An era5 reanalysis vertical profile correction method based on vertical first and cross variable second dual-axis sequential attention residual correction

Abstract

The application discloses an ERA5 reanalysis vertical profile correction method and system based on a vertical-then-cross-variable biaxial sequential attention residual correction, and belongs to the technical field of meteorological data processing. In view of the problems that the existing correction method is difficult to depict the complex dependence between multivariables in the vertical layer and between the variables, and the joint correction precision is insufficient, the ERA5 reanalysis data is converted into a geometric height from the ground and is jointly interpolated to a unified height grid together with sounding observation. Each variable is independently projected and superimposed with type embedding and height position coding. After being alternately coded along the height and then along the variable through multiple biaxial sequential attention modules, each variable is outputted through a special multilayer perception machine to obtain a residual correction quantity. After being multiplied by a variable-learnable weight, the residual correction quantity is superimposed back to the input profile to obtain a corrected profile. The application is used for numerical weather prediction, atmospheric detection and the like, and can consistently reduce the systematic deviation of the ERA5 system on multiple meteorological variables.

Description

Technical Field

[0001] This invention relates to the field of meteorological data processing technology, specifically to a method and system for correcting the vertical profile of ERA5 reanalysis data using radiosonde observations. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] ERA5 reanalysis data is gridded data obtained by the European Centre for Medium-Range Weather Forecasts (ECMWF) through numerical models to recalculate historical atmospheric conditions. There are systematic deviations between ERA5 and radiosonde measurements in the vertical distribution of elements such as temperature, pressure, and humidity, so radiosonde observations are needed to correct it.

[0004] Existing bias correction methods mainly include quantile mapping, model output statistics, and variational methods. These methods are limited by linear or stationarity assumptions, making it difficult to capture complex vertical covariance structures, and they have poor generalization ability under different meteorological conditions. At the same time, there has been insufficient research on deep learning schemes that use radiosonde data as supervision to jointly correct multiple meteorological variables in the ERA5 vertical profile.

[0005] Patent document CN109447260B discloses a method for correcting local numerical weather prediction products based on deep learning. The technical approach is as follows: a training dataset is constructed based on historical numerical weather prediction products and corresponding historical station observation data; a deep learning network model is trained to obtain a correction model; real-time forecast field data is then input into the trained correction model, and the correction result is output. This scheme provides an overall route for constructing a training set from historical data, training the network, and outputting the correction result. However, it does not address the geometric height conversion, spatiotemporal matching, and unified grid interpolation between radiosonde observations and reanalysis data, nor does it provide a network structure design for the complex dependencies between multiple meteorological variables in vertical layers and between variables.

[0006] Patent document CN110110482B discloses an algorithm for correcting and verifying the temperature deviation of a radiosonde characteristic layer. The steps include collecting and organizing radiosonde temperature profiles, converting the deviation correction amount from a time series into a spatial profile, using an interpolation algorithm to superimpose the correction amount, and verifying its temporal and spatial consistency with reanalysis data. This scheme involves the interpolation and comparison process between radiosonde data and reanalysis data; however, its spatial profile of the correction amount is derived from an existing time series of deviations, and it does not employ a deep learning network to jointly learn and correct the multivariate vertical profiles.

[0007] Patent document CN111239856B discloses a method for calculating the correction amount of radiosonde temperature radiation error. The method includes steps such as analyzing the deviation characteristics of different types of radiosondes, calculating the radiation correction amount using model background field data and known high-quality radiosondes, and verifying the systematic errors of the reanalysis data. It belongs to an additive correction framework that superimposes the correction amount based on the difference between the original radiosonde observation and the background field. This scheme corrects the radiation error for a single variable, temperature, and does not involve joint network learning correction for multi-variable vertical profiles.

