between the shoreline normal and the wind speed direction.

[0127] This invention, based on the core response mechanism of storm surge to onshore wind stress, clarifies the intrinsic relationship between maximum storm surge and onshore wind stress, providing a solid dynamic theoretical basis for the forecasting of maximum storm surge time. By setting the straight-line path equation of the typhoon and differentiating the onshore wind stress function, the location of the typhoon at the point of maximum wind stress is obtained. Furthermore, the theoretical analytical relationship between the maximum storm surge time and typhoon path parameters is derived, clearly revealing the influence of the shortest distance from the observation station to the typhoon path and the slope of the typhoon path on the lag of the maximum storm surge time. This theoretically explains the intrinsic connection between the typhoon path and the maximum storm surge time, breaking through the limitations of traditional methods that rely solely on experience to judge the maximum storm surge time, and laying a theoretical foundation for the accurate forecasting of the maximum storm surge time.

[0128] In some embodiments, when the distance between the observation station and the typhoon path is less than the radius of the typhoon's maximum wind speed, it is deduced that the typhoon center moves about 2 hours after passing the observation station, and the distance between the observation station and the typhoon center reaches the radius of the maximum wind speed. At this time, the onshore wind stress is the greatest, and the maximum water level rise occurs on the shore.

[0129] This invention addresses the special scenario where the distance between the observation station and the typhoon's path is less than the radius of the typhoon's maximum wind speed. Through theoretical derivation, it clarifies the occurrence pattern of maximum water rise in this scenario: approximately 2 hours after the typhoon center passes the observation station, the maximum water rise occurs when the distance between the observation station and the typhoon center reaches the radius of the maximum wind speed. This precisely defines the quantitative relationship between the time of maximum water rise and the typhoon's movement in this special scenario. It solves the problem that traditional methods cannot accurately determine the time of maximum water rise in this scenario, providing a clear and quantifiable theoretical basis for forecasting the time of maximum water rise under this type of typhoon path, and improving the accuracy and applicability of maximum water rise time forecasting under different typhoon path scenarios.

[0130] In some embodiments, step 4) involves statistically analyzing the wind direction distribution characteristics of the historical storm surge maximum rise time at marine stations in the target sea area, and combining this with the theoretical analytical relationship from step 3) to establish a statistical forecasting method for the maximum storm surge time in the target sea area. This method specifically includes:

[0131] Collect wind speed and direction data at the time of maximum storm surge at marine stations in the target sea area, draw wind direction compass diagrams, and obtain the average wind direction D and the root mean square error θ at the time of maximum storm surge.

[0132] Combining the theoretical analysis relationship in step 3), the time corresponding to the wind direction being in the range of D-θ to D+θ during the typhoon is taken as the possible period when the storm surge is at its maximum.

[0133] When the distance between the observation station and the typhoon's path is less than the radius of the typhoon's maximum wind speed, the forecast time for the maximum storm surge is directly taken as 2 hours after the typhoon makes landfall.

[0134] This invention obtains the average wind direction and root mean square error of the maximum storm surge at historical storm surge times from statistical data of marine stations in the target sea area, accurately extracting the statistical regularity of wind direction at the maximum storm surge time. Combining the theoretical analytical relationship between the maximum storm surge time and typhoon path, the invention identifies the time interval where the wind direction falls within a specific range as the possible period for the maximum storm surge. Furthermore, it establishes clear forecast time standards for scenarios where the distance between the observation station and the typhoon path is less than the radius of the maximum wind speed. This constructs a maximum storm surge time forecasting method that balances theoretical derivation and empirical statistics, ensuring both the theoretical validity of the method and its alignment with the actual storm surge characteristics of the target sea area. This effectively solves the problems of traditional methods failing to accurately forecast the maximum storm surge time and ignoring the lag in storm surge prediction, significantly improving the forecast accuracy of the maximum storm surge time.

[0135] In some embodiments, step 5) of forecasting the storm surge in the target sea area specifically includes:

[0136] Obtain real-time typhoon parameters for the target sea area, including typhoon path, central pressure, maximum wind speed, and radius of the strong wind circle;

[0137] Based on the wind field model selected in step 1) and the maximum wind speed radius obtained by inversion, real-time air pressure field and wind stress field data are calculated.

[0138] Substitute the pressure field and wind stress field data into the semi-theoretical and semi-empirical storm surge prediction formula after step 2) to calculate the storm surge data of the target sea area marine station hourly.

[0139] This invention acquires real-time typhoon parameters of the target sea area and, combined with an optimized wind field model and the inverted maximum wind speed radius, can quickly calculate real-time pressure field and wind stress field data, ensuring the real-time nature and accuracy of the forecast input data. By substituting the real-time pressure field and wind stress field data into the calibrated semi-theoretical and semi-empirical storm surge forecast formula, hourly calculations of storm surge data at marine stations can be obtained, achieving continuous and dynamic forecasting of storm surge processes. This overcomes the limitation of traditional empirical formulas, which can only predict the maximum storm surge and cannot reflect the entire storm surge process. The entire forecasting process has a simple calculation flow and clear steps, requires no high-end computing resources, has high computational efficiency, and can quickly output storm surge forecast results, meeting the timeliness requirements of storm surge early warning and forecasting.

[0140] Reference Figure 17 Secondly, the present invention provides a storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction system, comprising:

[0141] The wind field model optimization module is used to verify and optimize the typhoon wind field model that is suitable for the target sea area, and to obtain the maximum wind speed radius of the typhoon by inverting the typhoon wind circle data of the target sea area.

[0142] The forecast formula construction module is based on the hydrodynamic y-direction momentum equation. It integrates and simplifies along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge forecast formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. The undetermined coefficients of the forecast formula are calibrated using storm surge observation data from marine stations in the target sea area.

[0143] The theoretical relationship derivation module, based on the response mechanism of storm surge to onshore wind stress, derives the theoretical analytical relationship between the time of maximum surge and typhoon path, revealing the influence of typhoon path parameters on the time lag of maximum surge.

[0144] The time forecast module statistically analyzes the wind direction distribution characteristics of the maximum storm surge time in the target sea area, and combines theoretical analytical relationships to establish a statistical forecasting method for the maximum storm surge time in the target sea area.

[0145] The integrated forecasting module, based on the typhoon's maximum wind speed radius and a calibrated semi-theoretical and semi-empirical storm surge forecasting formula, forecasts the storm surge process in the target sea area. Combined with the statistical forecasting method for the maximum storm surge time, it achieves accurate prediction of the maximum storm surge time in the target sea area.

