Medium and long term surface temperature forecasting method based on multi-scale TransFuse pyramid network

Abstract

The invention discloses a surface temperature medium and long term forecasting method based on a multi-scale TransFuse pyramid network. The surface temperature medium and long term forecasting method comprises the steps of S1, acquiring original LST time sequence data and performing preprocessing; s2, constructing a three-dimensional time delay embedded feature tensor for the data preprocessed in the S1 by adopting a stepped cross-node tensor feature reconstruction method; s3, on the basis of the three-dimensional time delay embedded feature tensor constructed in the S2, meteorological features of different time scales are extracted in parallel through a dynamic multi-resolution convolution kernel group; s4, performing five-stage cascade operation on the meteorological features of different time scales extracted in the S3 to realize deep fusion of cross-scale features, and performing high-level semantic information integration through a global feature pyramid; and S5, finally outputting a multi-step prediction result through a regression prediction framework based on the fusion features obtained in the S4. According to the invention, an extensible technical normal form is effectively provided for high-precision meteorological prediction in a limited computing power scene, and important application potential is shown in actual business deployment.

Description

Technical Field

[0001] This application relates to the field of short-term surface temperature forecasting technology, specifically to a medium- and long-term surface temperature forecasting method based on a multi-scale TransFuse pyramid network (MS-TFPPN). Background Technology

[0002] Against the backdrop of escalating global climate change leading to more frequent extreme weather events, traditional statistical forecasting methods have gradually revealed systematic biases, making accurate and timely weather forecasts increasingly important. Currently widely used numerical weather prediction (NWP) models are based on mathematical equations of atmospheric physical processes for modeling and prediction; however, they still face many challenges in practical applications, including an incomplete understanding of complex physical mechanisms, difficulty in efficiently extracting effective information from massive amounts of observational data, and high computational resource requirements. In contrast, deep learning technology, with its powerful nonlinear modeling capabilities, automatic extraction of spatiotemporal features, and good generalization performance, provides a new solution for predicting meteorological elements such as temperature. Over the past two decades, land surface temperature (LST) time series prediction models have undergone significant technological evolution. Early methods mainly relied on traditional machine learning models such as artificial neural networks (ANNs) and support vector machines (SVMs). With the development of deep learning, hybrid architectures capable of characterizing high-order nonlinear relationships have gradually become a research hotspot. Hybrid models that integrate spatial and temporal modeling capabilities have shown outstanding performance. For example, architectures combining convolutional neural networks (CNNs) and long short-term memory networks (LSTMs) can utilize CNNs to extract spatial features from meteorological fields and leverage LSTMs to capture temporal dynamics. Furthermore, bidirectional LSTMs (Bi-LSTMs) have been applied to regional temperature forecasting to enhance sequence modeling capabilities; other methods have significantly expanded the forecast window by fusing multi-source climate data. In recent years, Transformer-type models based on self-attention mechanisms have received widespread attention due to their ability to capture long-range dependencies, while some specialized large-scale meteorological models have achieved significant improvements in forecast accuracy and efficiency on global reanalysis data. Despite significant progress in meteorological forecasting research, machine learning in this field still faces the critical challenge of coordinating the optimization of model architecture and data performance. The simplification of physical processes and the accumulation of initial errors in NWP models lead to a gradual increase in forecast bias, and their operation relies on supercomputing resources, making it difficult to achieve high-frequency updates and high-resolution output.

[0003] Application content

[0004] The purpose of this application is to provide a method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network. The specific technical solution is as follows:

[0005] A method for medium- and long-term land surface temperature (LST) forecasting based on a multi-scale TransFuse pyramid network includes: S1, acquiring raw LST time series data and preprocessing it; S2, constructing a three-dimensional time-delay embedding feature tensor from the preprocessed data in S1 using a stepwise cross-node tensor feature reconstruction method; S3, extracting meteorological features at different time scales in parallel using dynamic multi-resolution convolutional kernel groups based on the three-dimensional time-delay embedding feature tensor constructed in S2; S4, achieving deep fusion of cross-scale features by performing a five-stage cascade operation on the meteorological features extracted in S3, and integrating high-level semantic information through a global feature pyramid; S5, outputting multi-step prediction results based on the fused features obtained in S4 using a regression prediction framework.

