Antarctic ice surface temperature retrieval method based on physical constraint neural network

Abstract

The application provides an Antarctic ice surface temperature inversion method based on a physically constrained neural network, and belongs to the technical field of image processing, and comprises the following steps: a physically constrained residual neural network model construction step and an Antarctic ice surface temperature inversion step, the physically constrained residual neural network model construction step comprises the following steps: acquiring training sample data, and a model training step.The Antarctic ice surface temperature inversion method based on the physically constrained neural network has the advantages that the physically constrained residual neural network model is constructed, the nonlinear mapping relationship between brightness temperature, brightness temperature difference, observation geometric parameters and split window coefficients is learned through the residual neural network, the defects that the experience coefficients of a traditional split window algorithm cannot adapt to a polar environment are overcome, and the problem of insufficient fitting precision of a pure residual neural network model is solved.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, specifically, it relates to a method for inverting Antarctic ice surface temperature based on a physically constrained neural network. Background Technology

[0002] Antarctic ice surface temperature (IST) is a core parameter characterizing the energy balance of the Antarctic surface, directly regulating heat exchange between the surface and the lower atmosphere, and significantly influencing key climate processes such as glacier melting and polar albedo feedback. Due to the extreme natural environment of Antarctica, in-situ meteorological observation stations are extremely sparse and costly to maintain, making it difficult to meet the needs of large-scale, long-term continuous monitoring. Therefore, satellite thermal infrared remote sensing has become the most important means of acquiring Antarctic IST data.

[0003] The current mainstream remote sensing inversion methods based on thermal infrared brightness temperature data can be mainly divided into the following three types: Option 1: Single-Channel (SC) Inversion Algorithm. This option relies on radiative transfer models and atmospheric profile data to establish a regression relationship between simulated radiance and surface temperature based on the Stefan-Boltzmann law or Planck equation (Comiso, 1994; Veihelmann, 2001; Li, 2024). The limitation of the single-channel algorithm is that its inversion process requires real-time, accurate atmospheric profile data (such as water vapor and temperature profiles) as auxiliary parameters. However, high-precision atmospheric profile data for polar regions is extremely difficult to obtain, and the algorithm is highly sensitive to parameter errors. Furthermore, the stripe noise present in the thermal infrared band of some sensors also severely restricts the accuracy of this algorithm.

[0004] Option 2: Traditional Split-Window (SW) Algorithm. Addressing the limitation of single-channel algorithms that rely on atmospheric parameters, the split-window algorithm utilizes the difference in water vapor absorption between adjacent 11 μm and 12 μm thermal infrared windows. It inverts the IST (Intense Stress Interval) by combining the brightness temperatures of the two bands, achieving inversion without requiring prior knowledge of the atmospheric profile. Its classic calculation formula is: ; in, , To set the channel brightness temperature, Here, denoted as zenith angle, and a, b, c, d are empirical coefficients determined through multiple linear regression. For example, the internationally mainstream MODIS ice surface temperature product (MYD29) uses this algorithm; in addition, Zheng et al. (2022) applied it to FY-3D / MERSI-II thermal infrared data, Shi et al. (2025) applied it to the SDGSAT-1 satellite, and Kolbe et al. (2025) used it to establish the Copernicus Climate Change Service dataset (C3S IST).

[0005] Traditional split-window algorithms rely heavily on pre-fitted empirical coefficients. In the Antarctic environment, these coefficients cannot accurately represent the relationship between observed brightness temperature and the true IST. This leads to a significant amplification of inversion errors in certain regions, such as a C3S IST error as high as 5.74K.

[0006] Option 3: Purely Data-Driven Machine Learning Algorithms. Existing technologies are beginning to explore the introduction of purely data-driven models such as machine learning. This option uses a large amount of satellite-observed brightness temperature as input features and measured surface temperature as a label. It leverages the powerful nonlinear mapping capabilities of neural networks to directly output the predicted ice surface temperature end-to-end.

[0007] Purely data-driven methods rely entirely on the coverage and quality of training samples, lacking the underlying constraints of physical mechanisms. In Antarctica, due to the harsh environment, high-quality in-situ measured samples are extremely scarce and unevenly distributed. Under these extremely limited sample conditions, pure neural network models are prone to overfitting, leading to decreased generalization ability when applied across years, and inconsistencies in the physical logic of the inversion results. Summary of the Invention

[0008] To address the technical problems of low accuracy and large errors in existing Antarctic ice surface temperature inversion methods, this invention proposes an Antarctic ice surface temperature inversion method based on a physically constrained neural network, which can solve the above-mentioned problems.