[0146] This invention presents a semi-theoretical, semi-empirical storm surge forecasting and maximum flood rise time prediction system. Through the division of labor and cooperation among various functional modules, it achieves a systematic implementation of the entire process, including typhoon wind field model optimization, forecast formula construction, theoretical relationship derivation, time forecast method establishment, and comprehensive forecasting. Each module is highly targeted and logically connected, enabling modular implementation of key technical aspects of storm surge forecasting and improving the overall operability and engineering application capabilities of the method. The wind field model optimization module provides accurate typhoon parameters for forecasting, the forecast formula construction module provides a forecast model that fits the target sea area, the theoretical relationship derivation and time forecast establishment module achieves accurate forecasting of the maximum flood rise time, and the comprehensive forecasting module integrates the results of each step to achieve coordinated forecasting of the flood rise process and the maximum flood rise time. The system operates efficiently and provides accurate forecasts, can quickly respond to real-time typhoon data and output forecast results, and can be directly applied to storm surge early warning and forecasting work in target sea areas, possessing extremely strong practical application value.

[0147] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0148] Example:

[0149] 1. Wind field model validation

[0150] This invention requires combining typhoon path and typhoon structure to analyze the dynamic mechanism of storm surge. Therefore, the selection of the wind field model is crucial. This invention prioritizes the use of a typhoon wind field model.

[0151] The pressure field and wind field of a typhoon are the main driving forces of storm surge. The accuracy of the driving field almost determines the accuracy of storm surge forecasts. Currently, numerical wind fields are available for typhoon forecasts. Numerical wind fields can predict typhoon paths relatively well, but typhoon intensity can still have significant errors. Typhoon forecasts provide typhoon path and intensity parameters, and the pressure field and wind field can be calculated using traditional empirical typhoon models. With the improvement of meteorological satellite monitoring capabilities, typhoon location and intensity determination based on satellite remote monitoring data have achieved good accuracy. Under normal circumstances, the typhoon path and typhoon parameter forecast results can well meet the needs of storm surge forecasting. However, when constructing the wind field based on typhoon parameters, it is necessary to select appropriate empirical formulas. The typhoon path and wind circle dataset provided by the Shanghai Typhoon Institute of the China Meteorological Administration (Lu et al., 2017, 2022) provides wind circles for gale-force winds of level 12, 10, and 8, while the Japan Meteorological Agency (JMA) optimal typhoon path set provides wind circles for gale-force winds of level 10 and 7. The wind circle radius can be used to verify the typhoon model formulas.

[0152] Commonly used typhoon models include the formulas of Takahashi (1939), Fujita (1952), Myers (1954), Jelesnianski (1965, 1966), and Holland (1980). Typhoon forecasts provide maximum wind speed and central pressure, but not the radius R of the maximum wind speed. In some numerical forecasts, the radius of the maximum wind speed is usually expressed as an empirical function of central pressure and latitude. For example, Vickery et al. (2000) used the following formula to calculate R. (2)

[0153] In equation (2), The value of lat represents the difference between the central and peripheral air pressures of a typhoon, with latitude being the latitude. This formula often shows significant discrepancies compared to measured values, resulting in low fitting accuracy. This invention uses the optimal typhoon path set from the China Meteorological Administration to analyze the applicability of typhoon models. The dataset includes central air pressure, maximum wind speed, and the radii of wind circles for gale-force winds of levels 12, 10, and 8. The maximum wind speed radius of the typhoon is inferred from the three levels of gale-force wind circles. If the inferred maximum wind speed radius is consistent or similar, it indicates that the typhoon model used is applicable.

[0154] The Jelesnianski (1965) model has the following pressure field:

[0155] , (3)

[0156] In equation (3), The central pressure of the typhoon. This refers to the outer pressure of the typhoon. Let be the radius of maximum wind speed. Ignoring the Coriolis force, the corresponding wind field is...

[0157] (4)

[0158] In equation (4), This is the maximum wind speed of the typhoon.

[0159] It is generally believed that the wind field attenuation of the outer periphery of the typhoon calculated by equation (4) is slow, and the calculation speed is too high. Jelesnianski (1966) modified its model. At present, the commonly used wind field model is the Holland (1980) formula.

[0160] The three maximum wind speed radii were derived by inverting the wind circle. If they are consistent, it indicates that the model can correctly describe the typhoon structure. Based on the optimal typhoon path set and wind circle data from the China Meteorological Administration, the formulas of Jelesnianski (1965), Jelesnianski (1966), and Holland (1980) were verified. It was found that the Jelesnianski (1965) formula is most applicable to typhoons in the South China Sea. The derived maximum wind speed radii are shown in Figure 1.

[0161] As shown in the figures, the typhoon radius retrieved by the Jelesnianski (1965) model does not exhibit systematic bias, and its description of the typhoon structure is more reasonable. In the Jelesnianski (1966) model, the maximum wind speed radius retrieved from the 7-level gale circle is significantly larger than that retrieved from the 10-level gale circle (figure omitted). This indicates that the typhoon wind speed calculated by this model is outside the maximum wind speed radius, and the wind speed decays too rapidly. If the model is used for storm surge simulation, the simulated storm direction along the shoreline affected by the outer wind field will be underestimated. For the Holland (1980) model, the typhoon radius retrieved from the 3-level gale circle also does not exhibit systematic bias, but the calculated maximum wind speed radius is underestimated (figure omitted). Furthermore, the original dataset provides the maximum wind speed radius (RMW), but it does not match the various levels of gale circles, is too small, and is therefore unusable.

[0162] Therefore, in the forecasting of storm surges in the South China Sea, it is recommended to use the Jelesnianski (1965) formula to calculate the typhoon pressure field and wind field. The radius of maximum wind speed is derived by inverse calculation from the wind circle of the large wind, and the average value of the inversion radius of different wind circles is taken.

[0163] Furthermore, using JMA typhoon optimal track set data for verification, the Jelesnianski (1965) formula remains the most suitable. However, the correlation between the maximum wind speed radius retrieved from the two-stage wind circle and the CMA data is not as high.

