A method for predicting extreme rainfall of indian monsoon using tropical pacific subsurface sea temperature

Abstract

This invention discloses an EPSA attention mechanism and a dynamically weighted Huber loss function suitable for forecasting extreme precipitation in the Indian monsoon using tropical Pacific subsurface sea surface temperature. This addresses the significant bias in the intensity forecasting of extreme precipitation exhibited by basic deep learning models and traditional loss functions. The EPSA attention mechanism doubles the attention weight for extreme regions compared to ordinary regions, forcing the model to prioritize extreme precipitation-related features. The dynamically weighted Huber loss function identifies extreme samples through dynamic quantile thresholds and strengthens the penalty for extreme errors through a dual-weighting mechanism. This allows the model to retain the robustness of Huber loss to outliers while prioritizing the optimization of extreme precipitation forecast bias.

Description

Technical Field

[0001] This invention relates to the field of Indian monsoon extreme precipitation prediction technology, and in particular to a method suitable for predicting Indian monsoon extreme precipitation using tropical Pacific subsurface sea surface temperature. Background Technology

[0002] As a highly dynamic and influential component of the global climate system, the Indian monsoon profoundly shapes the climate pattern and ecological environment of southern Asia, especially the Indian subcontinent. Its interannual and interdecadal variability, leading to precipitation anomalies, directly impacts the water security, agricultural production, and even socio-economic stability of billions of people. For example, excessive rainfall in strong monsoon years often causes floods, while drought in weak monsoon years threatens food production.

[0003] Currently, research on the prediction of Indian monsoon variability is limited, and simulations of monsoon precipitation exhibit systematic biases. Machine learning, particularly deep learning, has become an emerging tool for meteorological forecasting, and using deep learning methods to predict Indian monsoon precipitation has significant practical implications. Many studies have shown that incorporating attention mechanisms into models can improve their efficiency and accuracy; however, attention mechanisms suitable for extreme precipitation events remain to be developed. Furthermore, traditional loss functions, such as mean squared error (MSE) and ordinary Huber loss, have significant limitations in forecasting extreme Indian monsoon precipitation: on the one hand, extreme precipitation samples constitute a small percentage of observed data (usually <10%), but have a crucial impact on agricultural production, water resource allocation, and disaster prevention and mitigation; ordinary loss functions are prone to insufficient accuracy due to "most ordinary samples dominating loss optimization." On the other hand, precipitation data exhibits a non-normal distribution, and the prediction error for extreme precipitation is often significantly greater than that for ordinary precipitation; fixed-weight loss functions struggle to balance the requirements of "robustness to fit ordinary samples" and "sensitivity to error in extreme samples." Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method suitable for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, in order to solve the problems of lack of attention mechanisms for extreme precipitation and large deviations in the intensity forecast of extreme precipitation by traditional loss functions.

[0005] Technical Solution: The present invention provides a method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, comprising the following steps:

[0006] (1) Collect tropical Pacific subsurface sea surface temperature data and Indian monsoon monthly precipitation observation data, perform monthly anomaly processing and zonal anomaly processing on the subsurface sea surface temperature data, and construct a training dataset;

[0007] (2) Construct an EPSA_CNN prediction model. The model introduces an EPSA attention mechanism between the convolutional layer and the fully connected layer to strengthen the feature weights of the extreme sea surface temperature anomaly region.

[0008] (3) The model is trained using the dynamically weighted Huber loss function. The loss function dynamically identifies extreme precipitation samples through quantile thresholds and uses a dual-weight mechanism to strengthen the penalty for extreme sample errors.

[0009] (4) Generate the Indian monsoon monthly precipitation forecast product based on the trained model and output the comparison results between the predicted value and the actual value.

[0010] Furthermore, in step (1), the subsurface sea surface temperature data of the tropical Pacific Ocean are selected from the temperature data of 16 layers 5m-300m below the sea surface within the range of 8°N-24°S and 120°E-90°W of the sea area, with a spatial resolution of 0.5°×0.5°.