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for inverting Antarctic ice surface temperature based on a physically constrained neural network includes: a step of constructing a physically constrained residual neural network model and a step of inverting Antarctic ice surface temperature. The physically constrained residual neural network model includes an input layer, a data-driven residual network, and a physically constrained network. The data-driven residual network includes residual blocks and a linear output layer. The step of constructing the physically constrained residual neural network model includes: Acquire training sample data, including data from channels 24 and 25 of the thermal infrared emission band in FY-3D / MERSI-II data, to construct a spatial feature matrix; acquire ice shelf surface temperature data from the geolocation products MYD03 and MYD29 of MODIS data and ice sheet surface temperature data from the MYD11 product, to construct ground truth labels. The model training steps include: The training sample data is input into the input layer, which sequentially performs linear transformation, batch normalization, and nonlinear activation to expand the dimension of the input data to the hidden layer dimension. and output feature vectors ; Feature vector The input data is fed into the residual block for processing. The residual block sequentially performs feature distribution reshaping, feature space reconstruction, and nonlinear activation on the input data. The processing result is then added element-wise to the input of the residual block. The sum is used as the output of the residual block and output to the linear output layer, compressing the high-dimensional features into a 4-dimensional vector, which is the coefficient vector. ; The coefficient vector The input is fed into the physical constraint network, which outputs the predicted ice surface temperature. Based on the predicted ice surface temperature The loss function is calculated using the true ice surface temperature IST value in the truth label, and the parameters in the physical constraint residual neural network model are iterated until convergence. The Antarctic ice surface temperature inversion step includes: acquiring data from channels 24 and 25 of the thermal infrared emission band in MERSI-II data in real time, preprocessing the data, and inputting it into the physical constraint residual neural network model, which then predicts and outputs the ice surface temperature.

[0010] Compared with the prior art, the advantages and positive effects of the present invention are as follows: The Antarctic ice surface temperature inversion method based on physical constraint neural network of the present invention constructs a physical constraint residual neural network model, and learns the nonlinear mapping relationship between brightness temperature, brightness temperature difference and observation geometric parameters and split window coefficient through the residual neural network. This not only overcomes the defect that the empirical coefficients of the traditional split window algorithm cannot adapt to the polar environment, but also makes up for the problem of insufficient fitting accuracy of the pure residual neural network model.

[0011] Instead of using the traditional end-to-end form of neural networks that directly output the target physical quantity (temperature), the output layer of the residual neural network is specifically configured to output four high-dimensional feature values. These four values ​​are mapped and equivalent to four unknown empirical coefficients in the split-window formula. This establishes a framework for an Antarctic ice surface temperature inversion model: "residual neural network estimates physical coefficients, and physical formulas forward deduce temperature," thus calculating the predicted temperature. The model learns physical coefficient mapping patterns that are not limited to specific years, rather than simply numerical fitting. It exhibits strong spatiotemporal generalization ability across years, meeting the needs of long-term operational monitoring.

[0012] This method is applied to the batch processing and data production of large-scale thermal infrared remote sensing data from the Fengyun-3D / MERSI-II satellite. The core technologies and methods described above are used to generate large-scale, high-precision ice surface temperature (IST) standard products for the Antarctic ice sheet.

[0013] Other features and advantages of the present invention will become clearer after reading the detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. Attached Figure Description

[0014] Figure 1 This is a flowchart of an embodiment of the Antarctic ice surface temperature inversion method based on a physically constrained neural network proposed in this invention; Figure 2 This is a neural network model architecture diagram of an embodiment of the Antarctic ice surface temperature inversion method based on physical constraint neural networks proposed in this invention; Figure 3 This is a comparison of inversion time and root mean square error under different model parameters in one embodiment of the Antarctic ice surface temperature inversion method based on physical constraint neural network proposed in this invention. Figure 4 This is a cross-year generalization ability assessment diagram of an embodiment of the Antarctic ice surface temperature inversion method based on physical constraint neural network proposed in this invention in the Antarctic ice sheet region. Detailed Implementation

[0015] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Example 1: Disadvantages of the traditional split-window algorithm: Because the traditional algorithm relies on static empirical coefficients that have been fitted in advance by multiple linear regression, and there are often no clear optimal coefficients for the Antarctic ice sheet region, the empirical coefficients cannot accurately characterize the nonlinear relationship when facing the polar environment with complex and varied underlying surface types, resulting in a large inversion error.

[0018] Disadvantages of pure machine learning algorithms: Because pure data-driven methods rely entirely on training sample data, and in-situ observation samples in Antarctica are extremely scarce and difficult to obtain, this method is prone to overfitting when observation conditions change, and lacks a clear physical constraint mechanism, which may lead to physical inconsistencies and poor robustness in the inversion results.