[0008] In summary, existing bias correction methods either rely on linear and stationary assumptions, making it difficult to characterize the complex dependencies between multiple variables such as temperature, air pressure, and specific humidity in vertical layers and among variables. Although processing procedures such as interpolation registration and additive correction of radiosonde and reanalysis data have been proposed, no dual-axis sequential attention network scheme has been found that uses radiosonde observations as supervision to jointly correct multiple meteorological variables in the ERA5 vertical profile. Summary of the Invention

[0009] Technical problems to be solved To address the shortcomings of existing bias correction methods in capturing the complex inter-layer and inter-variable dependencies of multiple variables such as temperature, air pressure, and specific humidity in the ERA5 vertical profile, and their insufficient generalization ability under different meteorological conditions, and considering the lack of research on deep learning schemes for multi-variable joint correction of the ERA5 vertical profile using radiosonde observations as supervision, this invention proposes an ERA5 reanalysis vertical profile correction method and system based on dual-axis sequential attention residual correction of vertical and cross-variable variables.

[0010] Technical solution In a first aspect, the present invention provides an ERA5 reanalysis vertical profile correction method based on biaxial sequential attention residual correction of vertical and transvariable parameters, comprising the following steps: Step 1, data configuration: using virtual temperature and combining ECMWF half-layer coefficients, the multi-layer mixed sigma-baric layer integral of ERA5 reanalysis data is converted into ground-level geometric height; after bilinear interpolation of ERA5 grid data to the coordinates of the target radiosonde station and time matching with the radiosonde release time, the converted ERA5 geometric height profile and the radiosonde geometric height profile are linearly interpolated together to a unified height grid, resulting in a grid covering a preset height range and divided at preset intervals. The input profile X is divided into H height layers, each containing F variables. These F variables include at least temperature T, air pressure p, specific humidity q, and a virtual temperature Tv derived from basic observations. Step two, feature embedding: Each variable in the input profile X is independently projected using a dedicated linear projection layer with non-shared weights. This is superimposed with learnable variable type embedding that encodes the physical attributes of the variables, and sinusoidal position encoding applied according to the height layer position, to obtain an initial representation. Step three, dual-axis sequential attention encoding: The initial representation is input into an encoder consisting of L stacked dual-axis sequential attention modules. Each dual-axis sequential attention module... First, multi-head self-attention is performed on each variable along H height layers to obtain a vertical self-attention representation. Then, multi-head self-attention is performed on the vertical self-attention representation along F variables at each height layer to obtain a cross-variable self-attention representation. The fixed order of vertical followed by cross-variable self-attention is repeated within each dual-axis sequential attention module. After each self-attention output, residual summation and layer normalization are applied. Within each module, after completing two self-attention operations (vertical followed by cross-variable self-attention), a position-wise feedforward network is applied. The output of this feedforward network, after residual summation and layer normalization, becomes the output of that module. The number of height layers H and the number of variables F obtained in step one determine... In step three, the input dimensions of vertical self-attention and cross-variable self-attention are defined. Step one provides an executable unified grid premise for the dual-axis sequential attention in step three. In step four, output projection: for each variable representation output by the encoder, a dedicated multilayer perceptron for that variable is used to map it to a scalar residual correction amount Δ at each height layer. In step five, residual superposition: a learnable weight w of the same length as the number of variables F is set. The residual correction amount Δ is multiplied element-wise with the weight w in the manner of Ŷ=X+Δ⊙w and then superimposed back onto the input profile X to obtain the corrected profile Ŷ. The w is jointly updated during training along with the other parameters of the network through backpropagation.

[0011] As an optional implementation, the unified height grid covers 0-20km and is divided at 100m intervals. The number of height layers H is 201, and the F variables are 8, including temperature T, air pressure p, specific humidity q, dew point temperature Td, temperature-dew point difference T-Td, virtual temperature Tv, zonal wind u, and meridional wind v.

[0012] As an optional implementation, the stacking number L of the dual-axis sequential attention module is 6, the internal dimension d_ff of the position-by-position feedforward network is 1024, and each feedforward network uses the GELU activation function.

