A method for average sea surface temperature prediction of a deep neural network

Abstract

The application belongs to the field of numerical prediction, and discloses a deep neural network mean sea surface temperature prediction method, wherein the sea surface temperature in reanalysis grid data information is selected as a prediction true value of a to-be-detected prediction area; data matching is performed to obtain a variable element data set matched in time and space levels; a sea surface temperature prediction training set is constructed; a multi-layer network structure of a mean sea surface temperature prediction model fusing spatial partial derivative value solving is built, and the idea of a Runge-Kutta method in a numerical mode is combined to complete multi-step prediction of the sea surface temperature. The application models the time and space characteristics of variables, overcomes the defects of discrete errors of a traditional numerical prediction method, poor interpretability of traditional deep learning, and strong data dependence, and combines existing prior knowledge in numerical prediction and certain training data to obtain more accurate element prediction results.

Description

Technical Field

[0001] This invention belongs to the field of numerical weather prediction technology, and in particular relates to a method for predicting average sea surface temperature using deep neural networks. Background Technology

[0002] Existing machine learning-based sea surface temperature prediction models typically employ data-driven prediction methods, such as LSTM models or convolutional neural networks (CNNs), which require extensive training data to achieve satisfactory results. Furthermore, machine learning only identifies the statistical relationship between the input and the system variables of interest to the model, without considering any physical laws, which may lead to deviations from physical laws in the results. Moreover, machine learning models can only reflect one correlation between input variable data and cannot generalize to factors beyond the training data, which may result in weak generalization ability of the model. Summary of the Invention

[0003] To address the aforementioned problems, it is necessary to construct a model capable of integrating physical information and spatiotemporal information of elements, while also enabling multi-step forecasting. This invention proposes a deep neural network-based method for forecasting average sea surface temperature, comprising the following steps:

[0004] S1: Select satellite observation data and reanalysis grid data as model data samples;

[0005] S2: Interpolation calculation: Using the linear interpolation method, daily mixed layer thickness data, daily sea surface zonal velocity data, daily sea surface zonal velocity data at a depth of 108m, daily sea surface meridional velocity data, daily sea surface meridional velocity data at a depth of 108m, daily sea surface temperature data, and daily sea temperature data at 108m are used to calculate the daily sea flow velocity data and daily sea temperature data at a depth of 10m in the mixed layer.

[0006] S3: Data matching. To match the satellite observation data with the reanalysis data, the spatial information of the grid data with the lowest spatial resolution is first selected as the reference grid point. The remaining variable data are interpolated and matched to the reference grid point. Then, the satellite observation data and the reanalysis data are matched on the time scale, and finally the two data are matched in both spatial and temporal dimensions.

[0007] S4: Construct a training set for sea surface temperature forecasts; where satellite-observed sea surface temperature data and reanalysis grid data are used as training sample features, and sea surface temperature data in the reanalysis data are used as sample labels;

[0008] S5: Construct a multi-layer network structure for a deep neural network model for predicting mean sea surface temperature that integrates numerical solutions for spatial partial derivatives. This model consists of the following three parts:

[0009] The first part uses a 3D-CNN convolutional layer as a data feature extraction module to obtain the feature matrix data after feature dimensionality reduction as input;

[0010] The second part is a 3D-CNN convolutional neural network, which uses spatial convolutional layers and employs a two-layer spatial convolutional module. Temporally, it selects the matrix obtained by fusing and reducing the spatiotemporal features of satellite observation data and reanalysis data as input.

[0011] The third part is the spatiotemporal convolutional neural network 3D-CNN-ConvLSTM, which includes the following:

[0012] The spatiotemporal convolutional LSTM layer uses a 3-layer spatiotemporal convolutional LSTM module, and the input is the matrix obtained by fusing the spatiotemporal features of satellite observation data and reanalysis data after dimensionality reduction.