[0019] To address the aforementioned issues, this embodiment proposes a method for inverting Antarctic ice surface temperature based on a physically constrained neural network. This method utilizes a machine learning approach guided by physics knowledge, leveraging the powerful nonlinear fitting capabilities of residual neural networks to dynamically estimate the coefficients of the split-window algorithm. Simultaneously, the physical formula for the split window is embedded as a physical constraint network layer in the model training process. This approach improves the accuracy and stability of the Antarctic ice sheet surface temperature inversion while ensuring physical interpretability.

[0020] See Figure 1 As shown, the Antarctic ice surface temperature inversion method based on physical constraint neural network in this embodiment includes: a step of constructing a physical constraint residual neural network model and a step of inverting the Antarctic ice surface temperature. The physical constraint residual neural network model includes an input layer, a data-driven residual network, and a physical constraint network. The data-driven residual network includes residual blocks and a linear output layer.

[0021] By constructing a physically constrained residual neural network model, the nonlinear mapping relationship between brightness temperature, brightness temperature difference, observation geometric parameters and split window coefficients was learned through the residual neural network. This not only overcomes the defect that the empirical coefficients of the traditional split window algorithm cannot adapt to the polar environment, but also makes up for the problem of insufficient fitting accuracy of the pure residual neural network model.

[0022] In terms of the "true temperature" reference label dataset required for constructing the residual neural network, airborne thermal infrared measurement data or in-situ automatic weather station data could theoretically be considered as alternatives. However, in practical engineering applications in Antarctica, due to the scarcity of measured data caused by the extreme Antarctic environment, neither airborne measurements nor weather station data can meet the residual network's requirement for a large number of true labels. These alternatives are not feasible due to the limited amount of objective data. Therefore, the Aqua / MODIS commercial products (MYD29 / MYD11) used in this invention serve as the reference benchmark, providing a large number of reliable samples for large-scale model training.

[0023] The steps for constructing a physically constrained residual neural network model include: Acquire training sample data, including data from channels 24 and 25 of the thermal infrared emission band in FY-3D / MERSI-II data, to construct a spatial feature matrix; and acquire ice shelf surface temperature data from the geolocation products MYD03 and MYD29 of MODIS data and ice sheet surface temperature data from the MYD11 product, to construct ground truth labels.

[0024] The model training steps include: The training sample data is input into the input layer, which then performs linear transformation, batch normalization, and non-linear activation in sequence, expanding the dimension of the input data to the hidden layer dimension. and output feature vectors .

[0025] Feature vector The input data is fed into a residual block for processing. The residual block sequentially performs feature distribution reshaping, feature space reconstruction, and nonlinear activation on the input data. The processing result is then element-wise added to the input of the residual block, and the sum is used as the output of the residual block and output to the linear output layer. This compresses the high-dimensional features into a 4-dimensional vector, which is the coefficient vector. .

[0026] This approach departs from the traditional end-to-end format of neural networks directly outputting the target physical quantity (temperature). Instead, the output layer of the residual neural network is specifically configured to output four high-dimensional feature values. These four values ​​are mapped and equivalent to four unknown empirical coefficients in the split-window formula. This establishes a framework for an Antarctic ice surface temperature inversion model: "residual neural network estimates physical coefficients, and physical formulas forward deduce temperature," thus calculating the predicted temperature. The model learns physical coefficient mapping patterns that are not limited to specific years, rather than simply numerical fitting. It exhibits strong spatiotemporal generalization capabilities across years, meeting the needs of long-term operational monitoring.

[0027] coefficient vector The input is fed into the physical constraint network, which outputs the predicted ice surface temperature.

[0028] To address the issue of highly concentrated values ​​of input feature terms (such as brightness difference) near zero in the split-window algorithm for Antarctic ice sheet surface temperature inversion, this invention abandons conventional activation functions in the nonlinear mapping of the residual blocks and adopts the Gaussian Error Linear Unit (GELU) activation function. In the residual network for Antarctic ice sheet surface temperature inversion, the GELU function is used to smooth near-zero sample features, thereby significantly improving the computational stability and model convergence speed under extreme polar low-temperature environments.

[0029] Based on ice surface temperature predictions The true value of ice surface temperature in the truth label Calculate the loss function and iterate over the parameters in the physical constraint residual neural network model until convergence.

[0030] The steps for inverting Antarctic ice surface temperature include: acquiring data from channels 24 and 25 of the thermal infrared emission band in MERSI-II data in real time, preprocessing the data, and then inputting it into a physically constrained residual neural network model. The physically constrained residual neural network model predicts the ice surface temperature as the inverted ice surface temperature and outputs it.

[0031] The model in this embodiment is applied to the batch processing and data production of large-scale thermal infrared remote sensing (FY-3D / MERSI-II) data from the Fengyun-3D satellite, and uses the above-mentioned core technologies and methods to generate large-scale, high-precision ice surface temperature (IST) standard products for the Antarctic ice sheet.