[0006] Preprocessing in S1 includes:

[0007] S1.1 Obtain historical LST data for the target area from a public database;

[0008] S1.2. Periodic components are removed using the constrained nonlinear least squares method. Let the length of the test set be... Define a compound cycle-trend model, expressed as:

[0009] ,

[0010] in, The unit is °C, representing the annual periodic amplitude, reflecting the intensity of temperature fluctuations throughout the year; its non-negative constraint ensures physical rationality; phase angle The unit is radians, which determines the timing of temperature peaks or troughs; linear trend coefficient. The unit is °C / day, representing the interannual rate of temperature change; a positive value indicates a warming trend. The intercept term... If the unit is °C, then it represents a temperature reference value; training set index Including total number of days Center front sky, The prediction step size is in days;

[0011] S1.3, Determine The optimal estimate of the parameters is used to construct an optimization problem, which is expressed as:

[0012] ,

[0013] Among them, the parameters are determined. Then, using After removing the compound cyclical-trend from the training set, a new dataset is obtained. , The length of the time series training set after deperiodicization is given, and then it is standardized.

[0014] When constructing the 3D time-delay embedding feature tensor in S2, the following are included:

[0015] S2.1 Construct the time delay embedding matrix, expressed as:

[0016] ,

[0017] in, The embedding dimension represents the number of historical observations contained within each time window, which determines the depth to which the model captures temporal dependencies. The prediction step size is the number of future time points that need to be predicted. This parameter represents the effective number of windows, ensuring that each window has a complete input / output pair.

[0018] S2.2, No. Feature tensors of each time window Through time delay operator And the expansion operation generates, expressed as:

[0019] ,

[0020] Among them, the time delay operator is , indicating from the original sequence Extract from the first To the Continuous observations;

[0021] S2.3, Define the multi-step prediction target matrix , expressed as:

[0022] .

[0023] When extracting meteorological features at different time scales in S3, the following are included:

[0024] S3.1 Define the fundamental frequency convolution kernel group, expressed as:

[0025] ,

[0026] The corresponding filter number is expressed as:

[0027] ,

[0028] in, The number of branches at multiple scales; For the first Branch convolution kernel width, The sampling interval; For the first Number of branch filters, Input feature dimension;

[0029] S3.2, No. The feature extraction expression for the branch is as follows:

[0030]

[0031] in, For a three-dimensional convolution kernel tensor, For bias terms;

[0032] S3.3, Convolution operation is defined as:

[0033] ,

[0034] Feature normalization uses layer normalization, expressed as:

[0035] ,

[0036] in, The mean of the feature dimensions; Standard deviation; For learnable parameters; ReLU is defined as... .

[0037] S4 includes:

[0038] S4.1, For adjacent branches and Concatenating along the feature dimension, it can be expressed as:

[0039] ,

[0040] Used to preserve multi-scale information at the original resolution and enhance the model's ability to represent multi-scale dynamic processes of meteorological systems;

[0041] S4.2, Dimensional compression and feature reorganization are achieved through 1×1 convolution, expressed as:

[0042]

[0043] in, , As a bottleneck dimension;

[0044] S4.3. Introduce a spatiotemporally constrained multi-head attention mechanism to model the correlation of local meteorological models, expressed as:

[0045]

[0046]

[0047] in, To output the projection matrix; set the key / query dimension to satisfy... ,here

[0048] ;

[0049] Number of attention heads

[0050]

[0051] Mask matrix

[0052] ;

[0053] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0054] ,

[0055] As the core component following the attention mechanism, the feedforward neural network's computational flow can be expressed as follows:

[0056] ,

[0057] The feedforward neural network operates in two stages: the expansion stage, which involves... From the dimension Expand to This enhances nonlinear expressive power; and during the compression stage, through... Compress the dimensions back To achieve characteristic distillation;

[0058] During gradient calculation, the parameter update of the feedforward neural network is expressed as:

[0059]

[0060] in, , It is the standard normal cumulative distribution function;

[0061] loss function The mathematical definition is expressed as:

[0062]

[0063] in, For the true value, This is a predicted value;

[0064] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0065] ;

[0066] S4.4. Three-point convolution is used to further extract local temporal features and enhance spatial continuity, expressed as:

[0067]

[0068] in, This operation complements the attention mechanism, with the attention layer capturing the correlation between important time nodes and the convolutional layer modeling the local smooth evolution pattern;

[0069] S4.5. By using skip connections to preserve the original feature information and alleviate gradient vanishing, it can be expressed as:

[0070] ,

[0071] Let the output characteristics of the adjacency fusion module be: ,in Indicates the first The output feature matrix of each module For the hidden layer dimension, This represents the number of fundamental frequency convolution kernels;

[0072] The global concatenation operation is expressed as:

[0073] ,

[0074] Reduce computational complexity by using a dynamic dimension compression strategy to define key / query dimensions. The number of attention heads is expressed as:

[0075]

[0076] The multi-head attention representation of Transformer is as follows:

[0077]

[0078] in, To output the projection matrix;

[0079] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0080] ;

[0081] The computation process of a feedforward neural network is as follows:

[0082] ,

[0083] The parameter update formula for a feedforward neural network is:

[0084] ,

[0085] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0086] ,

[0087] pass Convolution maps features back to the original space:

[0088]

[0089] in, Global residual joins are implemented using the dimensional projection function. Adapting to shallow features , expressed as:

[0090]

[0091] The final output features are ;

[0092] During backpropagation, the gradient can be decomposed into:

[0093] ,

[0094] When the gradient of the main path When it approaches zero, the identity matrix Ensure that shallow parameters can still be updated effectively.

[0095] S5 includes:

[0096] The features obtained in S4 Flattened The predicted value is mapped to the value through a fully connected network:

[0097]

[0098]

[0099]

[0100] The final output is the multi-step prediction result.

[0101] The beneficial effects of this application are as follows: the MS-TFPPN model constructed using the method proposed in this paper: the dynamic multi-resolution convolutional kernel group can capture short-term mutations (hourly fluctuations) and long-term trends (cross-day evolution) in parallel, effectively solving the problem that traditional methods cannot simultaneously model features at different scales. The five-stage cascaded fusion mechanism achieves optimized coupling between local details and global patterns. Through adaptive dimensionality compression technology, the model significantly reduces computational complexity while maintaining high accuracy. Compared with large models requiring a cluster of kilo-card GPUs, this invention can achieve real-time prediction in a single-card GPU environment (12th Gen Intel Core i9 configuration), greatly improving practicality. The stepwise cross-node tensor feature reconstruction method achieves full window coverage of prediction information through three-dimensional tensor representation, effectively reducing the information fragmentation problem of traditional two-dimensional matrix methods and significantly reducing the error accumulation effect of multi-step prediction.

[0102] Instruction manual illustrations

[0103] Figure 1 This is a flowchart illustrating the application process.

[0104] Figure 2 This is a schematic diagram of the MS-TFPPN model architecture in this application;

[0105] Figure 3 This represents the average RMSE value of the model in this application at each prediction step size;

[0106] Figure 4 Box plots showing the error distribution of each model in this application across 70 experiments at different geographical locations;

[0107] Figure 5 This represents the rank of each model in this application at each coordinate point and prediction step size;

[0108] Figure 6 The Friedman-Nemenyi test results for different models in this application;

[0109] Figure 7 This is a visual example of the predictions made by the MS-TFPPN model in this application. Specific Implementation

[0110] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this application. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0111] like Figure 1 and 2As shown, a medium- to long-term land surface temperature forecasting method based on a multi-scale TransFuse pyramid network includes:

[0112] S1. Obtain the raw LST time series data and perform preprocessing. Specifically:

[0113] S1.1 Obtain historical LST data for the target area from the NOAA-PSL database, spanning from January 1, 2019 to December 31, 2023, with a spatial resolution of 0.5° × 0.5°. Assume the original time series is... ,in Day. Randomly selected points in the region are shown in Table 1.

