A method, system, and storage medium for constructing dynamic models to predict typhoon path deflection on complex terrain.

Abstract

This invention proposes a dynamic system for predicting typhoon path deflection on complex terrain. The system includes: constructing a dynamic model based on the principle of geopotential vorticity conservation; introducing a terrain adjustment parameter α and a meridional adjustment velocity (MAV) to quantify the response of terrain changes to typhoon path deflection; iteratively integrating the dynamic model to adjust the meridional velocity component of the typhoon path in real time, generating typhoon trajectory prediction results; combining ensemble forecasting methods to generate multiple sets of typhoon path sets by changing initial parameters; and using a large language model to extract features and map parameters from the trajectory data to improve prediction accuracy. This systematically solves the problems of insufficient accuracy, low efficiency, and uncertainty quantification in typhoon path prediction under complex terrain, possessing significant scientific value and promising prospects for practical applications.

Description

Technical Field

[0001] This invention relates to the field of meteorological forecasting technology, and in particular to a method, system and storage medium for constructing dynamic models for predicting typhoon path deflection on complex terrain. Background Technology

[0002] Predicting the path of tropical cyclones (typhoons) is one of the core tasks of meteorological disaster prevention and mitigation. Accurate prediction of the movement path of tropical cyclones (TCs, i.e., typhoons) is crucial for disaster prevention and mitigation. However, when typhoon paths involve complex underlying terrain (such as the rugged Central Mountain Range of Taiwan), their intensity, speed, and direction often change drastically. This makes path prediction highly uncertain, potentially leading to delayed or inaccurate warnings, insufficient disaster preparedness, and increased risks of disasters such as heavy rain, strong winds, and flash floods. This is especially true in areas with complex terrain (such as Taiwan and the Philippine Islands), where the interaction between topography and typhoons significantly affects their trajectory. When typhoons approach or cross complex terrain such as mountains and islands, their paths often deflect dramatically due to factors such as topographic obstruction, channel effects, and beta effects (e.g., S-shaped bends, sudden turns, or detours), resulting in a significant decrease in the accuracy of traditional prediction models. Furthermore, there are further classifications based on the direction of typhoon path deflection, such as northward or southward deflection. These deflections are influenced by a variety of factors, including the typhoon's own intensity and size, as well as the environmental steering flow, reflecting the complex interaction between the typhoon's internal structure and the surrounding environmental conditions.

[0003] Historical observations and simulations have even revealed unusual typhoon path patterns where typhoons deviate or circulate around the landfall site. The mechanisms underlying typhoon path deflection are complex and diverse, including: topographic blocking effects (high mountains obstruct airflow, causing path deflection or deceleration), topographic channel effects (airflow is accelerated and guided by valleys, altering the typhoon's trajectory), topographic beta effects (similar to planetary beta effects, causing vortices to shift northwestward on mountain slopes), and changes in the typhoon's circulation structure.

[0004] These mechanisms have all been confirmed and explained in the literature through observation, numerical simulation, and idealized experiments. In general, the impact of complex terrain on typhoon paths is significant. Coupled with the limited historical typhoon observation data, predicting the deflection of typhoon paths passing through complex terrain has become one of the most challenging aspects of current forecasting.

[0005] The above problems lead to the following limitations in existing technologies:

[0006] (1) Oversimplification of topographic effects: Traditional numerical models (such as the Global Forecasting System, GFS) usually use coarse-resolution topographic data or simplified topographic parameterization schemes, which cannot accurately characterize the local gradient changes of steep terrain (such as the steep slopes of the Central Mountain Range in Taiwan, China). For example, the lifting and diversion effects of topography on airflow are often underestimated, leading to biased predictions of path deflection magnitude.

[0007] (2) The disconnect between static assumptions and actual dynamic processes: Most models assume that the intensity of the typhoon remains constant during its movement, ignoring the intensity decay caused by its interaction with the terrain (such as the breakup of the vortex core and the reorganization of the circulation after landfall). This static assumption leads to a discrepancy between the path deflection trend and actual observations, especially in the simulation of path correction after the typhoon crosses the terrain, where the error is significant.

[0008] (3) The contradiction between computational efficiency and accuracy: Although high-resolution regional models (such as WRF) can partially simulate the impact of terrain, they require massive computing resources and are difficult to meet the needs of real-time operational forecasting; while statistical models (such as climate persistence models) lack physical mechanism support and have insufficient generalization ability under complex terrain conditions.

[0009] (4) Lack of uncertainty quantification system: Existing methods mostly output a single deterministic path, and cannot quantify the risk of path deviation induced by terrain through ensemble forecasts (such as the probability of multimodal paths). This deficiency leads to insufficient emergency preparedness for sudden changes in typhoon paths (such as "discontinuous paths") in disaster prevention decision-making.

[0010] Recent studies have shown that the potential vortex conservation theory provides a physical framework for analyzing topographic-typhoon interactions. For example, idealized experiments have revealed that changes in topographic slope can induce meridional adjustments in typhoon paths (such as south-to-north corrected S-shaped trajectories). Our previous research (published in *Atmosphere*, Volume 15, 2024) constructed a dynamic model based on potential vortex conservation, verifying the coupling effect between topographic gradient and vortex intensity. However, this model still has the following limitations:

[0011] 1) The dynamic evolution of typhoon intensity was not included: Assuming that the vortex intensity is constant, it cannot reflect the feedback effect of the attenuation of core vorticity on the path deflection during landfall.

[0012] 2) Lack of efficient parameterization methods: It relies on high-resolution terrain data, which has high computational costs and makes it difficult to quickly generate ensemble forecasts;

[0013] 3) Insufficient historical data-driven capability: The lack of integration of machine learning techniques to explore the mapping relationship between historical typhoon paths and terrain parameters limits the model's calibration and generalization capabilities.