[0032] In some embodiments, the FY-3D / MERSI-II thermal infrared data and MODIS data are processed separately in the step of acquiring training sample data.

[0033] FY-3D / MERSI-II thermal infrared data preprocessing includes: preprocessing the acquired L1-level thermal infrared emission band data and L2-level cloud mask data from FY-3D / MERSI-II satellites to construct a standard spatial feature matrix. Specific sub-steps are as follows: (1) Latitude and longitude data reading: Read the latitude and longitude matrix from the FY-3D geolocation dataset GEO (Geolocation), and directly remove redundant data strips that do not include the Antarctic region by using a threshold judgment (the lowest latitude is greater than 60° south latitude), thereby improving the computation of batch data processing.

[0034] (2) Radiation calibration and Planck inverse transform: Extract MERSI-II channel 24 (11) ) and Channel 25 (12 The original observed count value DN is obtained, and the slope and intercept in the properties are read and converted into the actual radiance E (mW / (m2 cm sr)).

[0035] .

[0036] Subsequently, based on the effective center wavenumber wn of the sensor, the preliminary brightness temperature Te was calculated using the inverse function of Planck's radiation law: .

[0037] in, Radiance, and is Planck's constant.

[0038] Next, linear correction is performed using sensor calibration coefficients A and B to obtain the final high-precision channel brightness temperature matrix, which is also the brightness temperature matrix of the 24th channel. and the brightness temperature matrix of channel 25 : ; .

[0039] The brightness temperature correction factor for channel 24 is A. 24 = 1.00133, B 24 =−0.0734, the brightness temperature correction factor for channel 25 is A. 25 = 1.00065, B 25 = 0.0875.

[0040] (3) Spatial mask extraction and stereographic projection: Generate an effective pixel mask south of 60°S latitude, and then apply the brightness temperature matrix to this region. The satellite zenith angle matrix is ​​then subjected to polar stereo projection transformation. This transformation is then uniformly resampled to a standard Antarctic grid with a 1km resolution.

[0041] The EASE-Grid projection includes both the polar spherical Lambert azimuth equal-area projection for the Northern or Southern Hemisphere and a "corrected" cylindrical equal-area projection suitable for mid- and low-latitude regions. This technique uses the polar spherical Lambert azimuth equal-area projection for the Southern Hemisphere, as shown in the following formula: ; .

[0042] Where r is the column coordinate, s is the horizontal coordinate, ncols and nrows represent the number of columns and rows of the grid, r0 is the starting column, s0 is the starting row, R is the Earth's radius of 6371.228 km, C is the grid size of 4*1.002701, p represents latitude, and l represents longitude (in radians).

[0043] (4) Strict clear sky pixel selection based on bit operations: To address the issue of misclassification caused by the similarity in spectral characteristics between Antarctic ice and clouds, L2-level cloud mask products are used. Decimal cloud mask pixel values ​​are converted to 8-bit binary strings, and specific cloud state identifiers (bits 5 to 8) are rigorously extracted. Only valid pixels absolutely marked as "Clear Sky" are retained to generate a high-quality ClearMask matrix, which is then applied to the projected brightness temperature and zenith angle matrices, providing clear-sky input features for subsequent IST inversion.

[0044] In the technical solution of this embodiment, in order to provide "GroundTruth" training labels for the physical constraint residual network model, it is necessary to process the external standard reference data products (geolocation product MYD03, ice surface temperature product MYD29, and ice cover surface temperature product MYD11).

[0045] MODIS data preprocessing methods include: (1) Time matching: This invention first performs orbital-level time alignment on the downloaded MYD03, MYD29, and MYD11 datasets. By setting a strict time matching window, it ensures that the spatial matrices belong to the same observation time.

[0046] (2) Polar projection: In the original data, the spatial resolution of the latitude and longitude scientific datasets (SDS) that come with MYD29 and MYD11 is usually coarse and cannot achieve accurate pixel-level mapping with temperature pixels with a spatial resolution of 1 km. Therefore, the spatial latitude and longitude matrix of MYD03 is used.

[0047] (3) Clear sky pixel filtering: To improve data quality, this invention filters the raw data. The internal quality assessment (QA) layer of the dataset is read, and pixels with low confidence are removed, retaining only high-confidence pixels marked "GOOD". The cloud masking parameters include four confidence states: "cloudy", "uncertainclear", "probably clear", and "confident clear". If a pixel is in a "certain cloud" state, it is immediately identified as a cloud pixel and stripped of its cloud cover.