[0013] As an optional implementation, in step five, before the residual correction amount Δ is superimposed on the input profile X, it is first denormalized according to the standard deviation σ_i of the corresponding variable in the training set statistics to obtain Δ with the same physical scale as the input profile X, and then Ŷ=X+Δ⊙w is executed. The denormalization process is located between step four and step five.

[0014] As an optional implementation, the inverse normalization process is calculated as Δ_i = σ_i·Δ_i^norm, where Δ_i^norm is the residual correction of the i-th variable output by the network in the normalization space, and σ_i is the statistical standard deviation of the i-th variable on the training set.

[0015] As an optional implementation, the learnable weight w is initialized as a vector of all 1s with the same length as the number of variables F. During training, it is updated for each variable through backpropagation, and no explicit value range constraint is set.

[0016] As an optional implementation, the loss function used to train the encoder and multilayer perceptron is the mean squared error of the batch, height layer, and variable triple summation; the AdamW optimizer is used with an initial learning rate of 1×10⁻³ and a weight decay of 1×10⁻², coupled with 100 rounds of cosine annealing scheduling, a batch size of 16, and a network dropout rate of 0.1; all input variables are normalized to zero mean and unit variance according to the training set statistics before being fed into the network.

[0017] Secondly, this invention also provides an ERA5 reanalysis vertical profile correction system based on biaxial sequential attention residual correction of vertical and cross-variable parameters, comprising: a data configuration module, used to convert ERA5 reanalysis data into geometric height using virtual temperature and ECMWF half-layer coefficients, bilinearly interpolating ERA5 grid data and matching it with the radiosonde release time, then interpolating it together with the radiosonde geometric height profile to a unified height grid, outputting an input profile X covering H height layers, each layer containing F variables, and outputting H and F to a feature embedding module and a biaxial sequential attention encoding module as its input dimension configuration; a feature embedding module, connected to the data configuration module, receiving the input profile X, projecting each variable using a dedicated independent linear projection layer, superimposing learnable variable type embedding and sinusoidal position encoding applied according to the height layer position, and outputting an initial representation to the biaxial sequential attention encoding module; and a biaxial sequential attention encoding module, connected to the feature embedding module, receiving the initial representation, its input dimensions being configured by H and F output by the data configuration module, including... L stacked dual-axis sequential attention units. Each dual-axis sequential attention unit first performs multi-head self-attention on each variable along H height layers, then performs multi-head self-attention on each height layer along F variables. After each self-attention output, residual summation and layer normalization are applied. Within each unit, after the two self-attention operations, a position-wise feedforward network is applied. The output of this feedforward network, after residual summation and layer normalization, becomes the output of that unit. The output is encoded and represented by the output projection module. The output projection module is connected to the dual-axis sequential attention encoding module. For each variable, a dedicated multilayer perceptron is used to map the encoded representation to a scalar residual correction amount Δ at each height layer, and Δ is output to the residual superposition module. The residual superposition module is connected to the output projection module and the data configuration module, and stores the learnable weights w of the same length as the number of variables F. The residual correction amount Δ is multiplied element-wise with the weights w according to Ŷ=X+Δ⊙w and then superimposed back to the input profile X output by the data configuration module, and the corrected profile Ŷ is output. The w is updated by backpropagation feedback during the training phase.

[0018] Beneficial effects Because the dual-axis sequential attention model first along the height layer and then along the variable dimension, the network can capture two types of structures: how the same variable changes between different height layers and how different variables are related within the same height layer. Compared with traditional correction methods that assume linearity or stationarity, it can more fully characterize the complex dependencies of the vertical profile. Since the learnable weights w can learn the appropriate correction strength for each variable based on the training data, it avoids the undercorrection or overcorrection problems caused by applying a uniform correction strength to all variables. Since the inverse normalization process puts the residual correction amount on the same physical scale as the input profile, the physical unit of the correction result is traceable and recalculated. Attached Figure Description

[0019] Figure 1 This is an overall flowchart of the method of the present invention; Figure 2 This is a system module block diagram (system functional module structure block diagram) of the present invention. Figure 3 This is a flowchart of the internal processing of the dual-axis sequential attention encoding module of the present invention. Detailed Implementation

[0020] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Without conflict, the following embodiments and features described herein can be combined with each other.