[0164] 2. Semi-theoretical and semi-empirical forecasting method for storm surges

[0165] 2.1 Characteristics of Storm Gauge Increase

[0166] The varying paths, intensities, structures, and speeds of typhoons, along with the influence of topography and tides, result in highly complex storm surge phenomena along the coast of South China. In the northern South China Sea, 80% of typhoon movements are concentrated in the W-NNW range. When a typhoon is far from a particular marine station, the surrounding waters experience offshore winds. When the typhoon is closest to the station, wind speeds reach their maximum, with a generally westward (easterly) direction along the coast. As the typhoon moves westward, it gradually shifts to onshore winds, and wind speeds gradually decrease. Corresponding to this wind speed process, the area near the marine station also experiences offshore winds (with a westward coastal component), and the observed water level gradually rises, representing the leading wave (initial vibration stage) of the storm surge. When the typhoon center approaches the observation station and moves westward away, the surrounding waters shift to onshore winds. Under the pressure of air pressure, wind stress, and wave radiation stress, the water level rises sharply, representing the intensified stage of the storm surge. This forced wave is also accompanied by false tides. As the typhoon moves further west, the onshore winds gradually decrease and the water level recedes, but significant fluctuations remain, marking the aftershock phase of the storm surge. Figure 2 This describes the storm surge process at Shanwei station during Typhoon No. 1713 in 2017. The storm surge process at Shanwei station during Typhoon No. 1713 exhibited typical three-stage characteristics: initial surge, excitation, and aftershock. The storm surge process was closely related to the typhoon's path, movement speed, maximum wind speed radius, coastline orientation, and continental shelf morphology. For example, during Typhoon No. 1713, the storm surge at Guangzhou station (see...) Figure 3 This is significantly different from the situation at Shanwei Station. The Lingdingyang waters are shallow, the initial surge is not obvious, the initial surge is intense, and the storm surge decays rapidly. During a typhoon, storm surges on any coastal section are not entirely locally forced; they are closely related to the hydrodynamic processes of the surrounding waters and the coastal section.

[0167] 2.2 Analysis of the dynamic mechanism of storm surge

[0168] Storm surge is consistent with hydrodynamic equations, and Pugh (1987) provided an explanation for the storm surge mechanism. This invention uses the dynamic mechanism given by Pugh (1987) to analyze storm surge phenomena along the coast of South China.

[0169] Establish a right-handed coordinate system with the shoreline as the x-axis and the direction perpendicular to the shoreline as the y-axis (y-direction towards the shore is positive) (see... Figure 4 The origin of the coordinate system is taken as the location of the ocean station. Then, in the 2D total flow equations, the momentum equation in the y-direction is:

[0170] (5)

[0171] In equation (5), , These are the average vertical flow velocities in the x and y directions, respectively. Water level; It refers to air pressure; For sea surface wind stress; This is due to friction on the seabed. For water depth; The Coriolis force coefficient; The acceleration is due to gravity. Nearshore storm surge increases are also contributed by wave radiation stress, but this mechanism is not included in equation (5).

[0172] 1) Response of floodwaters to coastal winds

[0173] As a typhoon moves and approaches the coastline of South China, it generates strong winds along the coast, driving strong coastal currents. These strong currents produce Coriolis forces perpendicular to the shoreline, which balance the water level gradient forces perpendicular to the shoreline.

[0174] ,

[0175] This results in fluctuations in the water level along the coast. Integrating the equilibrium equation between the Coriolis force and the water level gradient force, we obtain...

[0176] (6)

[0177] In equation (6), This indicates the starting point of the integral section (on the shore, i.e., the location of the station); The endpoint of the integration section is taken as the boundary between the continental shelf and the continental slope (approximately at a water depth of 200m). Along the Guangdong coast, assuming a westward coastal current width of 100km and a velocity of 1m / s, we take... =5×10 -5 s -1 The water level at the shore was found to be 0.5m.

[0178] This mechanism is used to generate precursory storm surges during major storm surges. Similarly, the sustained flooding on the left bank of the landfall point caused by some typhoons is also due to this mechanism.

[0179] 2) Response of increased water level to onshore winds

[0180] During the movement of a typhoon, a certain section of the shore begins to experience onshore winds, and the storm surge enters the intensification stage. At this time, the storm surge is a forced wave driven by wind, air pressure, and waves. Onshore wind stress becomes the dominant driving force. In equation (5), the balance between the water level gradient force and the frictional force is considered.

[0181] .

[0182] Disregarding bottom friction, integrating along the y-direction yields the contribution of onshore wind stress to the water level rise at the shore.

[0183] (7)

[0184] When calculating wind stress, the Jelesnianshi (1965) formula is used to calculate the wind field. The formula for calculating wind stress is as follows:

[0185] (8)

[0186] In equation (8), air density; This represents the sea surface wind drag coefficient.

[0187] In the analysis of wind speed and water level rise along the South China coast, water level rise typically reaches its maximum when the onshore wind force is near its maximum. For example, during Typhoon No. 1713, the wind speed and water level rise at Shanwei station (see...) Figure 2 This demonstrates the role of onshore wind stress in the storm surge intensification phase.

[0188] Assuming a 30 m / s onshore wind, with an effective wind zone length of 50 km and a water depth of 30 m, the onshore wind stress is: (Air density is taken as 1.16 km / m3), and the water increase calculated according to formula (7) is 0.44 m. If the wind force has a length of 150 km, the water increase is 1.32 m. This illustrates the influence of the maximum wind speed radius on the water increase. For example, the radius of the wind circle of Typhoon No. 1822 with a wind force of level 10 is greater than 200 km, and the radius of the wind circle with a wind force of level 7 is greater than 500 km. As a result, large water increases were generally generated in eastern Guangdong and along the Pearl River Estuary.

[0189] 3) Response of water supply to air pressure

[0190] As a typhoon moves, the pressure difference at its center induces what is known as a meteorological tsunami. Let x denote the typhoon's movement pattern; the governing equation for meteorological tsunamis is (Pugh, 1987).

[0191] (9)

[0192] The increase in water level at the shore caused by air pressure

[0193] (10)

[0194] In formula (10), This represents the typhoon's moving speed. The formula shows that when the typhoon is stationary, the increase in water level is due to the hydrostatic effect. When the typhoon's moving speed... Less than the speed of shallow water wave propagation At that time, the storm surge caused by the movement of the low-pressure center increases with the increase of the movement speed. At that time, storm surges will resonate. At that time, storm surge will exhibit a negative phase. Typically, Storm surges increase with the speed of typhoon movement, demonstrating the significant impact of typhoon speed on storm surges. If the water depth is 30m, the meteorological tsunami is 12 / 11 times the hydrostatic effect. If the water depth is 10m, it is 4 / 3 times. Therefore, the open and shallow waters of the Lingdingyang area are conducive to the generation of significant meteorological tsunamis.

[0195] 4) Case Study on Storm Surge Mechanism

[0196] This paper analyzes some mechanisms of storm surge by combining storm surge data and typhoon tracks observed at marine stations. The influence of coastal winds on water levels is achieved through coastal currents. Therefore, it is necessary to calculate the current velocity distribution along the coast. Here, we first provide an estimate of the current velocity during a typhoon. In the momentum equation, we only consider the balance between the Coriolis force, wind stress, and bottom friction (approximately valid in open sea areas). Thus, the momentum equation simplifies to...