[0048] (4) Spatiotemporal matching with MERSI: Both MERSI and MODIS strip data have a period of 5 minutes. In this embodiment, spatiotemporal matching was performed on the two datasets for the Antarctic region, with a time window set to 30 minutes. Regions with identical geographical locations within the matching time were identified as the matched region. The MYD11 and MYD29 datasets were used as the reference ground truth (IST) for model construction, where MYD11 is the data for the Antarctic land region and MYD29 is the data for the Antarctic ice shelf region.

[0049] In some embodiments, the data-driven residual network includes several cascaded residual blocks. During the model training step, the feature vectors... The residuals are processed sequentially through each residual block, and the output features of the last residual block are then processed. The output is sent to a linear output layer for processing.

[0050] In some embodiments, the method for constructing the spatial feature matrix in the step of obtaining training sample data includes: Extract the raw observation counts DN from channels 24 and 25 of MERSI-II, and read the slope and intercept from the attributes to convert DN into actual radiance E.

[0051] Based on the effective center wavenumber wn of the sensor, the preliminary brightness temperature Te is calculated using the inverse function of Planck's radiation law.

[0052] Linear correction of the initial brightness temperature is performed using sensor calibration coefficients to obtain the channel brightness temperature matrix for both channels. and .

[0053] In the model training step, the brightness temperature matrix of channel 24 is... Brightness temperature difference between channels 24 and 25 Geometric correction items And truth labels are input to the input layer.

[0054] In some embodiments, geometric correction terms The calculation method is as follows: .

[0055] VZA stands for Satellite Zenith Angle.

[0056] The physically constrained neural network model constructed in this embodiment mainly consists of three core parts: an input layer, a data-driven residual network, and a physically constrained network. It aims to fit the nonlinear mapping between observed variables and split-window physical coefficients in a polar environment using a neural network. Its internal structure is as follows: Figure 2 As shown.

[0057] In the model training step, the training sample data is input into the input layer, specifically the brightness temperature of the MERSI 24th channel. Brightness temperature difference between channels 24 and 25 And the geometric correction term q.

[0058] ; .

[0059] Because the three features have different units, direct input would cause computational crashes. Therefore, they are converted into unitless, standardized numbers. Thus, in some embodiments, the model training step includes, before inputting the data into the input layer, a process of... , as well as The steps for normalization and concatenation into a three-dimensional feature vector x include: .

[0060] in, , These are the mean vector and standard deviation vector of a large-scale historical sample data, respectively. To prevent extremely small constants with a denominator of zero, the values ​​can be, but are not limited to, zero. .

[0061] Using a mean vector pre-statisticated on a large-scale historical sample set with standard deviation vector Standardization is performed to obtain dimensionless network input feature vectors. .

[0062] Normalized low-dimensional physical features The input is the first layer of the network. This layer sequentially performs linear transformations, batch normalization, and non-linear activations, expanding the dimension to the hidden layer dimension. Hidden layer dimension refers to the richness (number of channels) of features extracted within the network. The larger the value, the more details the network can capture.

[0063] In some embodiments, feature vectors The calculation method is as follows: .

[0064] in, The weight matrix represents the "importance" of each feature; the network learns to determine which feature has a greater impact on the final result. BN stands for Batch Normalization. These are network parameters, and these are bias terms used to provide a basic output. The output features are input to the mapping layer.

[0065] Feature vector Then it passes through N cascaded residual blocks in sequence. For the Lth residual block ( Let its input features be... The internal structure of the residual block is as follows: Figure 2 As shown.

[0066] Feature distribution reshaping: First, batch normalization is performed on the input features to smooth out internal covariate shifts. Internal covariate shifts refer to drastic changes in the numerical distribution of data during transmission between network layers, making the network difficult to train. In some embodiments, the residual block performs feature distribution reshaping on the input data as follows: .

[0067] Let L be the input feature vector of the Lth residual block. and These are the mean and variance of the samples in the current feature distribution renormalization layer, respectively. and These are learnable scaling and translation parameters used to bring drastically fluctuating data back to a reasonable distribution range. 'l' indicates that the current location is the 'l'-th hidden layer in the residual neural network. This represents the input feature vector of the l-th hidden layer.

[0068] In some embodiments, .

[0069] .

[0070] In the formula, m is the number of mini-batch samples in the current BN layer.

[0071] Feature space reconstruction (Linear): Subsequently, a fully connected layer is used for feature mapping of the same dimension. The fully connected layer performs a comprehensive matrix cross combination of all features extracted in the previous step to find deep mapping patterns.

[0072] The method for reconstructing the feature space of input data using residual blocks is as follows: .

[0073] This represents the weight matrix of the l-th hidden layer. This represents the bias term vector of the l-th hidden layer. This represents the output feature vector of the l-th hidden layer.