[0014] Historical observations indicate that typhoon paths in Taiwan can be categorized into "continuous paths" (maintaining an intact vortex structure) and "discontinuous paths" (with new low-pressure centers forming on the leeward side). The mechanisms involve complex interactions between topographic gradients, environmental wind fields, and vortex structures. Existing models struggle to analyze these multi-scale processes within a unified framework. Therefore, a novel model integrating physical mechanisms and data-driven techniques is urgently needed to achieve the following: dynamically coupling typhoon intensity and topographic feedback; constructing an efficient ensemble forecasting system; and historical data-driven parameter calibration.

[0015] This application addresses the aforementioned technical bottlenecks by proposing an innovative dynamic model and method, aiming to improve the accuracy and practicality of typhoon path prediction in complex terrain areas. Summary of the Invention

[0016] This invention proposes a dynamic model construction method and system for predicting typhoon path deflection in complex terrain, solving the problems of insufficient accuracy and practicality in existing typhoon path prediction for complex terrain areas. The technical solution of this invention is implemented as follows:

[0017] A method for constructing a dynamic model to predict typhoon path deflection over complex terrain includes the following steps:

[0018] Step S1: Based on the principle of conservation of geopotential vorticity and existing basic prediction models, the terrain adjustment parameter α and the meridional adjustment velocity MAV are introduced to quantify the response of terrain changes to typhoon path deflection, and then a dynamic model is constructed.

[0019] The terrain adjustment parameter α is calculated using the following formula:

[0020]

[0021] Among them, The Rossby number of the vortex. The core vorticity is a dimensionless value. For terrain gradient parameters, These are the planetary vorticity gradient parameters;

[0022] Speed ​​adjusted via the meridian MAV, or the instantaneous correction of typhoon north-south velocity to topographic changes, is expressed as:

[0023]

[0024] in, For the vortex reference time scale, The vortex velocity at the current time step. For terrain gradient, The reference y-vector;

[0025] Step S2: Model initialization; Obtain the initial state parameters of the typhoon, determine the reference constants in the basic model based on the environmental field at the forecast time, import the high-resolution topographic height field of the study area, and set the relevant variable parameters to complete the initialization;

[0026] Step S3: Single path simulation; Input the initial state parameters and initial conditions of the typhoon obtained in step S2 into the dynamic model, and output the typhoon path coordinate sequence for this simulation.

[0027] Step S4: Ensemble simulation and database construction; Based on the single simulation, construct an ensemble forecast experiment: According to the preset parameter space scheme, generate different combinations of initial conditions in batches; obtain a typhoon path trajectory image database covering various typical scenarios;

[0028] Step S5: Intelligent learning of trajectory images; Input the large amount of trajectory image data generated in step S4 into a pre-trained large language model or deep learning model to perform unsupervised or supervised feature learning, so that the model can predict the corresponding model parameter range or category based on an input trajectory image.

[0029] Step S6: Historical path mapping and parameter fitting; A portion of historically observed typhoon trajectory image data is used as the training set and input into the trained supervised / unsupervised learning model to extract the features of the real path. The most similar category or neighboring point is found in the learned simulated trajectory feature space, and then the model parameter combination that matches the real path is inferred. The model parameters are adjusted to make the simulated trajectory fit the real trajectory as closely as possible to complete the parameter calibration.

[0030] Step S7: Model prediction and validation; Another set of historically observed typhoon trajectory image data is used as the test set. The parameters obtained by the fitting / training method in step S6 are used to simulate the path in the model. The model's predicted trajectory set is compared with the actual observed paths of these typhoons. The forecast hit rate and deviation are statistically analyzed to verify the reliability of the model.

[0031] Furthermore, the dynamic model constructed based on the principle of conservation of potential vorticity is as follows:

[0032]

[0033] Where t is time and the potential vorticity Π is defined as:

[0034]

[0035] in, These are the base values ​​for the Coriolis parameter. y represents the latitudinal variation rate of planetary vorticity, and y represents the northward coordinate position. The relative vortex intensity is H, and the total fluid depth is H.

[0036]

[0037] Where D represents the fluid thickness in a static environment, η is the height of free surface disturbance caused by the typhoon vortex, and hB represents the height of the terrain below;

[0038] In the dynamic model, the vortex intensity ζ(t) is represented by a time-varying function, specifically:

[0039]

[0040] Where ζ(0) is the initial vortex intensity and τ is the decay time scale, which is determined by historical typhoon data or real-time observation.

[0041] Furthermore, the initial state parameters of the typhoon include the initial center location coordinates, initial intensity parameters, typhoon movement direction and speed, and the values ​​of f0 and β0 under the β-plane approximation determined based on the environmental field at the forecast time.

[0042] Furthermore, in step S3, the initial state parameters and initial conditions of the typhoon are input into the dynamic model. The numerical integration method is used to solve the vortex trajectory equation that includes the influence of terrain. The position change of the typhoon center is calculated at each time step. The potential vortex conservation principle is applied to calculate the α value. The MAV value is calculated in combination with the local terrain slope. The trajectory is corrected by the meridional and zonal velocity components of the typhoon. The process is repeated iteratively until the typhoon crosses the target terrain area or reaches the forecast duration. The initial state parameters and initial conditions of the typhoon are then input into the dynamic model.

[0043] Furthermore, in step S4: according to the preset parameter space scheme, generating different initial condition combinations in batches includes: fixing the incident angle and typhoon intensity in one set, only changing the initial landfall latitude position to generate multiple paths; fixing the landfall point in another set, setting different incident angles to generate multiple paths.

[0044] For each set of initial conditions, the model is run, all simulated path trajectory data are collected, the trajectory data is visualized as images or curves, and the corresponding parameter values ​​are labeled and stored in the "path-parameter" database. After a large number of simulations, a typhoon path trajectory image database covering various typical scenarios is obtained.