[0197] (11)

[0198] Linearize the bottom friction force. Solve the system of equations.

[0199]

[0200] get

[0201] (12)

[0202] In equation (12), The coefficient of linear bottom friction, with the dimension of velocity, was taken as 0.006 ft / s by Jelesnianski (1967) in a storm surge simulation experiment. Moon & Tang (1987), through model calibration using a satellite altimeter, obtained an optimal coefficient of 0.00255 m / s. This report uses the optimal coefficient obtained by Moon & Tang (1987) to estimate the flow velocity at the typhoon break surface.

[0203] Starting from Shanwei Station, a cross-section in the NNW-SSE direction is taken, with the cross-section orientation roughly perpendicular to the shoreline and the isobaths of the continental shelf. The cross-section length is limited to a water depth of 200m. The wind stress in the coastal and onshore directions is calculated using Equation (8). The flow velocity driven by the typhoon on the cross-section is calculated using Equation (12). The effects of coastal wind, onshore wind, and air pressure on storm surge are calculated using Equations (6), (7), and (10). Figure 5This paper presents the wind speed, water level rise, and the response of water level rise to coastal winds, onshore winds, and air pressure at the Shanwei station for Typhoon No. 1822. During the precursor water level rise phase, the response of water level rise to coastal winds is roughly the same. This demonstrates the dominant role of coastal winds in the initial stage of storm surge. As the typhoon moves, the coastal winds shift to onshore winds, and since wind stress is proportional to the square of wind speed, the water level rises sharply. This shows that onshore winds are the dominant driving force in the storm surge intensification phase. Because the path of Typhoon No. 1822 is relatively far from the Shanwei station, the air pressure effect is weak, i.e., a hydrostatic effect. The calculation of the coastal current assumes a balance between Coriolis force and frictional force. Figure 5 The increase in water level along the coast and the decrease in water level on the shore roughly cancel each other out in the initial stage of the ripple. This is due to the estimation method of the coastal current. This at least demonstrates the rationality of this mechanism.

[0204] 2.3 Semi-theoretical and semi-empirical formula establishment method

[0205] Analysis of the storm surge mechanism reveals that storm surges are primarily responses to coastal winds, onshore winds, and air pressure. This is reflected in the momentum equation as the balance between the water level gradient force and the Coriolis force, the water level gradient force and the onshore wind stress, and the air pressure effect. This invention derives the formulaic framework for storm surge forecasting from the fluid dynamics momentum equation. Figure 4 In the coordinate system shown, neglecting the convection and horizontal friction terms in the momentum equation (4.1) in the y-direction (perpendicular to the shore), integrating the equation toward the shore yields...

[0206] (13)

[0207] In equation (13), This indicates the starting point of the transect on the continental shelf, on the shore, i.e., the location of the observation station. =0); This indicates the outer boundary of the continental shelf section, the junction between the continental shelf and the continental slope. The width of the continental shelf in the northern South China Sea is approximately 200 km. =-200*103m; Our forecast volume is needed to increase the water level along the shore. The water level at the outermost point of the cross-section is shown. Since the integral cross-section is far from the shore, the water level in the open sea area is considered to be... It can be calculated based on the static pressure effect. Thus, in equation (13), the first and fourth terms on the right side are combined into one. .

[0208] Equation (13) also involves the bottom friction force. and flow rate , The calculation of storm surge mechanism is as follows. In the analysis of storm surge mechanism, it is assumed that the Coriolis force and friction force are in balance, and the flow velocity of the whole flow is calculated using equation (11). The resulting response of the storm surge to coastal winds is underestimated. Therefore, the approach is changed in the establishment of empirical formulas. The drag coefficient Cd of bottom friction is roughly equivalent to the wind drag coefficient under strong wind conditions. Therefore, the horizontal flow velocity is estimated as follows.

[0209] (14)

[0210] In equation (14), air density, The density of seawater, The value is approximately 0.033, which is close to the wind factor of the measured flow velocity during a typhoon. When calculating the flow velocity using typhoon parameters, since the typhoon path data is collected in 6-hour intervals, the calculation of the second term (local acceleration) on the right side of equation (13) is prone to large data jumps. Therefore, without considering the influence of local acceleration, the empirical formula is taken as follows. (15)

[0211] In Equation (15), the second term on the right represents the response of storm surge to air pressure, the third term represents the response to coastal winds, and the fourth term represents the response to onshore winds. This means that the three main dynamic mechanisms of storm surge are reflected in the formula; a, b, c, and d are undetermined coefficients obtained by regression from observation data.

[0212] For some observation stations, it is not suitable to integrate the momentum equation on a cross section approximately perpendicular to the shoreline, such as Guangzhou Station, Chiwan Station, and Haikou Station, so the form of equation (15) cannot be used. From equation (11), the flow velocity can be expressed as... , The function. Therefore, equation (15) can be further simplified to

[0213] (16)

[0214] In equation (16), , This represents the wind stress in the east and north directions at the observation station. Compared with equation (15), the dimensions of equation (16) are inconsistent, while the dimensions of equation (15) are consistent.

[0215] 2.4 Formula Calibration and Verification

[0216] This invention establishes semi-theoretical, semi-empirical formulas for 17 marine stations along the coasts of Guangdong, Hainan, and Guangxi. The distribution of stations and integral sections is as follows: Figure 6 .

[0217] When establishing the empirical formula using equation (15), the water depth at the integration section needs to be considered. The water depth data used is ETOPO2 data (NGDC, 2006). For wind stress calculation and velocity estimation, the best track set for tropical cyclones in the Northwest Pacific published by the China Meteorological Administration (CMA), and the dataset of gale circles based on this dataset (Lu et al, 2017, 2022) are mainly used. Furthermore, in the best track sets for tropical cyclones in the Northwest Pacific published by different institutions, such as the China Meteorological Administration and the Japan Meteorological Agency (JMA), there are significant differences in the typhoon tracks, intensities, and gale circles. During formula establishment, typhoon data will be selected based on the fitting accuracy of the formula.

[0218] 1) Formula calibration

[0219] Taking Zhapo Station as an example, the calibration and verification of the formula are illustrated. The integration section direction of Zhapo Station is NNW-SSE. 49 storm surges and 486 sets of data were selected for empirical formula fitting. When using Equation (15) to establish the fitting formula, the following formula is obtained:

[0220] (17)

[0221] The correlation coefficient was 0.762, and the root mean square error of the fit was 0.177m. The fitting results are as follows: Figure 7 .