[0021] To facilitate understanding of the technical solution of this invention, the main symbols involved in the specification will be explained below. In this embodiment of the invention, a uniform height grid covers 0–20 km, divided at 100 m intervals, with 201 height layers (H). Each height layer contains F=8 variables: temperature T, air pressure p, specific humidity q, dew point temperature Td, temperature-dew point difference T-Td, virtual temperature Tv, zonal wind u, and meridional wind v. The data source is a matched dataset of L-band radar radiosonde observations and ERA5 reanalysis data from Korla station from 2020 to 2023, with 2904 valid paired samples, divided into training, validation, and test sets in a ratio of 7:1.5:1.5.

[0022] refer to Figure 1 ERA5 reanalysis data and radiosonde observations first undergo data configuration (11) to complete conversion, interpolation and time matching, and obtain input profile X (10) on a unified grid. Then, it flows through feature embedding (12), dual-axis sequential attention encoding (13, marked "vertical first then cross-variable" in the figure), output projection (14), and residual superposition (15) to finally obtain the corrected profile Ŷ (16). Figure 1 In sections 11 to 16, the data is configured, feature embedding, biaxial sequential attention encoding, output projection, and residual superposition are unidirectionally connected in that order. The fixed order noted in box 13 corresponds to the processing order of biaxial sequential attention encoding.

[0023] The data configuration module (11) first converts the original multi-layer data of ERA5 reanalysis data, which was divided according to the mixed sigma-baric layer, into the actual geometric height above the ground by combining the virtual temperature and the half-layer coefficient published by ECMWF. The conversion is performed according to the standard method given in the definition of the 137 model layers published by ECMWF: the air pressure of the k-th half-layer is calculated as p_(k±1 / 2)=a_(k±1 / 2)+b_(k±1 / 2)·p_s, where a and b are the half-layer coefficients published by ECMWF, and p_s is the surface air pressure; the potential increment between adjacent half-layers is calculated as ΔΦ_k=R_d·T_(v,k)·ln(p_(k+1 / 2) / p_(k-1 / 2)), where R_d is the dry air gas constant, and T_(v,k) is the virtual temperature of the k-th layer; the potential of each model layer is obtained by accumulating the potential layer by layer from the surface potential Φ_s upwards, dividing it by the standard gravitational acceleration g_0 to obtain the potential height, and then subtracting the topographic height of the grid point to obtain the geometric height above the ground. Then, the ERA5 grid data is horizontally interpolated to the coordinates of the radiosonde station, and time matching is performed according to the actual radiosonde release time. Finally, the converted ERA5 height profile and the measured radiosonde height profile are interpolated together onto the same height grid to obtain an input profile X (10) with 8 variables per layer. Time matching is taken from the reanalysis time corresponding to the radiosonde release time (radiosondes are released twice a day, at 08:00 and 20:00 Beijing time, corresponding to 00:00 and 12:00 UTC). For the missing or quality-controlled abnormal layer values ​​in the profile, they are first set to invalid values, and then linear interpolation is performed to fill them along the height direction. For height layers without valid data outside the beginning and end of the unified grid, the values ​​of the nearest valid layer are extended and filled. After the above processing, the values ​​of each input profile are complete on all height layers of the unified grid. This step is equivalent to aligning two inconsistent data sets onto the same ruler, providing a unified and executable input dimension for subsequent network processing.

[0024] The feature embedding module (12) performs projection transformation on each variable in the input profile X (10) using a set of parameters specific to that variable. Different variables do not share parameters, thus avoiding different physical quantities being processed together by the same set of parameters. It also superimposes learnable codes that distinguish the types of variables, as well as sinusoidal position codes applied according to the height layer position, so that the network can distinguish which layer is being processed.