[0013] The physical information partial differential equation fusion layer incorporates the partial differential terms from the mixed layer temperature heat budget equation into the network for solution. The obtained partial differential terms are then calculated with the element variables. Combined with the difference calculation method in the traditional solution, the forecast output for the next time step is obtained.

[0014] The multi-step forecast layer, based on the basic idea of ​​the Runge-Kutta method, calculates the average slope of the forecast output at time i and the forecast output at time i+1. The average slope obtained is then used to calculate the average slope of the forecast output at time i+2, and so on, to obtain the result of the multi-step forecast.

[0015] Furthermore, the satellite observation data and reanalysis gridded data include daily downward solar shortwave radiation data, daily upward solar shortwave radiation data, daily downward solar longwave radiation data, daily upward solar longwave radiation data, daily sensible heat flux data, daily latent heat flux data, daily sea surface zonal current velocity data, daily sea surface meridional current velocity data, daily mixed layer thickness data, daily sea surface temperature data, daily temperature data 10m below the mixed layer, and daily current velocity data 10m below the mixed layer.

[0016] Furthermore, the construction of the sea surface temperature forecast training set includes a dataset composed of spatiotemporal matching of 12 environmental variable elements from satellite observation data and reanalysis grid data. In addition, 7-day environmental variable elements of 12 variables that are continuous in time are used as the temporal features of the training set, and the latitude and longitude data information of SST is constructed and added to the training set as the temporal features. Finally, two spatially and temporally continuous image forms of data are obtained, including daily downward solar shortwave radiation data, daily upward solar shortwave radiation data, daily downward solar longwave radiation data, daily upward solar longwave radiation data, daily sensible heat flux data, daily latent heat flux data, daily seawater zonal current velocity data, daily seawater meridional current velocity data, daily mixing layer thickness, daily seawater current velocity data 10m below the mixing layer, and daily seawater temperature data 10m below the mixing layer.

[0017] 3D-CNN uses 3×3×3 convolutional kernels for feature extraction, dimensionality reduction and fusion. Spatiotemporal convolutional LSTM uses 3×3×3 convolutional kernels for spatial feature extraction. The number of neurons in each layer of the 3-layer spatiotemporal convolutional LSTM is 64, 64 and 64 respectively; the number of neurons in each layer of the 3-layer spatial convolutional CNN is 16, 32 and 64 respectively.

[0018] Furthermore, the formula for calculating sea surface temperature is as follows:

[0019]

[0020] Q′=Q sw +Q lw +Q lhf +Q sf

[0021]

[0022]

[0023]

[0024] Where T′ m This represents the daily average sea surface temperature, where x represents latitude, y represents longitude, u represents the zonal sea surface current velocity, v represents the meridional sea surface current velocity, and h... m The thickness of the mixing layer is represented by ρ, and the density of seawater is taken as 1025 kg / m³. 3 C p The specific heat of seawater is 4000 J / kg, R represents the bias term, and Q′ represents the net heat flux over the sea surface. sw Q represents the net shortwave solar radiation flux absorbed by the sea surface. lw Q represents the net longwave solar radiation flux absorbed by the sea surface. lhf For latent heat flux, Qshf For sensible heat flux, the direction of heat absorption by the ocean is taken as positive; T d Represents the seawater temperature at 10m below the mixed layer, w e The velocity of the seawater at a depth of 10m in the mixed layer is given by the above method. Both values ​​are calculated using interpolation, where h is the seawater depth. 0.5 The seawater temperature at 0.5m below the mixing layer, v 0.5 The seawater flow velocity at 0.5m below the mixed layer, T i The seawater temperature at a depth of i meters in the mixed layer. This represents the trend term of temperature change over time. Based on this term and the Runge-Kutta method, multi-step temperature forecasting is achieved.