[0045] Furthermore, step S5, intelligent learning of trajectory images, specifically includes:

[0046] The model automatically extracts key features by analyzing the trajectory shape and maps each trajectory to the trajectory feature space. Key features include path deflection angle, whether an "S" shaped turn occurs, and maximum deviation distance.

[0047] Trajectories are categorized into multiple groups based on their morphological features using clustering or classification algorithms.

[0048] After training, the large language model predicts the range of model parameters or category corresponding to an input trajectory image.

[0049] Furthermore, the model predicts the corresponding model parameters based on an input trajectory image, including the range of the most likely incident angle, the initial intensity level, and the offset information of the landfall point for the typhoon.

[0050] Furthermore, in step S7, if the forecast deviation is large, return to step 6 to adjust and improve the parameter mapping method; if the effect is ideal, it proves that the model of the present invention has practical application value. In actual forecasts, when a new typhoon is approaching, its real-time observation parameters can be input into the model to quickly predict its possible path deflection set.

[0051] A typhoon track prediction system, comprising:

[0052] The dynamic model calculation module is used to execute the dynamic model construction method described above.

[0053] The ensemble forecast generation module is used to generate ensembles of typhoon paths and trajectories.

[0054] The large language model analysis module is used for feature learning and parameter mapping of trajectory data.

[0055] A computer-readable storage medium stores a computer program that, when executed by a processor, implements a dynamic model construction method for predicting typhoon path deflection on complex terrain, thereby generating a typhoon path prediction system.

[0056] Compared with existing technologies, this solution has the following advantages:

[0057] (1) Improve the accuracy of path prediction under complex terrain: By dynamically simulating the real-time coupling of typhoon intensity changes (such as vortex attenuation) and terrain feedback, the traditional model's assumption of constant intensity is overcome, and the interaction between typhoon and terrain (such as S-shaped deflection and path correction) is reflected more realistically, which significantly improves the accuracy of prediction.

[0058] (2) Efficient generation of probabilistic forecasts: Based on the parameterized ensemble forecasting system, a multi-scenario typhoon path trajectory library is quickly generated. Combined with the Large Language Model (LLM) to automatically extract trajectory features, the uncertainty of path deflection (such as confidence interval and probability density distribution) can be quantified, providing risk probability support for disaster prevention decision-making.

[0059] (3) Achieve automated parameter calibration: Utilize large language model to analyze historical typhoon path data and automatically retrieve the optimal model parameters (such as initial intensity and incident angle), which solves the problems of low efficiency and reliance on experience in traditional manual parameter tuning, and improves the applicability and operational capabilities of the model.

[0060] (4) Balancing physical realism and computational efficiency: The dynamic model is based on a simplified potential vortex conservation equation and combined with high-resolution terrain data (such as 250-meter DEM), which significantly reduces computational costs while ensuring the physical mechanism and meets the real-time forecasting requirements.

[0061] (5) Support multimodal path prediction: reveal potential abrupt changes in typhoon paths (such as discontinuous paths and detours) through ensemble forecasts, and enhance the early warning capability for path anomalies induced by complex terrain (such as sudden turns and spins).

[0062] (6) Interdisciplinary technology integration and innovation: For the first time, physical models and large language models are combined, which not only preserves the interpretability of dynamic mechanisms, but also uses AI technology to improve the efficiency of data processing and pattern recognition, providing a new methodology for the field of weather forecasting. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a schematic diagram of the model structure of the typhoon vortex passing over the terrain as described in this invention;

[0065] Figure 2 A schematic diagram simulating the path of a typhoon under an ideal, isolated mountain terrain.

[0066] Figure 3 This is a flowchart of the typhoon path prediction ensemble forecasting system proposed in this invention;

[0067] Figure 4 The curves showing the hourly variation of vortex intensity ζ(t) at different decay time scales τ are shown.

[0068] Figure 5 A schematic diagram of a simulated typhoon path under an ideal isolated mountain terrain.

[0069] Figure 6 A simulated diagram of typhoon paths under the topography of Taiwan, China;

[0070] Figure 7 A schematic diagram of a typhoon path simulation with varying incident angles under the topography of Taiwan, China;

[0071] Figure 8 A schematic diagram showing the historical typhoon paths and the range of most likely incident angles;

[0072] Figure 9 This is a flowchart of a method for constructing a dynamic model to predict typhoon path deflection on complex terrain, according to the present invention. Detailed Implementation

[0073] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0074] Regarding the problem of typhoon track prediction, our research group previously conducted theoretical and simulation studies, and published a paper entitled "An Innovative Dynamic Model for Predicting Typhoon Track Deflections over Complex Terrain" in the academic journal *Atmosphere*, Volume 15, 2024. The model and conclusions proposed in this study provide the theoretical basis and some technical solutions for this invention. In this paper, numerical experiments on idealized mountains and real terrain in Taiwan, China, verified the effectiveness of the model in capturing terrain-induced typhoon track deflections.

[0075] Based on the above research, this invention proposes an innovative dynamic model based on potential vorticity (PV) to predict typhoon path deflection on complex terrain. The core innovation of this model lies in introducing two key parameters: "terrain adjustment parameter" α and "meridional adjusting velocity" MAV, to quantitatively characterize the response of typhoon vortices to terrain changes. Through the dynamic interaction of these two parameters, the model can capture the deflection trend and magnitude of the typhoon's path when interacting with terrain. The theoretical basis and implementation scheme of the model are elaborated below. (See reference) Figure 9 )

[0076] I. Improvements to the theoretical model:

[0077] This model is based on the principle of conservation of atmospheric circulation potential vorticity under the β-plane approximation. Considering a strong cyclonic vortex moving over topography, its potential vorticity is approximated by neglecting viscosity and thermal effects. Satisfying the conservation equation (reference) Figure 1 ):

[0078]

[0079] Among them, potential vorticity Defined as:

[0080]

[0081] The meanings of each symbol are as follows: These are the base values ​​for the Coriolis parameter. β is the zonal variation rate of planetary vorticity, y is the north-facing coordinate position, ζ is the relative vorticity of the vortex, and H is the total fluid depth. Where D represents the fluid thickness under static conditions, and η is the height of free surface disturbance caused by the typhoon vortex (the bulge / depression of the equivalent ocean or atmospheric potential). This represents the height of the terrain below. The above potential vorticity equation shows that, under the condition of no external force, the potential vorticity, including the influence of terrain, remains constant as the airflow moves.