[0025] refer to Figure 3The dual-axis sequential attention encoding module (13) is the core processing step of this scheme. The initial representation (19) first executes the vertical self-attention representation (20), that is, each variable performs multi-head self-attention along H=201 height layers to understand the inter-layer correlation of the variable in the vertical direction, followed by residual summation and layer normalization (22); then executes the cross-variable self-attention representation (21), that is, each height layer performs multi-head self-attention along F=8 variables to understand the correlation between different variables in the same layer, followed by residual summation and layer normalization (22); then connects to the position-by-position feedforward network (23), and the output of the feedforward network (23) is used as the output of the unit after residual summation and layer normalization (22). This fixed order of vertical first and cross-variable second is repeated in each dual-axis sequential attention unit. In the figure, ×L (L=6) marks that this order is repeated 6 times in the module and the order is fixed and cannot be reversed; the final output encoding representation (24) is passed to Figure 2 The output projection module (14) is used. The internal dimension d_ff of the position-by-position feedforward network (23) is 1024, the GELU activation function is used, and the network dropout rate is 0.1.

[0026] refer to Figure 2 The data configuration module (11) outputs the input profile X (10) to the feature embedding module (12), and outputs the height layer number H and the number of variables F to the feature embedding module (12) and the dual-axis sequential attention encoding module (13) respectively through the labeled arrows, as the input dimension configuration of the two; the feature embedding module (12) outputs the initial representation to the dual-axis sequential attention encoding module (13); the dual-axis sequential attention encoding module (13) outputs the encoded representation to the output projection module (14); the output projection module (14) maps the representation of each variable processed by the encoder to a value of the variable at each height layer through a multilayer perceptron dedicated to the variable, namely the residual correction amount Δ (17), and outputs it to the residual superposition module (15); the residual superposition module (15) simultaneously receives the residual correction amount Δ (17) and the input profile X (10) output by the data configuration module (11), internally stores the learnable weights w (18) for each variable, and outputs the corrected profile Ŷ (16).

[0027] The residual superposition module (15) assigns a trainable scaling factor to each of the eight variables, namely a learnable weight w (18) for each variable. During training, the variable with the larger deviation learns a larger coefficient, and the variable with the smaller deviation learns a smaller coefficient. After multiplying the residual correction amount Δ (17) with the weight w of the corresponding variable, it is added back to the original input profile X (10) output by the data configuration module (11) to obtain the corrected profile Ŷ (16). The w is initialized as a vector of all 1s with the same length as the number of variables F. During training, it is updated for each variable through backpropagation, without setting explicit value range constraints.

[0028] The H=201 and F=8 output by the data configuration module (11) are not merely fixed hyperparameters, but directly determine the... Figure 3 The processing lengths of the vertical self-attention representation (20) and the cross-variable self-attention representation (21) are as follows: The vertical self-attention representation (20) performs self-attention on each variable at 201 height levels, and its sequence length is H=201; the cross-variable self-attention representation (21) performs self-attention on 8 variables at each height level, and its sequence length is F=8. Without the unified grid provided by the data configuration module (11), the dual-axis sequential attention encoding module (13) cannot determine the processing lengths of these two self-attention paths. The two are inseparable and have a sequential dependency relationship. This is also the technical reason why the data configuration module (11) is a necessary step before the dual-axis sequential attention encoding module (13).