[0025] Furthermore, feature fusion data is obtained through the feature extraction process of the 3D-CNN layers. Through the propagation process between layers, combined with a gating mechanism, the upper-layer memory information is adaptively updated, selectively transmitting memory information to avoid gradient explosion while capturing global spatiotemporal information. Through the working mechanisms of the input gate, forget gate, and memory gate, combined with spatial information extraction in the convolution process, the task of calculating partial differential terms in the prediction process is completed. The mathematical representation of the memory update output process is as follows:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] c t =f t c (t-1) +i t g t

[0032] h t =o t tanh(c t )

[0033] Among them, among them, For the input data, p, q, and r are the sizes of the three convolutional kernels, respectively, and W... xi Input gate pair at the current time The weight, W hi Input gate pair at the current time The weight, W is the hidden state from the previous moment. ci Input gate pair C at the current timet-1 The weight, C t-1 b is the cell state update value from the previous time step. i For the bias information of the input gate, b f For the bias information of the forget gate, W xf Forget the door pairing at the current moment The weight, W hf Forget the door pairing at the current moment The weight, W cf Forget the door to C at the current moment t-1 The weight, W if For the current time, the memory gate pair x t The weight, W hg For the current moment, remember the gate pair The weight, b hg For the bias information of the memory gate, W io Output gate pair χ at the current time. t The weight, W ho Output gate pair at the current moment The weight, b ho For the bias information of the output gate, f t For the Gate of Oblivion, c (t-1) For, i t For the input gate, g t For memory gates, h t The values ​​are obtained from the output gate and the cell state. To 3D convolution operation, o t For output gate, c t This is the unit state.

[0034] Furthermore, a computational graph between independent and dependent variables is constructed, and the automatic differentiation function of the neural network is used to solve the differential of the objective function. The difference before and after iteration of the physical equation is introduced into the loss function of the neural network. Based on the method of minimizing the loss function, the backpropagation mechanism of the neural network is used to iteratively optimize the differentiation result, so that the neural network can obtain the prediction result that satisfies the set physical laws.

[0035] Furthermore, based on the fundamental idea of ​​the Runge-Kutta method and combined with the traditional finite difference method, the satellite observation data from 7 days ago and the reanalysis data corresponding to the remaining 11 variables required by the equation are used as time series data inputs. Loss calculations are performed with the actual data from day (7+i) to obtain the forecast model for day i. The mathematical process is as follows:

[0036] Let: y(x) n+1 )=y(x n )+h′(∈) x n <∈ <xn+1 ,

[0037] Let: y'(x n )=f(x n ,y n )

[0038] We can obtain: y(x) n+1 )=y(x n )+hf(∈,y(∈))

[0039] Where: f(∈, y(∈)) is the interval (x... n ,x n+1 average slope on )

[0040] Take: x i+7 x i+m i∈1,2,3,...m>7

[0041] We get: y(x) i+m )=α(α(α(α(α(αy<∈<′(x i+1 )+βy′(x i+2 ))+βy′(x i+3 ))+βy′(x i+4 ))+βy′(x i+5 ))+βy′(x i+6 ))+βy′(x i+7 )

[0042] Where, x n and x n+1 Let h′(∈) be the input at the current moment and the predicted value in the future, respectively. Let h′(∈) be the differential trend term, y() be the algebraic calculation of the input data, f(,) be the differential relationship between the input variables expressed by the neural network, α be the weight coefficient of the current value on the predicted value, which is taken as 0.1, and β be the weight coefficient of the previous value on the predicted value, which is taken as 0.9.

[0043] By combining the partial differential terms obtained from the neural network, the sea surface temperature data for day m is obtained.

[0044] Furthermore, the feature selection method used in the 3D convolution process is the backward search algorithm without heuristics in the wrapper method.

[0045] The beneficial effects of this invention are as follows:

[0046] 1) A machine learning multi-step forecasting method for regional grid mean sea surface temperature is proposed. Previous forecasting methods based on mean sea surface temperature were mostly targeted at specific buoy points, while the face-to-face regional forecasting method makes the forecast more valuable for application.