[0011] Furthermore, in step (2), the EPSA_CNN model structure includes: 3 convolutional layers, each containing batch normalization, activation function and max pooling; 1 EPSA attention module, inserted between the convolutional layers and the fully connected layers; and 3 fully connected layers for outputting precipitation prediction values.

[0012] Furthermore, in step (2), the EPSA attention mechanism includes: a basic spatial attention module for generating spatial heterogeneous attention weights; a dynamic extreme threshold and mask generation module for dynamically dividing extreme regions and normal regions based on the actual distribution of the input temperature field; and an attention fusion module for combining the basic attention weights with the extreme mask so that the attention weight of the extreme region is twice that of the normal region.

[0013] Furthermore, the dynamic extreme threshold and mask generation module calculates the threshold using a quantile function, specifically:

[0014]

[0015] in The quantile calculation function satisfies , It is a quantile level, a scale specifically designed for locating extreme data. In this invention, it is set as follows: To include all rare but impactful extreme events; when When the extreme precipitation occurs, the sample is classified as an extreme precipitation sample; otherwise, it is classified as a normal precipitation sample.

[0016] Furthermore, in step (3), the expression for the dynamically weighted Huber loss function is:

[0017]

[0018] in , The first Observed values ​​and predicted values ​​for each sample It is the total number of samples. This means averaging the loss over all samples to ensure the scale interpretability of the loss values.

[0019] It depends on the observed values The weights, and the weight function expression is:

[0020]

[0021] when When the extreme precipitation threshold is exceeded, the weight is set to... ;when When it does not belong to extreme precipitation, the weight is taken as . =20.

[0022] The original Huber loss function is expressed as follows:

[0023]

[0024] in, It's a hyperparameter, set to 0.5, when | |≤ When |Huber loss is the MSE function; when | |> At that point, the loss becomes a linear function.

[0025] Furthermore, in step (3), the model training adopts the gradient descent method, the training set is divided by year, and a random batch training strategy is adopted.

[0026] Furthermore, in step (4), the forecast product includes a forecast sequence of Indian monsoon monthly precipitation for the next 1-18 months, and a comparison chart of the forecast values ​​and the actual values ​​is drawn.

[0027] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: It utilizes the EPSA attention mechanism and dynamically weighted Huber loss. On the one hand, considering the correlation between the intensity of subsurface sea surface temperature and the intensity of Indian monsoon precipitation, the EPSA attention mechanism combines "basic spatial attention" with "extreme enhancement masking" to strengthen the feature weights of extreme temperature anomaly regions. Simultaneously, normalization ensures a reasonable attention distribution. The addition of the EPSA attention mechanism to the network structure improves data utilization efficiency. On the other hand, the dynamically weighted Huber loss, through "quantile dynamic threshold identification of extreme samples" and "dual-weight mechanism to strengthen extreme error penalty," allows the model to retain the robustness of Huber loss to outliers while prioritizing... This method reduces forecast biases for extreme precipitation, meeting the core needs of meteorological fields for extreme event forecasting. Furthermore, it considers the significant interannual variation (cycle) of tropical Pacific subsurface sea surface temperature (SST) and its close correlation with the physical mechanisms of Indian monsoon precipitation intensity. Using tropical Pacific SST anomalies to predict Indian monsoon monthly precipitation requires fewer data and computational resources, offers faster computation speed, and longer prediction lead times. In addition to temporal anomalies, zonal anomalies are also calculated for tropical Pacific SST, highlighting meridional disturbances and better reflecting the eastward propagation characteristics of tropical Pacific SST anomalies. Attached Figure Description

[0028] Figure 1 This is a flowchart of the present invention;

[0029] Figure 2 This is a schematic diagram of the attention mechanism module of the present invention;

[0030] Figure 3 This is a diagram of the deep learning model architecture of the present invention;

[0031] Figure 4 This is a comparison chart of the predicted and actual values ​​of monthly precipitation in the Indian monsoon according to the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0033] like Figure 1 As shown, this invention provides a method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, comprising the following steps:

[0034] (1) Collect tropical Pacific subsurface sea surface temperature data and Indian monsoon monthly precipitation observation data, and preprocess the data to construct a training dataset; specifically as follows: select tropical Pacific subsurface sea surface temperature data of 16 layers below the sea surface of 8°N-24°S and 120°E-90°W, ranging from 5m to 300m, with a resolution of 0.5°×0.5°; the tropical Pacific subsurface sea surface temperature data processing is as follows: first calculate the monthly anomaly, and then calculate the zonal anomaly; Indian monsoon monthly precipitation is the target observation data.