[0029] The self-attention and feedforward calculations within the network are performed in the normalized numerical space. If the Δ_norm directly output by the network is added back to the original profile X (10) without processing, a unit mismatch will occur. That is, the network outputs a normalized number, while X is the actual reading with units. Therefore, after the output projection module (14) outputs Δ_norm and before the residual superposition module (15) executes Ŷ=X+Δ⊙w, an inverse normalization is inserted: according to Δ_i=σ_i·Δ_i^norm, the residual correction amount in the normalized space is multiplied by the statistical standard deviation σ_i of the variable on the training set, converted back to the same physical unit as X, and then residual superposition is performed. Examples of the statistical standard deviation σ_i values ​​of each variable on the training set are shown in the following table: Example Explanation (The following values ​​are illustrative examples used to illustrate the formula calculation process, not actual measured results): Suppose that at a certain height layer, the normalized residual correction amount Δ_T^norm for the network output of temperature T is 0.15, the statistical standard deviation of temperature on the training set is σ_T = 1.2K, and after inverse normalization, Δ_T = 1.2K × 0.15 = 0.18K; the original ERA5 temperature reading of this layer is X_T = 280.0K, the weight of each variable is w_T = 0.9, substituting into Ŷ = X + Δ⊙w, we get the corrected temperature Ŷ_T = 280.0K + 0.18K × 0.9 = 280.162K (this example is uniformly rounded to three decimal places). The normalized residual correction for the dew point temperature Td at the same altitude is Δ_Td^norm = -0.08, σ_Td = 1.5K. After inverse normalization, we get Δ_Td = 1.5K × (-0.08) = -0.12K. The original readings are X_Td = 270.0K and w_Td = 0.85. After correction, Ŷ_Td = 270.0K + (-0.12K) × 0.85 = 269.898K. The normalized residual correction for specific humidity q is Δ_q^norm = 0.06, σ_q = 0.4 g / kg. After inverse normalization, Δ_q = 0.4 × 0.06 = 0.024 g / kg. The original readings are X_q = 3.5 g / kg and w_q = 0.95. After correction, Ŷ_q = 3.5 g / kg + 0.024 g / kg × 0.95 = 3.5228 g / kg.

[0030] The verification data in this embodiment comes only from the single Korla station and has not yet been validated on test sets with different climate types or time periods. Therefore, the description of generalization ability improvement in this specification is limited to the generalization improvement under the climate conditions of Korla station and for different meteorological conditions (different seasons, different weather processes), and does not advocate coverage of other climate areas outside the climate conditions of Korla station.

[0031] The loss function used to train the encoder and the multilayer perceptron in the output projection module is the mean square error of the batch, height layer, and variable summation, and its calculation formula is: L = (1 / (B·H·F))·Σ_b Σ_h Σ_i (Ŷ_(h,i)^(b) - Y_(h,i)^(b))², where B is the batch size and Y is the sounding observation profile used for supervision; the embedding dimension and the number of attention heads are selected according to the computing power and data scale. In this example, a set of configurations is an embedding dimension of 128 and a number of heads of multi-head self-attention per channel of 4; the AdamW optimizer is used, with an initial learning rate of 1×10-³ and a weight decay of 1×10-², combined with 100 rounds of cosine annealing scheduling and a batch size of 16; all input variables are normalized to zero mean and unit variance according to the statistics of the training set before being sent into the network, and the output side is then converted back to physical scale by the aforementioned inverse normalization process.

[0032] On the reserved test set, the root mean square error (RMSE) of the profile corrected by the method of this embodiment relative to the original ERA5 profile, with radiosonde observations as a reference, is compared as follows (inventor's measured data): Note: The units of RMSE values ​​in the table vary depending on the variable and are consistent with the physical units of the variable itself; after relative improvement and correction, R² is a dimensionless quantity.

[0033] The table above shows that the RMSE of all eight variables decreased, with the improvement magnitude exhibiting a differentiated distribution: temperature T was already well calibrated using ERA5 data at this site, and the model only made a minor correction of 0.54% without overcorrection; virtual temperature, temperature-dew point difference, air pressure, and specific humidity, which have significant systematic biases, received significant corrections on the order of 15%–20%. This differentiated distribution is consistent with the design goal of the learnable weights w for each variable: w provides independent correction magnitude scaling for each variable, allowing the correction intensity to be differentiated according to the bias level of each variable.