[0047] 2) With physical information constraints as the goal, the physical information of the mixed layer temperature heat budget equation is integrated into the neural network, and the sea surface temperature forecast results are made to conform to physical laws through iterative optimization.

[0048] 3) Based on the automatic differentiation function of neural networks, by first constructing a calculation graph of independent and dependent variables, and then solving the differentiation through neural networks, combined with the traditional difference method and Runge-Kutta method, a theoretical basis for multi-step sea surface temperature prediction based on physical information is constructed.

[0049] 4) The input variables are pre-extracted using 3D-CNN and processed using the long-term data processing capability of ConvLSTM; the input information is then processed using the powerful spatial information extraction capability of 3D-CNN.

[0050] 5) The sea surface temperature data in the analysis data is used as the true value, and the network is optimized and iterated based on this. Combined with the multi-step forecast mathematical reasoning process, the multi-step forecast of sea surface temperature is completed and a good forecast effect is obtained. Attached Figure Description

[0051] Figure 1 A schematic diagram of the input method for the model of this invention;

[0052] Figure 2 Schematic diagram of the ConvLSTM structure of this invention;

[0053] Figure 3 A schematic diagram of automatic differentiation and partial derivative calculation of the neural network of this invention;

[0054] Figure 4 Experimental comparison of prediction time between the present invention and traditional algorithms;

[0055] Figure 5 After adding control variables and controlling the partial differential equations of physical information, the experimental comparison between the present invention and the traditional algorithm is shown in the figure.

[0056] Figure 6 The experimental comparison between the present invention and the traditional algorithm after incorporating the change in the prediction step size is shown in the figure. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0058] The purpose of this invention is to provide a deep neural network-based method for predicting average sea surface temperature (SPNON) that integrates spatial partial derivative numerical solutions.

[0059] To achieve this objective, the technical solution adopted by the present invention includes the following steps:

[0060] Includes the following steps:

[0061] S1: Select satellite observation data and reanalysis grid data as model data samples;

[0062] S2: Interpolation calculation: Using the linear interpolation method, daily mixed layer thickness data, daily sea surface zonal velocity data, daily sea surface zonal velocity data at a depth of 108m, daily sea surface meridional velocity data, daily sea surface meridional velocity data at a depth of 108m, daily sea surface temperature data, and daily sea temperature data at 108m are used to calculate the daily sea flow velocity data and daily sea temperature data at a depth of 10m in the mixed layer.

[0063] S3: Data matching. To match the satellite observation data with the reanalysis data, the spatial information of the grid data with the lowest spatial resolution is first selected as the reference grid point. The remaining variable data are interpolated and matched to the reference grid point. Then, the satellite observation data and the reanalysis data are matched on the time scale, and finally the two data are matched in both spatial and temporal dimensions.

[0064] S4: Construct a training set for sea surface temperature forecasts; where satellite-observed sea surface temperature data and reanalysis grid data are used as training sample features, and sea surface temperature data in the reanalysis data are used as sample labels;

[0065] S5: Construct a multi-layer network structure for a deep neural network model for predicting mean sea surface temperature that integrates numerical solutions for spatial partial derivatives. This model consists of the following three parts:

[0066] The first part uses a 3D-CNN convolutional layer as a data feature extraction module to obtain the feature matrix data after feature dimensionality reduction as input;

[0067] The second part is a 3D-CNN convolutional neural network, which uses spatial convolutional layers and employs a two-layer spatial convolutional module. Temporally, it selects the matrix obtained by fusing and reducing the spatiotemporal features of satellite observation data and reanalysis data as input.

[0068] The third part is the spatiotemporal convolutional neural network 3D-CNN-ConvLSTM, which includes the following:

[0069] The spatiotemporal convolutional LSTM layer uses a 3-layer spatiotemporal convolutional LSTM module, and the input is the matrix obtained by fusing the spatiotemporal features of satellite observation data and reanalysis data after dimensionality reduction.