[0035] (2) An EPSA attention mechanism was designed, which consists of four parts: feature compression module, basic space attention generation module, dynamic extreme threshold and mask generation module, attention fusion and feature weighting module.

[0036] Among them, the feature compression module:

[0037] 1×1 convolution achieves channel compression (the ratio is controlled by reduction, default is 8), reducing the parameter size while fusing cross-channel information;

[0038] LeakyReLU(0.1) preserves negative feature values ​​(such as "negative sea surface temperature anomalies" in meteorological data) and avoids "truncating" negative features by ReLU;

[0039] AdaptiveAvgPool2d(1) compresses the spatial dimension to 1×1, focuses on the global statistical features of the channel dimension, and provides a global basis for subsequent attention generation.

[0040] Basic Spatial Attention Generation Module:

[0041] Bilinear interpolation (F.interpolate) restores the compressed 1×1 features to their original spatial dimensions, ensuring that the attention map is aligned with the spatial dimensions of the input features;

[0042] 3×3 convolution (with padding) captures local spatial correlations (such as the “patchy” distribution of precipitation fields) and avoids the loss of spatial information caused by 1×1 convolution;

[0043] Sigmoid normalization ensures that the attention weights are in the 0-1 range, and can be directly used for feature weighting.

[0044] Dynamic extreme threshold and mask generation module:

[0045] Spatial dimension flattening (view(b,h×w)) ensures that quantile calculation covers precipitation samples across the entire space, avoiding interference from local extrema in threshold judgment;

[0046] torch.quantile calculates quantile thresholds by batch (default 90th quantile) to accommodate temperature differences in different batches of data;

[0047] 3×3 convolution smooth mask boundaries: avoids abrupt gradient changes at extreme region edges caused by "hard thresholding" and improves training stability.

[0048] Attention fusion and feature weighting module:

[0049] The weight doubling mechanism (base_attn + extreme_mask×base_attn) makes the attention weight of extreme regions twice that of ordinary regions, forcing the model to prioritize features related to extreme precipitation.

[0050] Spatial dimension summation normalization (sum(dim=(2,3))): avoids individual high-weight regions from overdoing features, ensures that the sum of attention weights at all spatial locations is 1, and guarantees the numerical stability of feature weighting.

[0051] A dynamically weighted Huber loss function was designed; specifically as follows: The core advantage of the Huber loss is that it uses a squared penalty for small errors to enhance fitting accuracy, and a linear penalty for large errors to avoid gradient explosion and improve robustness. Its mathematical expression is:

[0052]

[0053] in , These are the observed value and the predicted value, respectively.

[0054] This invention uses Huber loss as the basic loss function. The core advantage of Huber loss is that it applies a squared penalty to small errors to enhance fitting accuracy, and a linear penalty to large errors to avoid gradient explosion and improve robustness. Let the absolute prediction error... Then the basic Huber loss can be simplified as:

[0055]

[0056] in, The segmentation threshold of the Huber loss controls the switching boundary between the squared penalty and the linear penalty. This invention takes... The selection criteria are as follows: (1) The magnitude of monthly precipitation data of the Indian monsoon is usually between 0 and 1000 mm / month. The prediction error of ordinary samples is usually in the range of 0 to 20 mm, while the error of extreme samples can often reach more than 50 to 200 mm. (2) Referring to the general principles of Huber loss threshold selection, the standard deviation of precipitation data (approximately 50–150 mm / month) is scaled proportionally. Considering that this invention focuses on extreme precipitation forecasting and requires more aggressive identification of large error samples, the threshold is selected. (3) This threshold allows ordinary precipitation samples to enjoy the precise fitting of the square penalty and extreme precipitation samples to enjoy the robustness of the linear penalty, which is coordinated with the design of ordinary sample weight δ=0.5 and extreme sample weight α=3 in the dynamic weighting strategy of this invention.