[0222] The fitting results show that the fitted values ​​are significantly correlated with the measured water increase, and the fitting accuracy is high. The formula reflects the main mechanism of storm water increase and shows good applicability in practical applications. A constant 'a' is introduced in equation (15), and the formula is unconstrained. Adding a coefficient can improve the fitting accuracy, but it can cause fitting skewness. When the water increase is less than 0.6 m, the fitted values ​​are generally higher than the measured values. If the coefficient 'a' is removed from equation (15), the fitting formula obtained is: (18)

[0223] The fitting correlation coefficient was 0.756, and the root mean square error of the fit was 0.187 cm. The fitting results are shown in Figure 9.

[0224] The fitting results show that the constrained empirical formula () is effective. The fitting accuracy is very close to that of the unconstrained formula, and the fitting results are roughly evenly distributed on both sides of the perfectly fitted line at different stages of water inrush. This fitting is unbiased. However, for individual maximum water inrushes, the fitting accuracy of the constrained empirical formula decreases. From the perspective of overall forecast performance, this invention aims to establish an unbiased fitting formula.

[0225] It should be noted that, due to the large sample size used in establishing the formula, the sample size for large-scale water surges only accounts for a small portion. The overall fitting accuracy reaches 19 cm. However, for large-scale water surges, the fitting error is significantly greater than 19 cm. Furthermore, the forecast accuracy for large-scale water surges is more critical for early warning and forecasting.

[0226] 2) Formula applicability assessment

[0227] Path Type 1: The typhoon path passes south of the observation station, which is outside the radius of maximum wind speed. In formula development, storm surge data from this type of typhoon path were primarily selected for regression coefficients. The three main dynamic mechanisms of storm surge are well represented in the formula. The fitting results show that the formula can reproduce the storm surge process well. For example, for Typhoon 0312, the storm surge sequence of that typhoon was used in formula development, and the fitting results are as follows... Figure 9a It is evident that the formula fits the water increase process and peak value quite well.

[0228] Path Type 2: The typhoon path passes south of the observation station, which is within the radius of maximum wind speed. For this type of typhoon path, as the typhoon approaches the observation station, offshore winds are generated first, gradually increasing in strength. The offshore winds are at their maximum when the typhoon center is exactly within the radius of maximum wind speed. Then, the wind speed decreases, reaching its minimum and lowest pressure when the typhoon center is closest to the observation station. The wind speed then begins to increase again, and the wind direction shifts towards the shore. The towards-shore winds are strongest when the station is within the radius of maximum wind speed. This type of path makes it difficult to calculate westward coastal flow; therefore, it cannot reflect the balance between pressure gradient force and Coriolis force. This type of storm surge formula was not selected for empirical formula development. However, formula testing revealed that the regression formula is suitable for predicting the peak storm surge of this type of typhoon. Typhoons 8402, 8702, 9309, 0307, ​​and 1311 are all of this type; peak storm surges occurred when the typhoon center passed the station and shifted to towards the shore. See the results below. Figures 9b-9f .

[0229] The paths of typhoons No. 8402, 8702, 9309, 0307, ​​and 1311 are as follows: Figures 9a-9f The minimum distances between the Zhapo station and these five typhoon paths were 23.5 km, 22.1 km, 18.8 km, 41.7 km, and 3.5 km, respectively. The storm surges generated by these typhoon paths all occurred approximately 2 hours after the typhoon passed, precisely when the onshore winds were strongest. Therefore, this is an important basis for forecasting the timing of maximum storm surge.

[0230] Path Type 3: The typhoon path passes north of the station, within the radius of maximum wind speed. This type of typhoon first makes landfall on the eastern bank of the Zhapo station and passes north of the station. Initially, it is an offshore wind, which then turns into an onshore wind after the typhoon passes. Formula verification revealed that equation (18) is not suitable for predicting water level rise in this type of typhoon path, and the calculated results are too low. However, if the Coriolis force term (second term on the right) in equation (18) is not considered, and the formula is changed to...

[0231] , (19)

[0232] The coefficients of the formula are the same as those in equation (19), so the forecast of the peak water level increase can still be given. Typhoons 8908, 9302, and 1822 all made landfall on the east bank of Zhapo Station and passed north of the station. The shortest distances between Zhapo Station and the paths of these three typhoons are 4.6 km, 4.8 km, and 42.6 km, respectively. Among these three typhoons, the water level increase at Zhapo Station predicted by equation (19) is as follows: Figures 10a-10c .

[0233] As shown in the figure, the formula cannot predict the storm surge process of precursor storms because it does not consider the Coriolis effect. When the typhoon passes the observation station, the pressure effect and onshore winds play a dominant role, and the formula can reproduce the peak storm surge process relatively well. It can also roughly predict the receding storm surge process. The maximum storm surge also occurs when the onshore winds are strongest, about 2 hours after the typhoon passes the station.

[0234] 3. Forecast of the time of maximum water rise based on typhoon track

[0235] 3.1 Analysis of the impact of typhoon track on the timing of peak storm surge

[0236] 1) Statistics on Typhoons with Significant Water Increase at Marine Stations

[0237] This invention statistically analyzed typhoons that caused significant water level increases at various marine stations. Based on the typhoon's direction of movement, paths of typhoons moving in roughly the same direction were plotted. The location of the typhoon at the point of maximum water level increase (indicated by "#" in the diagram) and the location of the typhoon closest to the marine station (indicated by "+") were marked on the paths to facilitate understanding the relationship between maximum water level increase and typhoon path. For typhoons causing significant water level increases in Guangdong, except for Naozhou station, a maximum water level increase greater than 70 cm was used as the selection criterion. In Zhanjiang Bay, most typhoons caused water level increases greater than 70 cm. To avoid selecting too many typhoons, typhoon events with water level increases greater than 90 cm were selected.

[0238] Typhoons from the Northwest Pacific enter the South China Sea, typically following a W, WNW, or NW path. Along the eastern coast of Guangdong, WNW and NW-path typhoons generate prolonged onshore winds, favoring typhoon-induced flooding. Significant flooding is observed at the Shanwei station. Marine stations producing significant flooding are generally located to the right of the typhoon's path. For WNW and NW-path typhoons, the wind force is strongest when the typhoon is closest to the marine station, but this is usually not the moment of maximum flooding. Generally, maximum flooding occurs later than the time of minimum distance. Observational data shows that, generally, the greater the distance between the typhoon's path and the marine station, the later the lag between the maximum flooding and the minimum distance. When the typhoon's path passes the observation station, maximum flooding occurs approximately 2 hours later. For N-path typhoons, maximum flooding occurs earlier than the time of minimum distance from the marine station. At the time of maximum flooding, the typhoon's position at the marine station produces wind speeds nearly perpendicular to the shoreline. This can also be seen from the typhoon wind speed and water level process lines at the marine station. The maximum rise in water level generally occurs when the wind speed changes direction and the onshore wind is at its maximum.