[0074] In the network structure of this invention, it specifically refers to the clean data input to the current linear layer after the data from the previous layer has undergone feature distribution reshaping (batch normalization) for noise reduction and fluctuation smoothing. This represents the weight matrix for this layer. This is a core parameter that the network needs to continuously learn and adjust during training, using it to find the deep mapping relationship between brightness / temperature and the split window coefficient. This represents the bias vector for this layer. It is also an adjustable parameter that the network needs to learn. Mathematically, it is equivalent to the "intercept" of a linear equation, and its physical meaning is to provide a basic numerical compensation: ensuring that even if certain input features... When the value is 0, the neuron can still maintain flexible output capabilities, improving the upper limit of the model's fit. This represents the output feature vector of this layer. That is, the input data. After undergoing multiplication and combination of weight matrices and addition compensation of bias terms, new features are mapped to a completely new dimensional space. It is merely a linear intermediate result, which must then be fed into the next stage for nonlinear activation in order to truly acquire the ability to process data from the complex Antarctic environment.

[0075] Gaussian Error Linear Unit (GELU): Traditional networks often use the Rectified Linear Unit (ReLU) function, but in this invention, the feature terms of the split-window algorithm are highly concentrated around 0. The GELU activation function... The near-zero sample exhibits continuous and nearly linear response characteristics, enabling fine-grained processing of these samples and significantly improving computational stability in polar cryogenic environments. Its theoretical mathematical expression is as follows: .

[0076] in, The cumulative distribution function of the standard normal distribution. This is the error function, primarily used to describe the cumulative probability of a normal distribution. While the above formula is a rigorous mathematical definition of the GELU function, it contains complex... If the computer were to precisely calculate the integral of the error function in each model iteration, it would consume enormous computational resources, resulting in extremely slow model training when faced with massive amounts of polar remote sensing data.

[0077] Therefore, in order to accelerate the computation while ensuring inversion accuracy, this invention adopts a method based on the hyperbolic tangent function in the actual computation of the residual network. The approximate solution of is used to replace the original exact integral. Let the feature output after the mapping of the previous fully connected layer be . The nonlinear output after GELU activation The calculation method for nonlinear activation of the input data by the residual block in this embodiment is as follows: .

[0078] in, This represents the nonlinear output after GELU activation. This is the cumulative distribution function of the standard normal distribution.

[0079] The method in this embodiment utilizes a cubic polynomial ( )and The activation function approximates the response curve of the Gaussian error integral in the formula, significantly improving the forward propagation and gradient differentiation speed of the network with almost no loss of accuracy. Since the activation function itself is derived based on the Gaussian distribution assumption, its smoothness perfectly matches the objective distribution of the input features of this technique, thus effectively ensuring the model's convergence speed, training stability, and overall inversion accuracy of Antarctica.

[0080] Identity Skip Connection: Ultimately, this connects the nonlinear output of the residual block. Input of this residual block Element-wise addition is performed to ensure effective backpropagation of gradients in deep networks: .

[0081] In this embodiment, the physical constraint residual neural network model does not directly output the temperature, but instead outputs four dynamic numbers, corresponding to the four empirical coefficients a, b, c, and d in the split-window algorithm. That is, after... After deep feature extraction of each residual block, the output feature is... Passing through the final linear output layer, the high-dimensional features are compressed into a 4-dimensional vector. These four values ​​are directly and physically equivalent to the dynamic empirical coefficient vector C= in the split-window algorithm. .

[0082] In some embodiments, the coefficient vector C is calculated as follows: .

[0083] in, The weight matrix is ​​the linear output layer. Thus, the network achieves end-to-end dynamic inference from satellite-observed physical quantities directly to the coefficients of the split-window physical formula. These are network parameters.

[0084] In some embodiments, the physical relationship of the split-window algorithm is used to guide the gradient descent of the neural network. The coefficient vector generated by the residual neural network is then... Substituting the values ​​into the split-window physics formula from the previous steps, the predicted ice surface temperature is calculated. .

[0085] In this implementation, the expression for predicting ice surface temperature using the physical constraint network is as follows: .

[0086] Where VZA is the satellite zenith angle and SW is the split window algorithm.

[0087] The specific form of the SW function is: a, b, c, d are the coefficients in the coefficient vector C.

[0088] To optimize the neural network parameters, the module uses mean squared error (MSE) quantization estimation. The backpropagation loss Loss between the truth values ​​IST of MYD11 and MYD29 is updated.

[0089] In some embodiments, the loss function is: .

[0090] Where n represents the number of samples, This represents the predicted ice surface temperature for the i-th sample. This represents the true value of the ice surface temperature for the i-th sample.

[0091] This means using this method to retrieve the ice surface temperature based on the FY-3D / MERSI-II thermal infrared sensor.