[0034] It should be noted that treating derived variables such as temperature-dew point difference (T-Td) and virtual temperature (Tv) as independent correction channels alongside their basic variables is an intentional design of this invention, not an oversight. The systematic bias structure of derived variables in ERA5 differs from that of their basic variables (in the table above, the relative improvement in temperature T is only 0.54%, while temperature-dew point difference (T-Td) reaches 18.49% and virtual temperature (Tv) reaches 20.03%). Independent channels ensure that the correction strength of each variable is determined by its own bias level. If derived variables are only analytically recalculated from the corrected basic variables, their significant systematic biases cannot be specifically corrected. Accordingly, analytical derivation relationships are not mandatory between the corrected output variables. For downstream applications with strict thermodynamic consistency requirements, a post-processing step of analytically recalculating derived variables based on the corrected basic variables can be added after the output of this method. This post-processing is optional and not a necessary technical feature of this invention.

[0035] It should also be noted that the attention network in this invention is not an isolated abstract algorithm: its input is the ERA5 atmospheric physics measurement field after geometric height conversion and unified grid interpolation, and the supervision signal is the measured profile of the real atmosphere obtained by a radiosonde. The sequence length and channel structure of each processing stage of the network are directly determined by the height layering structure of the atmospheric profile (H height layers) and the composition of meteorological variables (F variables). The corrected output profile is used for downstream technical applications such as numerical weather prediction and atmospheric sounding inversion. The algorithm and the meteorological measurement data processing flow support each other and work together to objectively improve the accuracy of atmospheric vertical profile data.

[0036] It should be understood that the above description is only a specific embodiment of the present invention, used to illustrate the technical solution of the present invention, and not to limit it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for correcting the vertical profile in ERA5 reanalysis based on sequential attention residual correction of vertical and then cross-variable biaxial variables, characterized in that, The process includes the following steps: Step 1, Data Configuration: Using virtual temperature and combined with ECMWF half-layer coefficients, the multi-layer mixed sigma-baric layer integral of ERA5 reanalysis data is converted into geometric height above ground. The ERA5 grid data is bilinearly interpolated to the target radiosonde coordinates and time-matched with the radiosonde release time. The converted ERA5 geometric height profile and the radiosonde geometric height profile are then linearly interpolated together to a unified height grid, resulting in an input profile X∈R^(H×F) covering a preset height range and divided into H height layers at preset intervals. Each height layer contains F variables. At least including temperature T, air pressure p, specific humidity q, and virtual temperature Tv derived from basic observations; Step 2, Feature embedding: Each variable in the input profile X is independently projected using a linear projection layer dedicated to that variable and without shared weights, superimposed with learnable variable type embedding of the physical attributes of the encoded variable, and sinusoidal position encoding applied according to the height layer position, to obtain the initial representation; Step 3, Dual-axis sequential attention encoding: The initial representation is input into an encoder consisting of L stacked dual-axis sequential attention modules. Within each dual-axis sequential attention module, multi-head self-attention is first performed on each variable along H height layers. The force is used to obtain a vertical self-attention representation. Then, multi-head self-attention is performed on the vertical self-attention representation along F variables for each height layer to obtain a cross-variable self-attention representation. The fixed order of vertical followed by cross-variable is repeated within each dual-axis sequential attention module. After each self-attention output, residual summation and layer normalization are applied. Within each module, after completing two self-attention operations (vertical followed by cross-variable), a position-wise feedforward network is applied. The output of this feedforward network, after residual summation and layer normalization, becomes the output of that module. The number of height layers H and the number of variables F obtained in step one determine the vertical self-attention in step three. With respect to the input dimension of cross-variable self-attention, step one provides an executable unified grid premise for the biaxial sequential attention in step three; step four, output projection: for each variable representation output by the encoder, a dedicated multilayer perceptron for that variable is used to map it to a scalar residual correction amount Δ at each height layer; step five, residual superposition: set a pervariate learnable weight w of the same length as the number of variables F, and multiply the residual correction amount Δ element-wise with the weight w in the manner of Ŷ=X+Δ⊙w and then superimpose it back onto the input profile X to obtain the corrected profile Ŷ. The w is jointly updated during training along with the other parameters of the network through backpropagation.