[0114] Table 1

[0115]

[0116] S1.2. Periodic components are removed using the constrained nonlinear least squares method. Let the length of the test set be... Define a compound cycle-trend model, expressed as:

[0117] ,

[0118] in, The unit is °C, representing the annual periodic amplitude, reflecting the intensity of temperature fluctuations throughout the year; its non-negative constraint ensures physical rationality; phase angle The unit is radians, which determines the timing of temperature peaks or troughs; linear trend coefficient. The unit is °C / day, representing the interannual rate of temperature change; a positive value indicates a warming trend. The intercept term... If the unit is °C, then it represents a temperature reference value; training set index Including total number of days Center front sky, The prediction step size is in days;

[0119] S1.3, Determine The optimal estimate of the parameters is used to construct an optimization problem, which is expressed as:

[0120] ,

[0121] Among them, the parameters are determined. Then, using After removing the compound cyclical-trend from the training set, a new dataset is obtained. , The length of the time series training set after deperiodicization is given, and then it is standardized.

[0122] S2. The preprocessed data from S1 is used to construct a 3D time-delay embedding feature tensor using a stepwise cross-node tensor feature reconstruction method. Specifically, constructing the 3D time-delay embedding feature tensor includes:

[0123] S2.1 Construct the time delay embedding matrix, expressed as:

[0124] ,

[0125] in, The embedding dimension represents the number of historical observations contained within each time window, which determines the depth to which the model captures temporal dependencies. The prediction step size is the number of future time points that need to be predicted. This parameter represents the effective number of windows, ensuring that each window has a complete input / output pair.

[0126] S2.2, No. Feature tensors of each time window Through time delay operator And the expansion operation generates, expressed as:

[0127] ,

[0128] Among them, the time delay operator is , indicating from the original sequence Extract from the first To the Continuous observations;

[0129] S2.3, Define the multi-step prediction target matrix , expressed as:

[0130] .

[0131] S3. Based on the three-dimensional time-delay embedding feature tensor constructed in S2, meteorological features at different time scales are extracted in parallel using a dynamic multi-resolution convolutional kernel group. Specifically, the extraction of meteorological features at different time scales includes:

[0132] S3.1 Define the fundamental frequency convolution kernel group, expressed as:

[0133] ,

[0134] The corresponding filter number is expressed as:

[0135] ,

[0136] in, The number of branches at multiple scales; For the first Branch convolution kernel width, The sampling interval; For the first Number of branch filters, Input feature dimension;

[0137] S3.2, No. The feature extraction expression for the branch is as follows:

[0138]

[0139] in, For a three-dimensional convolution kernel tensor, For bias terms;

[0140] S3.3, Convolution operation is defined as:

[0141] ,

[0142] Feature normalization uses layer normalization, expressed as:

[0143] ,

[0144] in, The mean of the feature dimensions; Standard deviation; For learnable parameters; ReLU is defined as... .

[0145] S4. The meteorological features extracted from S3 at different time scales are fused through a five-stage cascade operation to achieve deep fusion of cross-scale features, and high-level semantic information is integrated through a global feature pyramid. Specifically, this includes:

[0146] S4.1, For adjacent branches and Concatenating along the feature dimension, it can be expressed as:

[0147] ,

[0148] Used to preserve multi-scale information at the original resolution and enhance the model's ability to represent multi-scale dynamic processes of meteorological systems;

[0149] S4.2, Dimensional compression and feature reorganization are achieved through 1×1 convolution, expressed as:

[0150]

[0151] in, , As a bottleneck dimension;

[0152] S4.3. Introduce a spatiotemporally constrained multi-head attention mechanism to model the correlation of local meteorological models, expressed as:

[0153]

[0154]

[0155] in, To output the projection matrix; set the key / query dimension to satisfy... ,here

[0156] ;

[0157] Number of attention heads

[0158]

[0159] Mask matrix

[0160] ;

[0161] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0162] ,

[0163] As the core component following the attention mechanism, the feedforward neural network's computational flow can be expressed as follows:

[0164] ,

[0165] The feedforward neural network operates in two stages: the expansion stage, which involves... From the dimension Expand to This enhances nonlinear expressive power; and during the compression stage, through... Compress the dimensions back To achieve characteristic distillation;

[0166] During gradient calculation, the parameter update of the feedforward neural network is expressed as:

[0167]

[0168] in, , It is the standard normal cumulative distribution function;

[0169] loss function The mathematical definition is expressed as:

[0170]

[0171] in, For the true value, This is a predicted value;

[0172] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0173] ;

[0174] S4.4. Three-point convolution is used to further extract local temporal features and enhance spatial continuity, expressed as:

[0175]

[0176] in, This operation complements the attention mechanism, with the attention layer capturing the correlation between important time nodes and the convolutional layer modeling the local smooth evolution pattern;

[0177] S4.5. By using skip connections to preserve the original feature information and alleviate gradient vanishing, it can be expressed as:

[0178] ,

[0179] Let the output characteristics of the adjacency fusion module be: ,in Indicates the first The output feature matrix of each module For the hidden layer dimension, This represents the number of fundamental frequency convolution kernels;

[0180] The global concatenation operation is expressed as:

[0181] ,

[0182] Reduce computational complexity by using a dynamic dimension compression strategy to define key / query dimensions. The number of attention heads is expressed as:

[0183]

[0184] The multi-head attention representation of Transformer is as follows:

[0185]

[0186] in, To output the projection matrix;

[0187] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0188] ;

[0189] The computation process of a feedforward neural network is as follows:

[0190] ,

[0191] The parameter update formula for a feedforward neural network is:

[0192] ,

[0193] The gradient vanishing effect is mitigated by using residual layers, which can be expressed as:

[0194] ,

[0195] pass Convolution maps features back to the original space:

[0196]

[0197] in, Global residual joins are implemented using the dimensional projection function. Adapting to shallow features , expressed as:

[0198]

[0199] The final output features are ;

[0200] During backpropagation, the gradient can be decomposed into:

[0201] ,

[0202] When the gradient of the main path When it approaches zero, the identity matrix Ensure that shallow parameters can still be updated effectively.

[0203] S5. Based on the fused features obtained in S4, the regression prediction framework is used to finally output multi-step prediction results. Specifically, this includes:

[0204] The features obtained in S4 Flattened The predicted value is mapped to the value through a fully connected network:

[0205]

[0206]

[0207]

[0208] The final output is the multi-step prediction result.

[0209] like Figure 3As shown in the average RMSE index, the MS-TFPPN model constructed by the method proposed in this paper exhibits the best average prediction accuracy under different geospatial locations and various prediction step sizes. Compared with BiLSTM, BP, LSTM, TCN, SVR and TFT, its average RMSE is reduced by 21.77%, 38.68%, 20.91%, 34.34%, 25.15% and 25.55%, respectively.

[0210] like Figure 4 As shown, the box plots of the RMSE index error distribution for each model in 70 experiments are presented. It can be observed that the MS-TFPPN model's box plot is located closest to the bottom, indicating that its overall RMSE value is smaller and its prediction error is lower. Simultaneously, the MS-TFPPN box length is also the shortest among all models, suggesting that its RMSE value has a smaller fluctuation range and its prediction results are more concentrated and stable. In contrast, other models such as BiLSTM, BP, LSTM, TCN, SVR, and TFT have higher box plot positions and longer boxes, indicating that their prediction errors are larger and have a wider fluctuation range, and their stability is not as good as the MS-TFPPN model. The next step, as... Figure 5 As shown, the calculations for the 7 models are performed. The RMSE rank (ranking) of the datasets is shown. Using the formula from the Friedman-Nemenyi test, we know that:

[0211]

[0212]