[0092] This step substitutes the coefficients dynamically output by the residual network into the split-window physical equation to calculate the predicted ice surface temperature. Then, using the mean squared error (MSE) between this predicted value and the baseline temperature as the loss function for backpropagation, a training method is constructed that uses an explicit split-window physical equation to guide and constrain the neural network's gradient descent. This mechanism effectively avoids overfitting of purely data-driven models on sparse polar sample sets, ensuring the physical authenticity and consistency of the Antarctic ice surface temperature inversion results in the extreme low-temperature range.

[0093] Finally, this loss function value (denoted as...) Guided by this, the gradient of the loss with respect to each network weight is obtained through backpropagation. The parameters in the residual neural network are iteratively updated according to the gradient descent rule. The core weight parameter update formula is as follows: .

[0094] In the formula, These are the learnable weight parameters in a residual neural network. The set learning rate. This refers to the gradient direction of the loss function with respect to the weights. By using split-window constraints, loss calculation, and gradient descent update settings, the network is iterated until convergence, thereby achieving high-precision dynamic fitting of the Antarctic IST.

[0095] In some embodiments, in order to achieve an optimal balance between inversion accuracy and computational resource consumption in the processing of massive remote sensing data, this invention adjusts the parameters of the data-driven residual neural network (number of hidden layer nodes). Rigorous controlled variable experiments were conducted with respect to the number of network layers (N).

[0096] Experimental results and parameter establishment are as follows Figure 3 As shown, the unit pixel inversion time exhibits a significant monotonically increasing trend with the increase of network node number and layer number. This indicates that increasing model depth and breadth leads to a sharp increase in computational cost, which is detrimental to the rapid real-time inversion of large-scale polar images. The root mean square error of the model does not decrease with the increase of network complexity. When the network structure parameters are set to... When N=32 and N=6, the root mean square error of the model reaches a global minimum of 1.07K (shown by the horizontal dashed line in the figure). A longitudinal comparison shows that although larger structures such as (64, 8) can also achieve approximately extremely low error levels, their inversion time cost is nearly twice that of (32, 6). Therefore, (32, 6) is established as the optimal model structure parameter for the Antarctic ice surface temperature inversion model.

[0097] Through optimization experiments with controlled variables, the optimal network depth that balances inversion accuracy and computational cost was clearly defined. For the inversion of Antarctic ice surface temperature, the optimal network structure configuration of 6 residual blocks with 32 hidden nodes per layer was adopted, based on network topology parameters specific to the underlying surface.

[0098] Comparative experiments have demonstrated the following advantages of the method in this embodiment: 1. Higher accuracy and lower error: As shown in Table 1, comparing model accuracy, the root mean square error of the method (SW-RN) of this invention is reduced to 1.07K, and the mean absolute error is as low as 0.75K. The RMSE of the pure residual network model (RN) is as high as 3.00K, while the RMSE of the traditional split window algorithm (SW) is 1.39K. This invention learns the nonlinear mapping relationship between brightness temperature, brightness temperature difference, and observed geometric parameters and split window coefficients through the residual network. This overcomes the deficiency of the traditional split window algorithm's empirical coefficients in adapting to the polar environment and also makes up for the insufficient fitting accuracy of the pure RN model. Tests show that this invention significantly reduces the RMSE of the ice sheet region by about 64% compared to the pure data-driven network.

[0099] Table 1. Comparison of accuracy of different methods Root mean square error / K 3.00 1.39 1.07 Mean absolute error / K 1.79 1.02 1.02 2. Strong cross-year spatiotemporal generalization capability, meeting the needs of long-term time-series business monitoring: based on cross-year migration performance evaluation Figure 4 The results show that when a model trained solely on 2021 data is directly applied to the period from 2022 to 2025, its coefficient of determination remains remarkably stable above 0.993 for five consecutive years. Although interannual variations lead to a very slow increase in both the root mean square error and the mean absolute error, the root mean square error still stands at 1.44K by 2025. The model learns a mapping of physical coefficients that is not limited to specific years, rather than simply performing numerical fitting.

[0100] 3. The underlying architecture aligns with the feature distribution, resulting in extremely fast model convergence and stable training. Technical inference: The GELU activation function, based on the Gaussian distribution assumption, is introduced into the network's internal computation. Since the feature values ​​of the split-window algorithm are highly concentrated near zero, GELU's smooth and mild nonlinear response near zero perfectly matches this data distribution. This fundamentally eliminates the risk of gradient explosion or vanishing gradients, significantly improving the overall model's training stability and computational efficiency per unit pixel.

[0101] 4. Fill the gap in domestically produced Antarctic ice sheet remote sensing IST products and achieve independent control over climate data.

[0102] Currently, large-scale remote sensing monitoring of Antarctic ice surface temperature relies heavily on foreign satellite data. While my country's independently developed Fengyun-3D / MERSI-II thermal infrared sensor possesses high spatial resolution observation capabilities, it has long lacked high-precision, operational Antarctic ice temperature data in polar regions.