[0070] The physical information partial differential equation fusion layer incorporates the partial differential terms from the mixed layer temperature heat budget equation into the network for solution. The obtained partial differential terms are then calculated with the element variables. Combined with the difference calculation method in the traditional solution, the forecast output for the next time step is obtained.

[0071] The multi-step forecast layer, based on the basic idea of ​​the Runge-Kutta method, calculates the average slope of the forecast output at time i and the forecast output at time i+1. The average slope obtained is then used to calculate the average slope of the forecast output at time i+2, and so on, to obtain the result of the multi-step forecast.

[0072] Furthermore, the satellite observation data and reanalysis gridded data include daily downward solar shortwave radiation data, daily upward solar shortwave radiation data, daily downward solar longwave radiation data, daily upward solar longwave radiation data, daily sensible heat flux data, daily latent heat flux data, daily sea surface zonal current velocity data, daily sea surface meridional current velocity data, daily mixed layer thickness data, daily sea surface temperature data, daily temperature data 10m below the mixed layer, and daily current velocity data 10m below the mixed layer.

[0073] Furthermore, the constructed element forecast training set includes a dataset composed of spatiotemporal matching of 12 environmental variable elements from satellite observation data and reanalysis grid data. In addition, 12 temporally continuous 7-day environmental variable elements are used as the temporal features of the training set, and the latitude and longitude data information of SST is constructed and added to the training set as temporal features. Finally, two spatially and temporally continuous image forms of data are obtained, including daily downward solar shortwave radiation data, daily upward solar shortwave radiation data, daily downward solar longwave radiation data, daily upward solar longwave radiation data, daily sensible heat flux data, daily latent heat flux data, daily seawater zonal velocity data, daily seawater meridional velocity data, daily mixing layer thickness, daily seawater velocity data 10m below the mixing layer, and daily seawater temperature data 10m below the mixing layer.

[0074] 3D-CNN uses 3×3×3 convolutional kernels for feature extraction, dimensionality reduction and fusion. Spatiotemporal convolutional LSTM uses 3×3×3 convolutional kernels for spatial feature extraction. The number of neurons in each layer of the 3-layer spatiotemporal convolutional LSTM is 64, 64 and 64 respectively; the number of neurons in each layer of the 3-layer spatial convolutional CNN is 16, 32 and 64 respectively.

[0075] Furthermore, the formula for calculating the sea surface temperature is as follows:

[0076]

[0077] Q′=Q sw +Q lw +Qlhf +Q sfh

[0078]

[0079]

[0080]

[0081] Where T′ m This represents the daily average sea surface temperature, where x represents latitude, y represents longitude, u represents the zonal sea surface current velocity, v represents the meridional sea surface current velocity, and h... m The thickness of the mixing layer is represented by ρ, and the density of seawater is taken as 1025 kg / m³. 3 C p The specific heat of seawater is 4000 J / kg, R represents the bias term, and Q′ represents the net heat flux over the sea surface. sw Q represents the net shortwave solar radiation flux absorbed by the sea surface. lw Q represents the net longwave solar radiation flux absorbed by the sea surface. lhf For latent heat flux, Q shf For sensible heat flux, the direction of heat absorption by the ocean is taken as positive; T d Represents the seawater temperature at 10m below the mixed layer, w e The velocity of the seawater at a depth of 10m in the mixed layer is given by the above method. Both values ​​are calculated using interpolation, where h is the seawater depth. 0.5 The seawater temperature at 0.5m below the mixing layer, v 0.5 The seawater flow velocity at 0.5m below the mixed layer, T i The seawater temperature at a depth of i meters in the mixed layer. This represents the trend term of temperature change over time. Based on this term and the Runge-Kutta method, multi-step temperature forecasting is achieved.