[0082] Figure 1 The diagram illustrates the principle behind the deflection of a typhoon vortex under the beta-plane approximation due to the influence of the terrain below: As the vortex rises along the windward slope of the terrain (right side of the diagram), it generates a positive meridional adjustment velocity (MAV), causing the path to deflect southward; after crossing the mountain peak, it descends along the leeward slope (right side of the diagram), generating a negative MAV that causes the path to correct northward, thus forming an "S"-shaped deflection trajectory. The α parameter is adjusted in real time according to the vortex intensity and the terrain slope, determining the magnitude of the deflection.

[0083] II. Model Simplification and Assumptions

[0084] To obtain an analytical vortex motion trajectory model, this invention introduces reasonable assumptions into the above basic equations to simplify computational complexity:

[0085] (1) Strong vortex point vortex assumption: It is assumed that the typhoon under consideration is a strong cyclonic vortex ( Its main circulation can be approximated as a system with an average core vorticity. The vortex is a point vortex. This means that the vortex field of a typhoon is concentrated near the center, and the contribution of the outer circulation to the path deflection can be represented by the core vortex.

[0086] (2) Small disturbance assumption: It is assumed that the free surface deformation and terrain height caused by the typhoon are small relative to the environmental depth, i.e. Based on this, the small perturbation approximation can further linearize and decompose the potential vortex equation.

[0087] (3) Assumption of Variable Vortex Intensity: Unlike previous models that assumed the typhoon intensity remained constant during its movement, this invention relaxes the assumption of constant vortex intensity. We let the relative vorticity ζ=ζ(t) evolve with time to characterize the possible weakening or strengthening of the typhoon's intensity when it makes landfall. For simplicity, the model uses an exponential decay function to describe the evolution of vortex intensity over time, i.e., it assumes... , where τ is the characteristic decay time scale (which can be set empirically based on historical typhoon decay rates). This improvement enables the model to reflect the impact of typhoon intensity changes on the path when interacting with terrain.

[0088] Under the above assumptions, the geopotential vorticity conservation equation can be simplified and solved, from which the influence of topography on vortex path deflection can be extracted. Through derivation, we summarize the influence of topography into two dynamic parameters: α and MAV. The topography adjustment parameter α is used to quantify the sensitivity of topographic changes to typhoon path deflection, while the meridional adjustment velocity MAV represents the meridional (north-south) velocity component of the typhoon introduced by topographic changes. Together, they determine the deflection trend and magnitude of the typhoon under the influence of topography.

[0089] The formula for calculating α is:

[0090]

[0091] Meridional adjustment speed of the vortex The (MAV) expression is:

[0092]

[0093] in This is the reference timescale for the vortex.

[0094] The model predicts the vortex trajectory iteratively. At each time step, the dimensionless velocity of the vortex (…) It consists of three parts:

[0095]

[0096] : Vortex velocity at the current time step;

[0097] MAV is the rate of adjustment in the meridional direction caused by terrain interaction.

[0098] III. Definition of Key Parameters:

[0099] The α and MAV introduced in this invention are derived from the analytical solution of the above potential vortex equation:

[0100] The model incorporates terrain adjustment parameters (α) and meridional adjustment velocity (MAV) to quantify and simulate the guiding effect of terrain on the vortex path:

[0101] 3.1 Topographic Adjustment Parameter α: α reflects the response coefficient of the typhoon track to changes in topographic height. The larger the α value, the more sensitive the typhoon track is to topographic relief, and the more significant the deflection. Derivation shows that α is positively correlated with the typhoon vortex intensity and the steepness of the terrain: when the dimensionless relative vorticity of the typhoon (… Or Rossby number Larger vortex gradients relative to planetary rotation At higher elevations, α increases accordingly. This means that strong typhoons (high vorticity) will have a stronger tendency to deflect the path on steep terrain (high rate of terrain change). Conversely, under conditions of weak typhoons or gentle terrain, the value of α is smaller, and the effect of terrain on path deflection is limited. It is important to emphasize that α is not a constant, but rather changes dynamically during the typhoon's movement: it adjusts in real time with the evolution of vortex intensity and the terrain features of the region, thus reflecting the nonlinear complexity of typhoon-terrain interaction in reality.

[0102] 3.2 MAV (Meridional Adjusted Velocity): MAV describes the immediate impact of topographic changes on the north-south movement speed of a typhoon. According to the model, the magnitude of MAV is directly proportional to the parameter α and the rate of change of topographic height at the typhoon's current location. Intuitively speaking, when a typhoon rises along the windward slope of the terrain (positive... When the terrain elevation increases, a positive (southward or downward) meridional adjustment velocity is generated, causing the typhoon's path to deflect further south; conversely, when the typhoon crosses the mountaintop and descends along the leeward slope (negative), a downward adjustment velocity is generated. When MAV is negative (a northward or upward speed adjustment), it causes a northward correction in the typhoon's path. This combination of southward and northward corrections often results in an "S-shaped" curve characteristic of the typhoon's path. Calculating MAV allows the model to more realistically simulate the immediate effect of terrain steepness on the typhoon's trajectory: steep slopes have high MAV values, causing sharp deflections; flat areas have lower MAV values, and the typhoon moves more closely along its inertial trajectory.