[0103] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for inverting Antarctic ice surface temperature based on a physically constrained neural network, characterized in that, include: The steps for constructing a physically constrained residual neural network model and retrieving Antarctic ice surface temperature include: the physically constrained residual neural network model comprising an input layer, a data-driven residual network, and a physically constrained network; the data-driven residual network comprising residual blocks and a linear output layer; and the steps for constructing the physically constrained residual neural network model include: Acquire training sample data, including data from channels 24 and 25 of the thermal infrared emission band in FY-3D / MERSI-II data, to construct a spatial feature matrix; acquire ice shelf surface temperature data from the geolocation products MYD03 and MYD29 of MODIS data and ice sheet surface temperature data from the MYD11 product, to construct ground truth labels. The model training steps include: The training sample data is input into the input layer, which sequentially performs linear transformation, batch normalization, and nonlinear activation to expand the dimension of the input data to the hidden layer dimension. and output feature vectors ; Feature vector The input data is fed into the residual block for processing. The residual block sequentially performs feature distribution reshaping, feature space reconstruction, and nonlinear activation on the input data. The processing result is then added element-wise to the input of the residual block. The sum is used as the output of the residual block and output to the linear output layer, compressing the high-dimensional features into a 4-dimensional vector, which is the coefficient vector. ; The coefficient vector The input is fed into the physical constraint network, which outputs the predicted ice surface temperature. Based on the predicted ice surface temperature The true value of ice surface temperature in the truth label Calculate the loss function and iterate the parameters in the physical constraint residual neural network model until convergence; The Antarctic ice surface temperature inversion step includes: acquiring data from channels 24 and 25 of the thermal infrared emission band in MERSI-II data in real time, preprocessing the data, and inputting it into the physical constraint residual neural network model; the physical constraint residual neural network model predicts the ice surface temperature as the inverted ice surface temperature and outputs it. In the step of obtaining training sample data, the methods for constructing the spatial feature matrix include: Extract the raw observation count values ​​DN from channels 24 and 25 of MERSI-II, and read the slope and intercept from the attributes to convert DN into actual radiance E; Based on the effective center wavenumber wn of the sensor, the preliminary brightness temperature Te is calculated using the inverse function of Planck's radiation law. The initial brightness temperature is linearly corrected using sensor calibration coefficients to obtain the channel brightness temperature matrix for both channels. and ; In the model training step, the brightness temperature matrix of channel 24 is... Brightness temperature difference between channels 24 and 25 Geometric correction items And truth labels are input to the input layer; The expression for the prediction of ice surface temperature by the physical constraint network is as follows: ; Where VZA is the satellite zenith angle and SW is the split window algorithm.

2. The method according to claim 1, characterized in that, The data-driven residual network comprises several cascaded residual blocks. During the model training step, the feature vectors... The residuals are processed sequentially through each residual block, and the output features of the last residual block are then processed. The output is sent to the linear output layer for processing.

3. The method according to claim 1, characterized in that, Geometric correction terms The calculation method is as follows: ； VZA stands for Satellite Zenith Angle.

4. The method according to claim 3, characterized in that, Before inputting data into the input layer, the model training step also includes... , as well as Normalize and concatenate into a three-dimensional feature vector. The steps include: ； in, , These are the mean vector and standard deviation vector of the historical sample data, respectively. To prevent extremely small constants with a denominator of zero.

5. The method according to claim 4, characterized in that, Feature vector The calculation method is as follows: ； in, Let BN be the weight matrix, and let BN denote the batch normalization function. These are network parameters.

6. The method according to claim 5, characterized in that, The method for feature distribution reshaping of the input data by the residual block is as follows: ; For the first The input feature vector of each residual block, and These are the mean and variance of the samples in the current feature distribution renormalization layer, respectively. and These are the scaling and translation parameters that the network can learn. This indicates that the current position is the th in the residual neural network. A hidden layer, Indicates the first The input feature vector of each hidden layer; The method for reconstructing the feature space of the input data using the residual block is as follows: ； Indicates the first The weight matrix of each hidden layer Indicates the first The bias term vector of each hidden layer Indicates the first The output feature vectors of each hidden layer; The method for nonlinear activation of the input data by the residual block is as follows: ； in, This represents the nonlinear output after GELU activation. This is the cumulative distribution function of the standard normal distribution.

7. The method according to claim 2, characterized in that, The coefficient vector C is calculated as follows: ； in, The weight matrix of the linear output layer. These are network parameters.

8. The method according to claim 1, characterized in that, The loss function is: ; Where n represents the number of samples, This represents the predicted ice surface temperature for the i-th sample. This represents the true value of the ice surface temperature for the i-th sample.

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