[0057] The threshold for extreme precipitation needs to be dynamically determined based on the actual distribution of observed data, rather than using a fixed value. This invention calculates the extreme precipitation threshold using a quantile function. The formula is as follows:

[0058]

[0059] in The quantile calculation function satisfies In this invention This is to include all rare but impactful extreme events. When When the extreme precipitation occurs, the sample is classified as an extreme precipitation sample; otherwise, it is classified as a normal precipitation sample.

[0060] To prioritize the learning of extreme samples, this invention designs a dual-weight coefficient: assigning high weight to extreme samples. In this invention Assign weights to ordinary samples that are consistent with Huber's segmentation threshold. This achieves a robust fit to balance ordinary samples, and the weighting function is expressed as:

[0061]

[0062] Finally, the dynamically weighted Huber loss function is the mean of the product of the base Huber loss and the weight function, as shown in the following formula:

[0063]

[0064] in , The first Observed values ​​and predicted values ​​for each sample This means averaging the loss over all samples to ensure the scale interpretability of the loss values.

[0065] An EPSA attention mechanism is introduced between the convolutional and fully connected layers of a CNN model. Figure 2The improved EPSA_CNN model includes: 3 convolutional layers, an EPSA module, and 3 fully connected layers; each convolutional layer includes: a batch normalization layer, an activation function layer, and a max pooling layer. The model framework is as follows: Figure 3 As shown.

[0066] The convolutional layers of the EPSA_CNN model in this invention are as follows: The first convolutional layer has 16 input channels (corresponding to 16 layers of sea surface temperature data) and 32 output channels, using a 3×3 convolutional kernel with a stride of 1 and padding of 1, followed by a batch normalization layer, a ReLU activation function, and 2×2 max pooling; the second convolutional layer has 32 input channels and 64 output channels, with the same configuration as the first layer; the third convolutional layer has 64 input channels and 128 output channels, with the same configuration as the first layer. In the EPSA attention module, the channel compression ratio is set to 8, 1×1 convolution is used to achieve feature compression, LeakyReLU(0.1) is used to retain negative feature values, bilinear interpolation is used to restore spatial dimensions, 3×3 convolution (with padding of 1) is used to capture local spatial correlations, the attention weights are normalized using the Sigmoid function, the weight multiplier for extreme regions is 2, and the extreme threshold quantile level τ=0.9. The fully connected layers are as follows: The first fully connected layer takes the feature vector after the feature map is flattened as input and outputs a 256-dimensional feature vector, using ReLU activation and Dropout(0.5); the second fully connected layer takes the 256-dimensional feature vector as input and outputs a 128-dimensional feature vector, using ReLU activation and Dropout(0.5); the third fully connected layer takes the 128-dimensional feature vector as input and outputs a 1-dimensional feature vector (monthly precipitation prediction value), with no activation function.

[0067] (3) Based on the training set and the EPSA_CNN model, the model is trained using the dynamically weighted Huber loss function; specifically as follows: the processed data is divided into training set and test set according to the year, and the training set is randomly divided into batches to train the model; the gradient descent method is used to compare the model results with the target data.

[0068] The model was trained using the Adam optimizer, with an initial learning rate of 1×10⁻⁶. -3 The weight decay coefficient is 1×10 −4 The learning rate scheduling uses the ReduceLROnPlateau strategy (factor 0.5, patience value 10). The batch size is set to 32, the maximum number of training epochs is 200, and an early stopping strategy is adopted (training stops when the validation set loss does not decrease for 30 consecutive epochs). The training set, validation set, and test set are divided in a 7:1.5:1.5 ratio according to year, and a random batching strategy is used during training. The Huber loss switching threshold δ=20 (unit: mm / month), the extreme sample weight α=3, the normal sample weight δ=0.5, and the extreme threshold quantile level τ=0.9.