[0103] IV. Model Implementation and Path Prediction:

[0104] Using the aforementioned α and MAV, the model establishes the dynamic equations for the evolution of the typhoon vortex center position over time. By numerically integrating these equations, the predicted trajectory of the typhoon under the influence of topography can be obtained.

[0105] The model first adjusts the initial typhoon parameters (initial position, initial intensity ζ(0), direction of motion, velocity, vortex attenuation characteristic time, etc.) in real time by introducing α and MAV correction terms to obtain the actual path that includes the effect of terrain. Through this mechanism, the model can simulate the process of typhoons being deflected or even turned by terrain. In particular, in the idealized experiment, we use an isolated axisymmetric mountain to represent complex terrain to simulate and verify the model. The results show that when the typhoon vortex approaches the mountain, the model can reproduce the typical "S-shaped" path deflection characteristics—first deflecting to one side of the mountain (usually the south side), then correcting to the other side (the north side) after passing the mountain peak.

[0106] The degree of deflection of a typhoon's path depends on factors such as its landfall location, angle of incidence, and vortex intensity. If a typhoon directly impacts the central peak of a mountain range, the steep terrain causes a large α (accuracy angle) and a significant increase in MAV (magnitude of vortex), resulting in a pronounced S-shaped deflection. If the typhoon passes north or south of the mountain range, where the terrain slope is gentler, the path deflection is only minor. Simultaneously, a smaller angle of incidence (the angle between the typhoon's path and the terrain normal) indicates that the typhoon's path is more parallel to the mountain's extension, meaning the typhoon lingers near the mountains for a longer period and exhibits greater path curvature. Conversely, a larger angle of incidence (more perpendicular to the mountain range) results in a shorter interaction time and less deflection (see reference). Figure 2 ).

[0107] Figure 2 This diagram illustrates a simulated typhoon path under an ideal, isolated mountain terrain. It shows a set of simulated typhoon paths under different initial conditions within a single-peak ideal mountain (bell-shaped) environment. It can be seen that when the typhoon directly impacts the mountain peak (trajectories 2, 5, 8, and 11), the path exhibits a significant S-shaped bend, deviating southward and then northward. If the typhoon passes over the mountain from a more northerly position (trajectories 1, 4, 7, and 10) or a more southerly position (trajectories 3, 6, 9, and 12), the path deflects only slightly due to the weaker influence of the terrain. The comparison of different incident angles in the diagram verifies the conclusion that a smaller incident angle results in a more significant path deflection (δ represents the path deflection distance).

[0108] Furthermore, the greater the vortex intensity, the higher the α value and the stronger the MAV effect, thus strong typhoons exhibit more significant path deflection than weak typhoons. These simulation analyses demonstrate that the model of this invention can reveal the key factors of typhoon-topographic interaction and accurately reflect its qualitative trends, theoretically providing an effective tool for typhoon path forecasting in complex terrain.

[0109] The algorithm of this invention combines physical models and artificial intelligence analysis, and is described in the following steps (see reference). Figure 3 ):

[0110] Step 1: Model Initialization. Obtain the initial state parameters of the typhoon, including the initial center location coordinates (latitude and longitude), initial intensity parameters (such as maximum wind speed or initial relative vorticity ζ(0)), typhoon movement direction and speed, etc. Determine the values ​​of f0 and β0 under the β-plane approximation based on the environmental field at the forecast time, and import the high-resolution topographic height field of the study area. Set up the vortex intensity evolution model (determined empirically) (refer to...). Figure 4 (Hourly variation curves of vortex intensity ζ(t) at different decay time scales τ).

[0111] Step 2: Single Path Simulation. Input the initial conditions described above into the dynamic model. Solve the vortex trajectory equation, which includes the influence of terrain, using numerical integration. Calculate the positional change of the typhoon center at each time step. Specifically, apply the principle of potential vortex conservation to calculate the α value, combine it with the local terrain slope to calculate the MAV, and correct the trajectory using the typhoon's meridional and zonal velocity components. Repeat the iteration until the typhoon crosses the target terrain area or reaches the predicted duration, and output the typhoon path coordinate sequence for this simulation.

[0112] Step 3: Ensemble Simulation and Database Construction. Based on the single simulation, construct an ensemble forecast experiment: generate different combinations of initial conditions in batches according to a preset parameter space scheme. For example, in one ensemble, fix the incident angle and typhoon intensity, and only change the initial landfall latitude (how much northward), generating multiple paths (see reference). Figure 5 A schematic diagram of a typhoon path simulation under an ideal isolated mountain terrain (simulation results of typhoon path with a fixed incident angle and varying attenuation time scales and landing positions). Figure 6 A simulated typhoon path diagram of Taiwan's topography (simulation results of typhoon paths with a fixed incident angle and varying attenuation time scales and landfall locations); in another dataset, with a fixed landfall point and different incident angles, multiple paths are generated (see reference). Figure 7 (A schematic diagram of a typhoon track simulation with varying incident angles under the topography of Taiwan, China (simulation results of typhoon track with varying incident angles at a fixed initial position, varying initial latitude). The model is run for each set of initial conditions, and all simulated track data are collected. The track data is visualized as images or curves (scaled to a uniform coordinate system), and the corresponding parameter values ​​are labeled and stored in the "Path-Parameter" database. After extensive simulations, this step will yield a database of typhoon track images covering various typical scenarios.)