[0239] Green path, increase water level by 70cm~100cm; Pink path, increase by 101cm~150cm; Red path, increase by >150cm.

[0240] "+" indicates the point where the typhoon is closest to the observation station, and "#" indicates the typhoon's position at the time of maximum water level rise. The same applies to the following figures.

[0241] 2) Theoretical relationship between the time of maximum flood surge and typhoon path

[0242] Statistically, the timing of maximum storm surge appears to be correlated with the typhoon's path, based on observational data. This invention will now theoretically analyze this relationship. In the response mechanism of storm surge to onshore wind stress, equation (7) shows that the onshore water level gradient is greatest when the onshore wind stress is maximum. The maximum water level gradient corresponds to the maximum water level at the shore. Based on measured wind speeds and storm surge processes, during strong typhoons, the wind speed is roughly perpendicular to the shoreline when maximum storm surge occurs. Therefore, assuming that maximum storm surge occurs when the wind stress perpendicular to the shoreline is maximum, this study explores the relationship between the timing of maximum storm surge and the typhoon's path. Figure 4 In the coordinate system shown, assuming the typhoon's path is a straight line, its path equation is:

[0243] (20)

[0244] The actual maximum water level rise occurs outside the radius of the maximum wind speed, and the influence of typhoon movement on wind speed is not considered (only for the convenience of calculating the analytical solution). First, consider the case where the observation station is outside the radius of the typhoon's maximum wind speed. Use equation (4) to calculate the typhoon wind speed outside the radius of the maximum wind speed. Record the onshore wind stress at the observation station. Take as

[0245] , (twenty one)

[0246] assumed The constants are defined when the maximum wind speed and the radius of the maximum wind speed of the typhoon remain unchanged. The maximum value is only related to the typhoon path. When taking the maximum value, there must be

[0247] ,

[0248] Therefore, we obtain

[0249]

[0250] Organized

[0251]

[0252] Substituting the typhoon path equation (20) into the above equation, we get

[0253] .

[0254] When b < 0, solve for the result.

[0255] , (22a)

[0256] (22b)

[0257] In the above formula, Represents the shortest distance from the origin of the coordinate system to the typhoon's path (e.g., Figure 11 ), .

[0258] like Figure 11 As shown, the maximum onshore wind stress occurs at the origin when the typhoon reaches point A. The length of line segment AB is...

[0259] .

[0260] The length of line segment BC is Then there is

[0261] .(twenty three)

[0262] Equation (23) shows that the time of maximum water level rise at the observation station during typhoon movement is related to the distance from the observation station to the path. related, The larger the typhoon, the later the peak flood season. Furthermore, it is also related to the typhoon's movement direction (…). This relates to the direction of typhoon movement. Equation (23) can be rewritten as...

[0263] .

[0264] but and Relationship such as Figure 12 As shown. The larger the value, the shorter the time lag before the maximum water rise occurs. In other words, for the Shanwei station, the maximum water rise occurs faster after a NW-type typhoon passes the station (reaching its minimum distance) than a WNW-type typhoon. This theoretical analysis is consistent with observational phenomena.

[0265] Now, let's consider the scenario where the typhoon's path passes through the observation station. In this case, the formula for calculating the onshore wind stress is:

[0266] . (twenty four)

[0267] If the path range is not considered, equation (24) does not have a maximum value. The onshore wind stress reaches its maximum when the distance between the observation station and the typhoon is exactly the radius of the maximum wind speed. Since the radius of the maximum wind speed is usually tens of kilometers, after the typhoon center passes the observation station, it moves for about 2 hours, and the distance between the observation station and the typhoon center is greater than the radius of the maximum wind speed. In the observation data, typhoons that pass the observation station often reach their maximum water level increase after 2 hours.

[0268] 3.2 The impact of typhoon landfall angle on water level rise

[0269] Equation (7) shows that when the onshore wind stress is at its maximum, the onshore water level gradient is at its maximum, and the water level rise is also at its maximum. Equation (22) gives the location where the maximum onshore wind stress occurs in different directions of movement for a straight-moving typhoon. This location is only a function of the direction of movement; therefore, the variation of the maximum onshore wind stress with the landfall angle can be calculated using equations (21) and (22). When the typhoon path passes within a circle centered at the observation station and with a radius R of maximum wind speed, the maximum onshore wind speed is calculated using equation (24).

[0270] In equation (24), let be . When the maximum value is obtained, it is denoted as Then there is

[0271] (25)

[0272] The radius of maximum wind speed, R, is used as the unit of distance. The typhoon path is given by equation (20). In this invention, b is taken as -6R, -4R, -2R, and 0 respectively to calculate the maximum onshore wind stress at the origin of the typhoon in different directions of movement. Maximum onshore wind stress and The ratio is as follows Figure 13When the onshore wind stress reaches its maximum in different directions of movement, the location of the typhoon center is as follows: Figure 14 . Figure 14 In the middle, when the typhoon path intersects with the curve in the figure, the wind stress on the shore at the origin is the greatest.

[0273] As shown in the figure, when b is -6R, -4R, and -2R, the maximum onshore wind stress generated by typhoons moving parallel to the shoreline (at an angle of 0° or 180°) is relatively small, less than 0.2. When the typhoon moves along the coastline and reaches the point (-R, 0) (west of the observation station, at a distance R from the station), the maximum onshore wind stress occurs. =0.9397 For a typhoon moving parallel to the coastline, the onshore wind stress decreases sharply as the distance between the path and the coastline increases. When the distance to the coastline is R (b = -R), =0.55 Therefore, for typhoons moving parallel to the shoreline, if the distance from the shoreline is greater than the radius R of the maximum wind speed, the coastal flooding will be minimal. A typhoon passing the observation station, if moving in a 160° direction, can generate a shore-to-shore wind stress that can reach [amount missing]. (The maximum increase in water level occurs when the typhoon moves onto a circle with radius R centered at the origin.) This means that a 20° angle between the typhoon's direction of movement and the shoreline is most conducive to increased water level along the coast. At a 70° angle, the maximum onshore wind stress is zero. In observational data, some typhoons whose paths were roughly parallel to the shoreline did not produce significant water level increases.