[0069] (4) Generate a comparison chart of the predicted and actual values ​​of monthly precipitation in the Indian monsoon region. For example... Figure 4 As shown, the actual prediction results show that the trend of the predicted values ​​of Indian monsoon monthly precipitation with a forecast lead time of 1-18 months is consistent with the actual values, and the intensity of extreme precipitation predicted by the model is comparable to the intensity of the actual values. This indicates that the deep learning model using the EPSA attention mechanism and the dynamically weighted Huber loss function can accurately predict extreme precipitation in the Indian monsoon.

Claims

1. A method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, characterized in that, Includes the following steps: (1) Collect tropical Pacific subsurface sea surface temperature data and Indian monsoon monthly precipitation observation data, perform monthly anomaly processing and zonal anomaly processing on the subsurface sea surface temperature data, and construct a training dataset; (2) Construct an EPSA_CNN prediction model. The model introduces an EPSA attention mechanism between the convolutional layer and the fully connected layer to strengthen the feature weights of the extreme sea surface temperature anomaly region. (3) The model is trained using the dynamically weighted Huber loss function. The loss function dynamically identifies extreme precipitation samples through quantile thresholds and uses a dual-weight mechanism to strengthen the penalty for extreme sample errors. (4) Generate the Indian monsoon monthly precipitation forecast product based on the trained model and output the comparison results between the predicted value and the actual value.

2. The method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 1, is characterized in that... In step (1), the subsurface sea surface temperature data of the tropical Pacific Ocean are selected from the temperature data of 16 layers 5m-300m below the sea surface within the range of 8°N-24°S and 120°E-90°W of the sea area, with a spatial resolution of 0.5°×0.5°.

3. The method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 1, is characterized in that... In step (2), the EPSA_CNN model structure includes: 3 convolutional layers, each containing batch normalization, activation function and max pooling; 1 EPSA attention module, inserted between the convolutional layers and the fully connected layers; and 3 fully connected layers for outputting precipitation prediction values.

4. A method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 1, is characterized in that... In step (2), the EPSA attention mechanism includes: a basic spatial attention module for generating spatial heterogeneous attention weights; a dynamic extreme threshold and mask generation module for dynamically dividing extreme regions and normal regions based on the actual distribution of the input temperature field; and an attention fusion module for combining the basic attention weights with the extreme mask so that the attention weight of the extreme region is twice that of the normal region.

5. A method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 4, is characterized in that... The dynamic extreme threshold and mask generation module calculates the threshold using a quantile function, specifically: ； in The quantile calculation function satisfies , It is the quantile level, a scale specifically designed for locating extreme data; when When the extreme precipitation occurs, the sample is classified as an extreme precipitation sample; otherwise, it is classified as a normal precipitation sample.

6. A method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 1, is characterized in that... In step (3), the expression for the dynamically weighted Huber loss function is: ； in , The first Observed values ​​and predicted values ​​for each sample It is the total number of samples. This means averaging the loss over all samples to ensure the interpretability of the loss values ​​at different scales. It depends on the observed values The weights, and the weight function expression is: ； The original Huber loss function is expressed as follows: ； in, It is a hyperparameter when | |≤ When |Huber loss is the MSE function; when | |> At that point, the loss becomes a linear function.

7. A method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 1, is characterized in that... In step (3), the model training adopts the gradient descent method, the training set is divided by year, and a random batch training strategy is adopted.

8. A method for forecasting extreme precipitation in the Indian monsoon using subsurface sea surface temperature in the tropical Pacific, as described in claim 1, is characterized in that... In step (4), the forecast product includes the Indian monsoon monthly precipitation forecast series for the next 1-18 months, and a comparison chart of the forecast values ​​and the actual values ​​is drawn.

Images