[0113] Step 4: Intelligent Learning of Trajectory Images. The large amount of trajectory image data generated in Step 3 is input into a pre-trained large language model or deep learning model for unsupervised or supervised feature learning. The model automatically extracts key features (such as path deflection angle, whether an "S" shaped turn occurs, maximum deviation distance, etc.) by analyzing the trajectory shape and maps each trajectory to a feature space. Through clustering or classification algorithms, the trajectories can be categorized according to their morphological features. For example, the features of trajectories of different intensity groups and different travel angle groups will differ. After training, the large language model will be able to predict the corresponding model parameter range or category based on an input trajectory image. This lays the foundation for inferring model parameters using historical real paths.

[0114] Step 5: Historical Path Mapping and Parameter Fitting. Input historically observed typhoon path data (such as satellite cloud image trajectories or ground station paths) into the trained AI model. The model extracts features from these real paths and searches for the most similar categories or nearest neighbors in the learned simulated trajectory feature space, thereby inferring the model parameter combination that matches the real path. For example, the model will provide information such as the most likely range of incident angles, initial intensity level, and landfall point offset for this historical typhoon (see reference). Figure 8 For typhoon cases in the training set, model parameters are adjusted to make the simulated path closely resemble the real path, thus completing parameter calibration. 70% of historical typhoons are used as the training set to optimize the model parameter selection method.

[0115] Step 6: Model Prediction and Validation. For the remaining 30% of historical typhoons (test set), the parameters obtained from fitting / training in Step 5 are used to simulate the path in the model, or the AI ​​model directly predicts their future path set. The model-predicted trajectory set is compared with the actual observed paths of these typhoons, and the forecast hit rate and deviation are statistically analyzed to verify the reliability of the model. If the deviation is large, return to Step 5 to adjust and improve the parameter mapping method; if the effect is ideal, it proves that the model and algorithm of this invention have practical application value. Finally, in actual forecasting, when a new typhoon is approaching, its real-time observation parameters can be input into the AI ​​model to quickly predict its possible path deflection set, providing decision-making reference for meteorological departments. This process, by combining a physical model with a data-driven AI model, realizes an automated process for typhoon path prediction from "simulation—learning—matching—forecasting," significantly improving the intelligence level and accuracy of typhoon path prediction in complex environments.

[0116] Figure 3This is a flowchart of the typhoon track prediction ensemble forecasting system proposed in this invention. The diagram illustrates the workflow combining dynamic model prediction and large language model analysis: from left to right, 1. First, model initialization is performed, setting initial typhoon parameters and environmental conditions; 2. A single simulation of the dynamic model is performed as a baseline prediction; 3. Next, a simulated trajectory database (variables such as changing incident angle, landfall location, and typhoon intensity attenuation time) is generated using ensemble simulation principles; 4. Then, the trajectory database is trained using a large language model in a multimodal manner to learn typhoon trajectory characteristics; 5. Next, historical typhoon tracks are mapped to the parameter space for model calibration; 6. Finally, ensemble track prediction is performed for new typhoons. The modules in the diagram are interconnected, reflecting the overall innovative concept and implementation steps of this invention.

[0117] This invention features several technical innovations, overcoming the limitations of existing technologies and providing a new approach to typhoon path prediction in complex terrain. The specific innovations are summarized below:

[0118] 1. Dynamic Vortex Intensity Simulation: The model breaks the traditional assumption of a constant typhoon intensity, allowing the vortex intensity ζ to evolve over time, i.e., ζ = ζ(t). By introducing a time function (such as an exponential decay function) to characterize the weakening of typhoon intensity, the model of this invention can more realistically simulate the intensity change process of typhoons as they approach land and complex terrain, thereby improving the accuracy of path deflection forecasts.

[0119] 2. Ensemble Forecasting System Construction: Based on this dynamic model, this invention establishes an ensemble forecasting system for typhoon track prediction. By changing initial conditions such as initial vortex intensity, starting position, and incident angle, the model is repeatedly run to simulate and generate a large library of parametric images of typhoon tracks under different scenarios. This ensemble method can systematically consider the impact of initial uncertainties on track prediction, providing probability distribution support for forecasting.

[0120] 3. Parameter Space Design and Trajectory Ensemble: This invention proposes a parameter space experimental design scheme for constructing ensemble forecasts. For example, a set of trajectories can be generated by fixing the typhoon intensity and incident angle, and only changing the initial landfall latitude of the typhoon; then, the intensity or incident angle can be changed again to repeat the generation. This method of systematically changing a single parameter can obtain a family of trajectories, making the sensitivity of the path to specific parameters readily apparent, and forming a dense trajectories for statistical analysis. Through a comprehensive experiment in the parameter space, this invention obtains comprehensive path deflection sample data.

[0121] 4. Introducing Large Language Models to Aid Analysis: For a large amount of simulated typhoon trajectory data, this invention innovatively utilizes large language models from artificial intelligence (such as ChatGPT, Deepseek, and Gemini) to recognize and learn from the trajectory images. Specifically, by using pre-trained large-scale deep learning models to analyze the simulated trajectory image data, path morphology features (such as "S-shaped" curves, deflection angles, etc.) can be automatically extracted, transforming complex trajectory shape information into feature vectors or descriptive labels. This AI-enabled method significantly improves the pattern recognition capability for massive trajectory data, laying the foundation for subsequent parameter fitting based on historical data.

[0122] 5. Historical Typhoon Data Mapping Training: This invention utilizes historical typhoon landfall path data to calibrate and validate the model. A large number of historical typhoon paths that made landfall in complex terrain areas of my country and surrounding regions are selected, and 70% of these samples are used as the training set input into the AI ​​model to learn the mapping relationship between these real paths in the model's parameter space. In other words, the extracted trajectory features are compared with trajectories in the model simulation library to find the model parameters (including initial intensity, incident angle, landfall location, etc.) that best reproduce each historical path. Through this historical path mapping, the optimal combination of model parameters corresponding to real typhoons can be deduced, providing the model with a calibration basis with clear physical meaning.