2. The method according to claim 1, characterized in that, The unified height grid covers 0-20km and is divided into 100m intervals. The number of height layers H is 201. The F variables are 8 in total, including temperature T, air pressure p, specific humidity q, dew point temperature Td, temperature-dew point difference T-Td, virtual temperature Tv, zonal wind u, and meridional wind v.

3. The method according to claim 2, characterized in that, The stacking number L of the dual-axis sequential attention module is 6, the internal dimension d_ff of the position-by-position feedforward network is 1024, and each feedforward network uses the GELU activation function.

4. The method according to claim 1, characterized in that, In step five, before the residual correction amount Δ is superimposed on the input profile X, it is first denormalized according to the standard deviation σ_i of the corresponding variable in the training set statistics to obtain Δ at the same physical scale as the input profile X, and then Ŷ=X+Δ⊙w is executed. The denormalization process is located between step four and step five.

5. The method according to claim 4, characterized in that, The inverse normalization process is calculated as Δ_i = σ_i·Δ_i^norm, where Δ_i^norm is the residual correction of the i-th variable output by the network in the normalization space, and σ_i is the statistical standard deviation of the i-th variable in the training set.

6. The method according to claim 1, characterized in that, The learnable weight w is initialized as a vector of all 1s of the same length as the number of variables F. During training, it is updated for each variable through backpropagation, without any explicit constraints on the range of values.

7. The method according to claim 1, characterized in that, The loss function used to train the encoder and multilayer perceptron is the mean squared error of the batch, height layer, and variable summation. The AdamW optimizer is used with an initial learning rate of 1×10⁻³ and a weight decay of 1×10⁻², along with 100 rounds of cosine annealing scheduling, a batch size of 16, and a network dropout rate of 0.

1. All input variables are normalized to zero mean and unit variance according to the training set statistics before being fed into the network.

8. An ERA5 reanalysis vertical profile correction system based on biaxial sequential attention residual correction of vertical and then cross-variable variables, characterized in that, include: The data configuration module is used to convert ERA5 reanalysis data into geometric height using virtual temperature and ECMWF half-layer coefficients, bilinearly interpolate ERA5 grid data and time-match it according to the radiosonde release time, and then interpolate it together with the radiosonde geometric height profile to a unified height grid. It outputs an input profile X covering H height layers, each containing F variables, and outputs H and F to the feature embedding module and the dual-axis sequential attention encoding module as their input dimension configuration. The feature embedding module, connected to the data configuration module, receives the input profile X, projects each variable using a dedicated independent linear projection layer, and superimposes learnable variable type embedding and sinusoidal position encoding applied according to the height layer position. The initial representation is output to the dual-axis sequential attention encoding module. The dual-axis sequential attention encoding module is connected to the feature embedding module and receives the initial representation. Its input dimensions are configured by H and F output by the data configuration module. It contains L stacked dual-axis sequential attention units. Each dual-axis sequential attention unit first performs multi-head self-attention on each variable along H height layers, and then performs multi-head self-attention on each height layer along F variables. After each self-attention output, it is connected to residual summation and layer normalization. Each unit is connected to a position-wise feedforward network after two self-attention operations. The output of the feedforward network is used as the output of the unit after residual summation and layer normalization. The output encoded representation is output to the output projection module. The output projection module, connected to the dual-axis sequential attention encoding module, maps the encoded representation of each variable to a scalar residual correction amount Δ at each height layer using a dedicated multilayer perceptron for that variable, and outputs Δ to the residual superposition module. The residual superposition module, connected to the output projection module and the data configuration module, stores the learnable weights w of the same length as the number of variables F. It multiplies the residual correction amount Δ element-wise with the weights w according to Ŷ=X+Δ⊙w and then superimposes the result back onto the input profile X output by the data configuration module, outputting the corrected profile Ŷ. The w is updated by backpropagation feedback during the training phase.

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