[0082] Furthermore, feature fusion data is obtained through the feature extraction process of the 3D-CNN layers. Through the propagation process between layers, combined with a gating mechanism, the upper-layer memory information is adaptively updated, selectively transmitting memory information to avoid gradient explosion while capturing global spatiotemporal information. Through the working mechanisms of the input gate, forget gate, and memory gate, combined with spatial information extraction in the convolution process, the task of calculating partial differential terms in the prediction process is completed. The mathematical representation of the memory update output process is as follows:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] c t =f t c (t-1) +i t g t

[0089] h t =o t tanh(c t )

[0090] in, For the input data, p, q, and r are the sizes of the three convolutional kernels, respectively, and W... xi Input gate pair at the current time The weight, W hi Input gate pair at the current time The weight, W is the hidden state from the previous moment. ci Input gate pair C at the current time t-1 The weight, C t-1 b is the cell state update value from the previous time step. i For the bias information of the input gate, b f For the bias information of the forget gate, W xf Forget the door pairing at the current moment The weight, W hf Forget the door pairing at the current moment The weight, W cf Forget the door to C at the current moment t-1 The weight, W if For the current moment, remember the gate pair The weight, W hg For the current moment, remember the gate pair The weight, b hg For the bias information of the memory gate, W io Output gate pair at the current moment The weight, W ho Output gate pair at the current moment The weight, b ho For the bias information of the output gate, f t For the Gate of Oblivion, c (t-1) For, i t For the input gate, g t For memory gates, h t C is the value obtained from the output gate and the cell state. 3D (x t ) for 3D convolution operation, o t For output gate, c t This is the unit state.

[0091] Furthermore, a computational graph between independent and dependent variables is constructed, and the automatic differentiation function of the neural network is used to solve the differential of the objective function. The difference before and after iteration of the physical equation is introduced into the loss function of the neural network. Based on the method of minimizing the loss function, the backpropagation mechanism of the neural network is used to iteratively optimize the differentiation result, so that the neural network can obtain the prediction result that satisfies the set physical laws.

[0092] Furthermore, based on the fundamental idea of ​​the Runge-Kutta method and combined with the traditional finite difference method, the satellite observation data from 7 days ago and the reanalysis data corresponding to the remaining 11 variables required by the equation are used as time series data inputs. Loss calculations are performed with the actual data from day (7+i) to obtain the forecast model for day i. The mathematical process is as follows:

[0093] Let: y(x) n+1 )=y(x n )+h′(∈) x n <∈ <x n+1 ,

[0094] Let: y'(x n )=f(x n ,y n )

[0095] We can obtain: y(x) n+1 )=y(x n )+hf(∈,y(∈))

[0096] Where: f(∈, y(∈)) is the interval (x... n ,x n+1 average slope on )

[0097] Take: x i+7 x i+m i∈1,2,3,...m>7

[0098] We get: y(x) i+m )=α(α(α(α(α(αy<∈<′(x i+1 )+βy′(x i+2 ))+βy′(x i+3 ))+βy′(x i+4 ))+βy′(x i+5 ))+βy′(x i+6 ))+βy′(x i+7 )

[0099] Where, xn and x n+1 Let h′(∈) be the current input and the future predicted value, respectively. Let h′(∈) be the differential trend term, y() be the algebraic calculation of the input data, f(,) be the differential relationship between the input variables expressed by the neural network, α be the weight coefficient of the current value on the predicted value, which is set to 0.1, and β be the weight coefficient of the previous value on the predicted value, which is set to 0.9.

[0100] By combining the partial differential terms obtained from the neural network, the sea surface temperature data for day m is obtained.

[0101] Furthermore, the feature selection method used in the 3D convolution process is the backward search algorithm without heuristics in the wrapper method.