[0123] 6. Independent Testing and Ensemble Forecasting Application: Using the remaining 30% of historical typhoon paths as a test set, predictions are made using the model parameters obtained from the above fitting, i.e., the model generates corresponding ensemble forecasts of paths. The effectiveness of the model and parameter selection is verified by comparing the degree of agreement between the model's predictions and the actual paths. Once the reliability of the model has been verified using historical data, the ensemble forecasting system of this invention can be used for real-time operations: when a new typhoon approaches, the initial parameters obtained from real-time observations are input, and the corresponding model parameters are quickly selected through the trained parameter mapping. The ensemble forecasting system generates a set of possible future paths, thereby providing forecasting departments with a probability estimate and uncertainty range of typhoon path deflection.

[0124] The above innovations work together to enable this invention to not only achieve breakthroughs in theoretical models, but also to establish a complete new process in practical forecasting applications, from model simulation to intelligent analysis, then to historical verification and real-time prediction, which significantly improves the intelligence and accuracy of typhoon path prediction under complex terrain conditions.

[0125] The following verification is based on four specific embodiments:

[0126] Example 1: Improved dynamic model construction and verification.

[0127] Model equations: A two-dimensional nonlinear shallow water equation system based on potential vortex conservation or its simplified form (point vortex model) is adopted, as described in the background section. The key lies in the vorticity term. Using a time-varying form, for example .parameter τ is set based on the initial intensity of the typhoon and the expected attenuation timescale.

[0128] Parameter settings: Refer to the parameter settings in Chen (2024) paper, such as the initial... , (used for calculating initial) ), , Depends on latitude. The key terrain parameter α is calculated using a formula. MAV is based on α and... calculate.

[0129] Dynamic model calculation: Following the dynamic model calculation process in Section 4.2, a time step (e.g., 150s) and high-resolution DEM data (e.g., 250m resolution data from Taiwan) are used.

[0130] Model Validation:

[0131] Ideal terrain: Using Zhongxing Mountain to simulate the CMR of Taiwan, respectively, the following changes were made. With the τ value, run the dynamic model and observe the effect of intensity decay on path deflection (such as S-shaped trajectory curvature). Compare. Under the condition that the intensity remains constant, verify the effect of the time-varying intensity term. (Reference) Figure 5 .

[0132] Real Topography: Utilizing actual topographic data of Taiwan, China. Historical typhoon examples (such as Soudelor) are selected, and intensities are estimated based on changes before and after landfall. And τ. Run the model and compare it with the observation path to evaluate the improvement effect of adding time-varying intensity and varying incident angle. Refer to Figure 7.

[0133] Example 2: Generation of a parameterized set forecast database.

[0134] Parameter space definition: For the topography of Taiwan, define the range of variation for key parameters:

[0135] initial longitude For example, 122°E - 124°E

[0136] initial latitude For example, 21°N - 26°N

[0137] Initial intensity: Corresponds to different typhoon levels (e.g., 2x1) ¹To 8x1 ¹)

[0138] Incident angle γ: for example, 120 to 200°

[0139] Decay timescale τ: for example, values ​​of 5, 10, 15, 20, 25, or 30 hours.

[0140] Parameter sampling: Sampling is performed within the defined parameter space. Parameter combinations can be generated using methods such as grid sampling and Latin hypercube sampling.

[0141] Model execution and data storage: For each parameter combination, the dynamic model constructed in Example 1 is run to simulate the typhoon path. The simulation results (path coordinate sequence, key moment positions, etc.) are saved as a standardized image and stored in the database along with the corresponding parameter set.

[0142] Specific scan ( Figure 5 (Conceptual Implementation): Perform fixed longitude and variable latitude scans to generate a subset of dense path images for subsequent analysis or LLM training.

[0143] Example 3: LLM training and parameter identification.

[0144] LLM Selection and Preparation: Select a multimodal LLM with image understanding capabilities (e.g., similar models or open-source alternatives such as GPT-4o, Claude 3, etc.). Prepare the "parameter-path image" database generated in Example 2 as training data.

[0145] Model fine-tuning: Fine-tuning the selected LLM. The input is the path image, and the output is the corresponding model parameter set. , , (e.g., γ, τ). The training objective is to minimize the difference between the predicted parameters and the true parameters in the database.

[0146] Parameter identification application: After training, this LLM can be used to analyze new typhoon path images (whether historical observations or real-time radar / satellite image sequences) and quickly estimate the corresponding initial parameters of the dynamic model. Reference Figure 3 process.

[0147] Example 4: Historical Typhoon Verification and Ensemble Forecasting Application.

[0148] Data partitioning: The database of best historical typhoon paths in Taiwan was divided into a 70% training set and a 30% test set.

[0149] Training phase: Using the typhoon path images in the training set, the optimal set of initial parameters for the dynamic model is identified for each typhoon in the training set through the LLM trained in Example 3.

[0150] Testing phase: For each typhoon in the test set:

[0151] Input its path image into LLM to obtain the initial parameter set for prediction { }={ , , , , k,...}.

[0152] exist{ A small perturbation is made around the object to generate a small set of parameters. }

[0153] use{ } or{ Each parameter group in} serves as an initial condition, and the dynamic model is run to generate a deterministic forecast (or ensemble forecast) path.

[0154] The predicted path is compared with the actual observed path of the typhoon. The predictive performance of the entire method is evaluated using indicators such as the incident angle of small disturbances and the calculation path error. (Reference) Figure 8 The comparison method.

[0155] This invention systematically solves the problems of insufficient accuracy, low efficiency, and uncertainty in typhoon path prediction under complex terrain through innovations such as dynamic intensity modeling, ensemble forecast generation, and AI-driven parameter optimization. It has significant scientific value and promising prospects for practical applications.