[0274] When a typhoon moves toward the shore perpendicular to the coastline, the maximum onshore wind stress it generates is 0.342. ( Figure 14 (At the intersection of the four curves). When the typhoon reaches (0,R), the onshore wind stress is at its maximum. .

[0275] Assuming a westward movement of the typhoon is represented by a direction of movement of 180°, as the direction of movement deviates northward (from 180° to 90°), the maximum onshore wind stress at the origin gradually increases. When the path deviates to pass through (-R, 0), the onshore wind stress reaches its extreme value. =0.9397 Then, deflecting northward, when passing (0, R), the path is perpendicular to the shoreline, and the onshore wind stress decreases to... =0.342 In other words, the storm surge is greatest along the coast at the radius R of maximum wind speed, to the right of the typhoon's landfall point.

[0276] 3.3 Statistical forecasting method for the time of maximum water level rise

[0277] The wind speed and direction at each of the maximum storm surge times recorded at the marine stations were calculated. The wind speeds corresponding to each maximum storm surge time were plotted using a compass chart (see results for some stations). Figure 15 This is to understand the prevailing wind direction distribution when the maximum flood surge occurs. In the figure, the red arrows represent the average direction of the concentrated wind direction area, and the arrow lengths are hypothetical, not actual wind speeds.

[0278] Given the statistical patterns of wind direction distribution during peak flood season, a forecasting method for the timing of peak flood season can be established based on the typhoon path and the statistical patterns of various stations. Using the historical average wind direction D and the root mean square deviation θ, the time intervals from D-θ to D+θ during the typhoon are considered as the possible periods for peak flood season.

[0279] The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method and system provided by this invention have the following beneficial effects:

[0280] This invention first selects a typhoon wind field model suitable for the target sea area, and then uses the wind circle data to invert the typhoon's maximum wind speed radius. This solves the problem that the maximum wind speed radius is fitted by the central pressure in the traditional method and has a large deviation from the actual measurement, thus providing an accurate basis for typhoon dynamic parameters for storm surge forecasting.

[0281] A semi-theoretical and semi-empirical water increase prediction formula is constructed based on the momentum equation of fluid dynamics. It takes into account the core dynamic mechanisms such as pressure gradient force, Coriolis force, and wind stress, and overcomes the shortcomings of traditional empirical formulas that lack theoretical support. At the same time, by simplifying the equations and calibrating the measured coefficients, the amount of calculation is greatly reduced, and the problems of high computational resource requirements and long time consumption in numerical prediction are solved.

[0282] Two forecast formulas, a basic type and a simplified type, are provided for different observation station terrain features, which improves the adaptability of the method. Furthermore, the coefficients are calibrated by two fitting methods, a constrained type and an unconstrained type, which takes into account the accuracy requirements of unbiased fitting and maximum water increase forecast.

[0283] A method for predicting the maximum flood time was established by combining theoretical derivation and statistical analysis. It not only revealed the intrinsic relationship between typhoon path and maximum flood time through dynamic principles, but also used historical observation data to statistically analyze wind direction distribution patterns, thus solving the problems of traditional methods being unable to accurately predict the maximum flood time and ignoring the lag of flood.

[0284] The method of this invention has low computational cost and high forecasting efficiency. It does not require high-end computing resources and can simultaneously achieve accurate forecasting of storm surge increase process and maximum increase time. Moreover, the required number of observation samples is far lower than that of machine learning methods. It makes full use of the observation data from the dense marine stations along the South China Sea coast, meeting the timeliness and accuracy requirements of storm surge early warning and forecasting.

[0285] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for semi-theoretical and semi-empirical forecasting of storm surges and prediction of maximum rise time, characterized in that, Includes the following steps: 1) Verify and select the typhoon wind field model that is suitable for the target sea area, and use the typhoon gale circle data of the target sea area to invert and obtain the radius of the typhoon's maximum wind speed. 2) Based on the y-axis momentum equation of hydrodynamics, the equation is integrated and simplified along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge prediction formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. The undetermined coefficients of the prediction formula are calibrated using storm surge observation data from marine stations in the target sea area. 3) Based on the response mechanism of storm surge to onshore wind stress, the theoretical analytical relationship between the time of maximum surge and typhoon path is derived, revealing the influence of typhoon path parameters on the time lag of maximum surge. 4) Analyze the wind direction distribution characteristics of the historical storm surge maximum rise time at marine stations in the target sea area, and combine the theoretical analytical relationship in step 3) to establish a statistical forecasting method for the maximum storm surge time in the target sea area. 5) Based on the typhoon's maximum wind speed radius obtained in step 1) and the semi-theoretical and semi-empirical storm surge forecasting formula calibrated in step 2), the storm surge process in the target sea area is predicted. Combined with the statistical forecasting method in step 4), the maximum storm surge time in the target sea area is accurately predicted.

2. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 1, characterized in that, Step 1) verifies and selects the typhoon wind field model suitable for the target sea area, and uses the typhoon gale circle data of the target sea area to invert and obtain the typhoon's maximum wind speed radius, specifically including: The typhoon wind field models of Jelesnianski (1965), Jelesnianski (1966), and Holland (1980) were selected as candidate models to obtain the optimal typhoon path set and wind circle data for the target sea area. The wind circle data includes the radius of wind circles for level 8, level 10, and level 12 winds. Based on each candidate model, the maximum wind speed radius of the typhoon is retrieved using wind circle data of different levels. If the maximum wind speed radius corresponding to different levels of wind circles retrieved by the same candidate model is consistent or similar, then the candidate model is determined to be suitable for the target sea area. The average value of the maximum wind speed radius corresponding to the wind circles of different levels of gale obtained by the candidate model adapted to the target sea area is taken as the maximum wind speed radius of the typhoon in the target sea area.

3. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 2, characterized in that, The target sea area is the South China Sea, and the suitable typhoon wind field model is the Jelesnianski (1965) model, whose pressure field and wind field calculation formulas are as follows: Where p(r) is the air pressure at the typhoon radius r, p0 is the air pressure at the typhoon center, p∞ is the air pressure on the outer periphery of the typhoon, R is the radius of the typhoon's maximum wind speed, V is the wind speed at the typhoon radius r, and W R This is the maximum wind speed of the typhoon.

4. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 1, characterized in that, In step 2), based on the hydrodynamic momentum equation in the y-direction, the equation is integrated and simplified along the shelf direction perpendicular to the coastline to construct a semi-theoretical, semi-empirical storm surge prediction formula that incorporates pressure gradient force, Coriolis force, and wind stress dynamics. Specifically, this includes: A right-handed coordinate system is established with the shoreline as the x-axis and the direction perpendicular to the shoreline towards the shore as the y-axis. The y-momentum equation in the two-dimensional full flow equation of fluid dynamics is selected. The convection term and the horizontal friction term are ignored. The integral is performed along the y-axis from the boundary between the continental shelf and the continental slope to the shore. By combining the open sea water level and air pressure terms in the integrated results, assuming that the seabed friction force is proportional to the sea surface wind stress, estimating the horizontal flow velocity, and simplifying the Coriolis force integral term, a semi-theoretical and semi-empirical water increase forecasting formula is obtained, which uses the shore-side water increase as the forecast quantity and includes the air pressure response, coastal wind response, and onshore wind response. The formula is in the following form: Where ηs is the shore-side water level rise, a, b, c are undetermined coefficients, ρ is the seawater density, g is the gravitational acceleration, p∞ is the outer air pressure of the typhoon, ps is the shore-side air pressure, f is the Coriolis force coefficient, u is the average vertical velocity in the x-direction, τay is the wind stress in the y-direction of the sea surface, h is the water depth, ys is the shore-side coordinates, and ye is the coordinates at the boundary between the continental shelf and the continental slope. For observation stations that are not suitable for cross-sectional integration along the vertical shoreline, the forecast formula is simplified to include the shoreline pressure difference, easterly wind stress, and northerly wind stress: ， in, These represent the wind stresses to the east and north of the observation station, respectively.

5. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 4, characterized in that, Step 2) involves calibrating the undetermined coefficients of the forecast formula using storm surge observation data from marine stations in the target sea area. Specifically, this includes: Multiple storm surge observation data from marine stations in the target sea area were selected, and the water level increase data, corresponding typhoon parameters, and wind stress data for each storm surge were extracted. By employing both constrained fitting (a=0) and unconstrained fitting (a≠0) methods, and using the least squares method to fit the observed data with the forecast formula, the optimal solution for the undetermined coefficients was obtained through calibration. With unbiased fitting as the goal, the coefficient set whose fitting results are evenly distributed on both sides of the perfect fitting line is selected as the final calibration result. If the accuracy of the maximum water increase forecast is the key requirement, the coefficient set of unconstrained fitting is selected.

6. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 1, characterized in that, Step 3) derives the theoretical analytical relationship between the time of maximum flood surge and the typhoon path based on the response mechanism of storm surge to onshore wind stress, specifically including: Assuming that the maximum increase in water level occurs at the shore when the onshore wind stress perpendicular to the shoreline is the maximum, the Jelesnianski (1965) model is selected to calculate the onshore wind stress outside the radius of the typhoon's maximum wind speed. Setting the straight path equation of the typhoon By differentiating the onshore wind stress function and setting the derivative to 0, and combining it with the typhoon path equation, the coordinates of the typhoon's location when the onshore wind stress is maximum can be obtained. Based on the typhoon's location coordinates, a formula for the relative distance between the typhoon and the observation station at the time of maximum water rise is derived, revealing the shortest distance d from the observation station to the typhoon's path. min The theoretical analytical relationship between the typhoon path slope k and the time lag of maximum water level rise: Where, d AC θ represents the distance the typhoon travels from its closest point to the location corresponding to the maximum water level rise, and θ is the angle between the shoreline normal and the wind speed direction.

7. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 6, characterized in that, When the distance between the observation station and the typhoon's path is less than the radius of the typhoon's maximum wind speed, it can be deduced that the typhoon's center moves about 2 hours after passing the observation station, and the distance between the observation station and the typhoon's center reaches the radius of the maximum wind speed. At this time, the onshore wind stress is the greatest, and the maximum water level rise occurs on the shore.

8. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 1, characterized in that, Step 4) involves statistically analyzing the wind direction distribution characteristics of the historical storm surge maximum rise time at marine stations in the target sea area. Combined with the theoretical analytical relationships from Step 3), a statistical forecasting method for the maximum storm surge time in the target sea area is established, specifically including: Collect wind speed and direction data at the time of maximum storm surge at marine stations in the target sea area, draw wind direction compass diagrams, and obtain the average wind direction D and the root mean square error θ at the time of maximum storm surge. Combining the theoretical analysis relationship in step 3), the time corresponding to the wind direction being in the range of D-θ to D+θ during the typhoon is taken as the possible period when the storm surge is at its maximum. When the distance between the observation station and the typhoon's path is less than the radius of the typhoon's maximum wind speed, the forecast time for the maximum storm surge is directly taken as 2 hours after the typhoon makes landfall.

9. The storm surge semi-theoretical and semi-empirical forecasting and maximum rise time prediction method as described in claim 1, characterized in that, Step 5) involves forecasting the storm surge in the target sea area, specifically including: Obtain real-time typhoon parameters for the target sea area, including typhoon path, central pressure, maximum wind speed, and radius of the strong wind circle; Based on the wind field model selected in step 1) and the maximum wind speed radius obtained by inversion, real-time air pressure field and wind stress field data are calculated. Substitute the pressure field and wind stress field data into the semi-theoretical and semi-empirical storm surge prediction formula after step 2) to calculate the storm surge data of the target sea area marine station hourly.

10. A semi-theoretical, semi-empirical storm surge forecasting and maximum rise time prediction system, characterized in that, include: The wind field model optimization module is used to verify and optimize the typhoon wind field model that is suitable for the target sea area, and to obtain the maximum wind speed radius of the typhoon by inverting the typhoon wind circle data of the target sea area. The forecast formula construction module is based on the hydrodynamic y-direction momentum equation. It integrates and simplifies along the shelf direction perpendicular to the coastline to construct a semi-theoretical and semi-empirical storm surge forecast formula that includes pressure gradient force, Coriolis force, and wind stress dynamic mechanism. The undetermined coefficients of the forecast formula are calibrated using storm surge observation data from marine stations in the target sea area. The theoretical relationship derivation module, based on the response mechanism of storm surge to onshore wind stress, derives the theoretical analytical relationship between the time of maximum surge and typhoon path, revealing the influence of typhoon path parameters on the time lag of maximum surge. The time forecast module statistically analyzes the wind direction distribution characteristics of the maximum storm surge time in the target sea area, and combines theoretical analytical relationships to establish a statistical forecasting method for the maximum storm surge time in the target sea area. The integrated forecasting module, based on the typhoon's maximum wind speed radius and a calibrated semi-theoretical and semi-empirical storm surge forecasting formula, forecasts the storm surge process in the target sea area. Combined with the statistical forecasting method for the maximum storm surge time, it achieves accurate prediction of the maximum storm surge time in the target sea area.

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