[0102] To make the technical solution and beneficial effects of the present invention clearer, the present invention will be further described below with reference to practical examples. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0103] Example

[0104] This invention proposes a method that uses satellite observation data from the same time point in the preceding 7 days, along with reanalysis data of 11 variables required at the same time point in the preceding 7 days, as model input. Figure 1 As shown, for example, the historical time-based forecast data input to the model is F. t-7 F t-6 F t-5 F t-4 F t-3 F t-2 F t-1 And reanalyze sea surface temperature data F at m future moments. t+i It serves as the true value and also as the input to the model.

[0105] 1. Temperature heat budget equation for the mixed layer

[0106] Previous studies have shown that calculating sea surface temperature based on the heat budget equation for the mixed layer temperature is feasible. However, as a complex partial differential equation, traditional methods suffer from low efficiency and unstable results. Furthermore, without initial conditions, traditional methods cannot guarantee an accurate solution for sea surface temperature. With the development of artificial intelligence, solving complex partial differential equations is expected to be more efficient and accurate. Based on the automatic differentiation function of neural networks and a data-driven iterative optimization process, this study combines traditional finite difference methods with the basic ideas of Runge-Kutta and uses data-driven methods to correct certain bias terms in the equation to obtain more accurate prediction results. The formula for the target partial differential equation is:

[0107]

[0108] Q′=Q sw +Q lw +Q lhf +Q sf

[0109]

[0110]

[0111]

[0112] Where T m This represents the daily average sea surface temperature, where x represents latitude, y represents longitude, u represents the zonal sea surface current velocity, v represents the meridional sea surface current velocity, and h... m The thickness of the mixing layer is represented by ρ, and the density of seawater is taken as 1025 kg / m³. 3 C p The specific heat of seawater is represented by 4000 J·kg / K, and R represents the bias term.

[0113] Q′ represents the net heat flux over the sea surface, Q sw Q represents the net shortwave solar radiation flux absorbed by the sea surface. lw Q represents the net longwave solar radiation flux absorbed by the sea surface. lhf For latent heat flux, Q shf For sensible heat flux, the direction of heat absorption by the ocean is taken as positive; T d Represents the seawater temperature at 10m below the mixed layer, w e The velocity of the seawater at 10m below the mixed layer is calculated by interpolation. h is the depth of the seawater, which is taken as 108 here.

[0114] This represents the trend term of temperature change over time. Based on this term, and using the basic idea of ​​the Runge-Kutta method and the traditional difference method, multi-step temperature forecasting is achieved.

[0115] 2. Deep Neural Network Model Integrating Spatial Partial Derivative Numerical Solution

[0116] For spatiotemporal feature modeling, drawing on image recognition research, the spatial feature matrix is ​​transformed into two-dimensional image numerical values; based on the traditional difference algorithm and Runge-Kutta method, and drawing on the basic method of solving partial differential equations by neural networks, a deep neural network method for predicting average sea surface temperature is proposed, which integrates the numerical solution of spatial partial derivatives.

[0117] CNN stands for Convolutional Neural Network. It takes spatial matrix data as input and extracts and outputs information through convolution operations. The structure and operation flow of a CNN are mainly as follows: In the form of.

[0118] LSTM is a variant of recurrent neural network (RNN). It takes sequential data (usually time series data) as input, recursively moves in the direction of sequence evolution, and all nodes (recurrent units) are connected in a chain.

[0119] In the ConvLSTM structure, some fully connected operations in LSTM are replaced with convolutional operations. While retaining the strong temporal data processing capabilities of the original LSTM, it improves the ability to capture spatial information of the data, making it very suitable for processing data with spatiotemporal structures. For example... Figure 2 As shown, the data is first fused using a 3D-CNN. The fused data is then passed to a ConvLSTM, where a gating mechanism adaptively updates the data information passed to the upper layers. When the model has only one layer, the module input is χ. t When the number of model layers is greater than 1, the input is the output of the lower-level model.