[0156] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic model construction method for predicting a typhoon path deflection on complex terrain, characterized by, The method comprises the following steps: Step S1: Based on the principle of potential vorticity conservation and existing basic prediction models, a terrain adjustment parameter a and a meridian adjustment velocity MAV are introduced to quantify the response of terrain changes to typhoon path deflection, and a dynamic model is constructed; The terrain adjustment parameter a is calculated by the following formula: ， wherein, Rossby number of the vortex, dimensionless core vorticity, terrain gradient parameter, planetary vorticity gradient parameter; By adjusting the speed in the meridional direction The expression of MAV is as follows: ， wherein, is a vortex reference timescale, is a current time step vortex velocity, is a terrain gradient, is a reference y vector; Step S2: Model initialization; obtaining the initial state parameters of the typhoon, determining the reference constants in the basic model according to the environmental field at the prediction time, adjusting the high-resolution terrain height field of the research area, and setting related variable parameters to complete the initialization; Step S3: Single path simulation; the initial state parameters of the typhoon obtained in step S2 are input into the dynamic model as initial conditions, and the typhoon path coordinate sequence of this simulation is output; Step S4: Ensemble simulation and database construction; based on single simulation, an ensemble prediction test is constructed: different initial condition combinations are generated in batches according to the preset parameter space scheme; a typhoon path trajectory image database covering various typical scenarios is obtained; Step S5: Trajectory image intelligent learning; a large number of trajectory image data generated in step S4 are input into a pre-trained large language model or deep learning model for unsupervised or supervised feature learning, so that the model can realize the function of predicting the corresponding model parameter range or category according to the input trajectory image; Step S6: Historical path mapping and parameter fitting; a part of the typhoon trajectory image data actually observed in history is input into the trained supervised / unsupervised learning model as a training set, the features of the real path are extracted, and the most similar category or adjacent point in the learned simulation trajectory feature space is found, and then the model parameter combination matching the real path is inferred, and the simulation trajectory is adjusted to fit the real trajectory as much as possible to complete parameter calibration; Step S7: Model prediction and verification; another part of the typhoon trajectory image data actually observed in history is used as a test set, and the parameters obtained by the fitting / training method in step S6 are set in the model for path simulation, the model prediction trajectory set is compared with the actual observation paths of these typhoons, the hit rate and deviation are counted, and the reliability of the model is verified.

2. The method of claim 1, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. The dynamic model based on the principle of potential vorticity conservation is: ， Where t is time and the potential vorticity Π is defined as: ， where is the base value of the Coriolis parameter, is the planetary vorticity zonal variation rate, y is the northward coordinate position, is the relative vorticity strength of the vortex, H is the total fluid depth and ， Where D represents the fluid thickness under static environment, η is the free surface disturbance height caused by typhoon vortex, and hB represents the height of the underlying terrain; In the dynamic model, the vortex intensity ζ(t) is represented by a time-varying function, specifically: ， where ζ(0) is the initial vortex intensity, is the decay timescale, determined from historical typhoon data or real-time observations.

3. The method of claim 2, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. The initial state parameters of the typhoon include the initial center position coordinates, the initial intensity parameter, the typhoon moving direction and speed, and the values of f0 and β0 on the β plane determined according to the environmental field at the prediction time.

4. The method of claim 1, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. In the step S3, the initial state parameters of the typhoon obtained are input into a dynamic model, a numerical integration method is used to solve a vortex trajectory equation containing terrain influence, the position change of the typhoon center is calculated at each time step, the value of a is calculated by applying the principle of potential vorticity conservation, the value of MAV is calculated in combination with the local terrain slope, the trajectory is corrected through the meridional and latitudinal velocity components of the typhoon, and iteration is repeated until the typhoon crosses the target terrain area or reaches the prediction length, and the initial state parameters of the typhoon obtained are input into a dynamic model.

5. The method of claim 1, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. In the step S4: According to a preset parameter space scheme, different initial condition combinations are batch generated, including: fixing the incident angle and the typhoon intensity in one set, changing only the initial landing latitude position to generate multiple paths; fixing the landing point in another set, setting different incident angles respectively to generate multiple paths; For each initial condition group, the model is run, all simulated path trajectory data are collected, the trajectory data are visualized as images or curves, and the corresponding parameter values are labeled, and stored in a "path-parameter" database, and a typhoon path trajectory image database covering various typical scenarios is obtained through a large number of simulations.

6. The method of claim 1, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. The step S5 intelligent learning of the trajectory image specifically includes: The model automatically extracts key features by analyzing the trajectory shape and maps each trajectory to a trajectory feature space, wherein the key features include the path deflection angle, whether an "S" type turning appears, and the maximum deviation distance; Through clustering or classification algorithms, the trajectories are classified into multiple different groups according to the morphological features; After training, the large language model predicts the corresponding model parameter range or category according to the input of a trajectory image.

7. The method of claim 1, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. The model predicts the corresponding model parameters according to the input of a trajectory image, including giving the most likely incident angle range, initial intensity level and landing point offset information of the typhoon.

8. The method of claim 1, wherein the dynamic model is constructed by using a numerical weather prediction model and a statistical model. In the step S7, if the prediction deviation is large, return to step 6 to adjust and improve the parameter mapping method; if the effect is ideal, it proves that the model has practical application value, and when a new typhoon arrives in actual prediction, the real-time observation parameters can be input into the model to quickly predict the possible path deflection set. 9.A typhoon track prediction system, characterized in that, It includes: The dynamic model calculation module is used to execute the dynamic model construction method in any one of claims 1-8; The ensemble prediction generation module is used to generate a set of typhoon path trajectories; The large language model analysis module is used to learn features and map parameters of trajectory data.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, when the program is executed by the processor, a dynamic model construction method for predicting typhoon path deflection on complex terrain in any one of claims 1-8 is realized, and a typhoon path prediction system in claim 9 is further generated.

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