[0213] in, It follows a set of degrees of freedom of (7-1, (7-1)). (70-1)) that is (6,414) Distribution, this is the degrees of freedom when comparing 7 methods on 70 datasets. At the significance level Below, with degrees of freedom (6, 414) The critical value for the distribution is 2.143. (Calculated...) The value of 45.6445 exceeds the critical value, therefore the null hypothesis is rejected. To further compare the performance of different SVR models in pairs, the Nemenyi posterior test is used, and the critical difference (CD) is calculated according to the above formula. To determine a significant difference between them, CD must exceed a specified threshold:

[0214]

[0215] Based on the CD value, we can calculate the ARD between every two models. Combined with... Figure 6and 7 Based on the formulas for the Friedman and Nemenyi tests, a clear conclusion can be drawn: the MS-TFPPN model has a significant advantage in land surface temperature prediction tasks, and its performance is statistically significantly better than other comparative models. Neither BiLSTM, BP, LSTM, TCN, SVR, nor TFT can compete with MS-TFPPN in overall performance.

[0216] Figure 7 This paper presents the 64-day absolute error distribution of the MS-TFPPN model over a large area. Overall, the absolute error values ​​are low in most areas, indicating that the model's predictions are close to the actual observations and possess high prediction accuracy. In terms of error distribution, some local areas have relatively large errors, possibly due to the influence of complex terrain, land use changes, and other factors, making it more difficult for the model to simulate temperature changes in these areas. Furthermore, the error level fluctuates over different time periods, possibly due to weather changes and data quality. However, overall, the model's average absolute error over a large area is within an acceptable range, meeting the accuracy requirements for temperature prediction in practical applications. It is also noteworthy that the spatiotemporal ST-RMSE in this experiment is only 2.6565, a decrease compared to the 3.1660 error under 64 steps in Section 3. This demonstrates that the MS-TFPPN model not only maintains high prediction accuracy in large-scale predictions but also exhibits stronger stability and adaptability. This result further validates the model's superior performance in handling complex spatiotemporal data, providing strong support for its promotion and use in practical applications.

[0217] In summary, this application provides a scalable technical paradigm for high-precision weather forecasting in scenarios with limited computing power, and demonstrates significant application potential in actual operational deployments.

Claims

1. A method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network, characterized in that, include: S1. Obtain the raw LST time series data and perform preprocessing; S2. Construct a three-dimensional time-delay embedding feature tensor from the preprocessed data in S1 using the stepwise cross-node tensor feature reconstruction method; S3. Based on the three-dimensional time-delay embedding feature tensor constructed in S2, meteorological features at different time scales are extracted in parallel through a dynamic multi-resolution convolution kernel group. S4. The meteorological features at different time scales extracted in S3 are fused together through a five-stage cascade operation to achieve deep fusion of cross-scale features, and high-level semantic information is integrated through a global feature pyramid. S5. Based on the fusion features obtained in S4, the multi-step prediction results are finally output through the regression prediction framework.

2. The method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network as described in claim 1, characterized in that, The preprocessing in S1 includes: S1.1 Obtain historical LST data for the target area from a public database; S1.

2. Periodic components are removed using the constrained nonlinear least squares method. Let the length of the test set be... Define a compound cycle-trend model, expressed as: ， in, The unit is °C, representing the annual periodic amplitude, reflecting the intensity of temperature fluctuations throughout the year; its non-negative constraint ensures physical rationality; phase angle The unit is radians, which determines the timing of temperature peaks or troughs; linear trend coefficient. The unit is °C / day, representing the interannual rate of temperature change; a positive value indicates a warming trend. The intercept term... If the unit is °C, then it represents a temperature reference value; training set index Including total number of days Center front sky, The prediction step size is in days; S1.3, Determine The optimal estimate of the parameters is used to construct an optimization problem, which is expressed as: ， Among them, the parameters are determined. Then, using After removing the compound cyclical-trend from the training set, a new dataset is obtained. , The length of the time series training set after deperiodicization is given, and then it is standardized.

3. The method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network as described in claim 2, characterized in that, The construction of the three-dimensional time-delay embedding feature tensor in S2 includes: S2.1 Construct the time delay embedding matrix, expressed as: ， in, The embedding dimension represents the number of historical observations contained within each time window, which determines the depth to which the model captures temporal dependencies. The prediction step size is the number of future time points that need to be predicted. This parameter represents the effective number of windows, ensuring that each window has a complete input / output pair. S2.2, No. Feature tensors of each time window Through time delay operator And the expansion operation generates, expressed as: ， Among them, the time delay operator is , indicating from the original sequence Extract from the first To the Continuous observations; S2.3, Define the multi-step prediction target matrix , expressed as: 。 4. The method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network as described in claim 3, characterized in that, The extraction of meteorological features at different time scales in S3 includes: S3.1 Define the fundamental frequency convolution kernel group, expressed as: ， The corresponding filter number is expressed as: ， in, The number of branches at multiple scales; For the first Branch convolution kernel width, The sampling interval; For the first Number of branch filters, Input feature dimension; S3.2, No. The feature extraction expression for the branch is as follows: ； in, For a three-dimensional convolution kernel tensor, For bias terms; S3.3, Convolution operation is defined as: ， Feature normalization uses layer normalization, expressed as: ， in, The mean of the feature dimensions; Standard deviation; For learnable parameters; ReLU is defined as... .

5. The method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network as described in claim 4, characterized in that... S4 includes: S4.1, For adjacent branches and Concatenating along the feature dimension, it can be expressed as: ， Used to preserve multi-scale information at the original resolution and enhance the model's ability to represent multi-scale dynamic processes of meteorological systems; S4.2, Dimensional compression and feature reorganization are achieved through 1×1 convolution, expressed as: ； in, , As a bottleneck dimension; S4.

3. Introduce a spatiotemporally constrained multi-head attention mechanism to model the correlation of local meteorological models, expressed as: ； ； in, To output the projection matrix; set the key / query dimension to satisfy... ,here ； Number of attention heads ； Mask matrix ； The gradient vanishing effect is mitigated by using residual layers, which can be expressed as: ； As the core component following the attention mechanism, the feedforward neural network's computational flow can be expressed as follows: ， The feedforward neural network operates in two stages: the expansion stage, which involves... From the dimension Expand to This enhances nonlinear expressive power; and during the compression stage, through... Compress the dimensions back To achieve characteristic distillation; During gradient calculation, the parameter update of the feedforward neural network is expressed as: ； in, , It is the standard normal cumulative distribution function; loss function The mathematical definition is expressed as: ； in, For the true value, This is a predicted value; The gradient vanishing effect is mitigated by using residual layers, which can be expressed as: ； S4.

4. Three-point convolution is used to further extract local temporal features and enhance spatial continuity, expressed as: ； in, This operation complements the attention mechanism, with the attention layer capturing the correlation between important time nodes and the convolutional layer modeling the local smooth evolution pattern; S4.

5. By using skip connections to preserve the original feature information and alleviate gradient vanishing, it can be expressed as: ， Let the output characteristics of the adjacency fusion module be: ,in Indicates the first The output feature matrix of each module For the hidden layer dimension, This represents the number of fundamental frequency convolution kernels; The global concatenation operation is expressed as: ， Reduce computational complexity by using a dynamic dimension compression strategy to define key / query dimensions. The number of attention heads is expressed as: ； The multi-head attention representation of Transformer is as follows: ； in, To output the projection matrix; The gradient vanishing effect is mitigated by using residual layers, which can be expressed as: ； The computation process of a feedforward neural network is as follows: ， The parameter update formula for a feedforward neural network is: ， The gradient vanishing effect is mitigated by using residual layers, which can be expressed as: ， pass Convolution maps features back to the original space: ； in, Global residual joins are implemented using the dimensional projection function. Adapting to shallow features , expressed as: ； The final output features are ; During backpropagation, the gradient can be decomposed into: ， When the gradient of the main path When it approaches zero, the identity matrix Ensure that shallow parameters can still be updated effectively.

6. The method for medium- and long-term land surface temperature forecasting based on a multi-scale TransFuse pyramid network as described in claim 5, characterized in that, S5 includes: The features obtained in S4 Flattened The predicted value is mapped to the value through a fully connected network: ； ； ； The final output is the multi-step prediction result.

Images