[0120]

[0121]

[0122]

[0123] g t =tanh(W if χ t +b ig +W hg h (t-1) +b hg )

[0124]

[0125] c t =f t c (t-1) +i t g t

[0126] h t =o t tanh(c t )

[0127] in, For the input data, p, q, and r are the sizes of the three convolutional kernels, respectively, and W... xi Input gate pair at the current time The weight, W hi Input gate pair at the current time The weight, W is the hidden state from the previous moment. ci Input gate pair C at the current time t-1 The weight, C t-1 b is the cell state update value from the previous time step. i For the bias information of the input gate, b f For the bias information of the forget gate, W xf Forget the door to x at the current moment t The weight, W hf Forget the door pairing at the current moment The weight, W cf Forget the door to C at the current moment t-1 The weight, W if For the current time, the memory gate pair x t The weight, W hg For the current moment, remember the gate pair The weight, b hg For the bias information of the memory gate, W io Output gate pair x at the current time. t The weight, W ho Output gate pair at the current moment The weight, b ho For the bias information of the output gate, f t For the Gate of Oblivion, c (t-1) For, i t For the input gate, g t For memory gates, h t C is the value obtained from the output gate and the cell state. 3D (χ t ) for 3D convolution operation, o t For output gate, c t This is the unit state.

[0128] Using 3D-CNN-ConvLSTM to predict sea surface temperature in multiple steps, the whole process can be divided into three parts: feature aggregation, memory update, and physical information fusion.

[0129] 1) Feature aggregation

[0130] At the same time step: feature information is extracted using 3D-CNN, with the input being 3D spatiotemporal data X, X∈R. B×T×C×H×W The process of feature aggregation can be represented by the following formula:

[0131]

[0132] Where * represents the convolution operation in 3D-CNN, ω(p,q,r) represents the size of the convolution kernel, and P, Q, and R represent the number of feature channels, latitude, and longitude of the input data.

[0133] 2) Memory update

[0134] Through the propagation process between layers, combined with a gating mechanism, the upper-layer memory information is adaptively updated. Information is selectively passed to memory, avoiding gradient explosion while grasping global spatiotemporal information. By utilizing the working mechanisms of the input gate, forget gate, and memory gate, combined with spatial information extraction during convolution, the task of calculating partial differential terms in the prediction process is completed. The mathematical representation of the memory update output process is as follows:

[0135]

[0136]

[0137]

[0138] 3) Physical information fusion

[0139] By utilizing the automatic differentiation function of neural networks, partial derivatives can be calculated on constructed data, such as... Figure 3 The specific steps include:

[0140] (1) Construct the dataset,

[0141] (2) Construct a neural network alternative model u for the solution u(x) of the partial differential equation. NN (x; θ), where θ is the initialization parameter;

[0142] (3) Through the automatic differentiation function and arithmetic operations of the neural network, the constructed alternative model u NN Substituting (x; θ) into the master equation, we obtain the target network f. NN (x; θ);

[0143] (4) Define the loss function by the root mean square error between the input data and the real data:

[0144]

[0145] (5) The constructed neural network is trained by minimizing the loss function L(θ), and the optimal parameters are found. The network structure is then optimized iteratively.

[0146] θ * =argmin(L(θ))

[0147] 3. Output calculated using the difference-Runge-Kutta algorithm.

[0148] The satellite observation data from 7 days ago and the reanalysis data of the remaining 11 variables required for the equation are used as time-series data inputs; loss calculations are performed with the actual data from day 7+i to obtain the forecast model for day i. This is then processed through the output gate. t The partial derivatives of temperature with respect to longitude and latitude were obtained. These results were then used to calculate the derivative of temperature with respect to time. Integrating this derivative yielded the desired forecast temperature. The specific mathematical expression of the calculation process is as follows:

[0149] o t =σ(W io x t +b io +W ho h (t-1) +b ho )

[0150] Let: y(x) n+1 )=y(x n )+h′(∈)x n <∈ <x n+1 ,

[0151] Let: y′(x n )=f(x n ,y n )

[0152] We can obtain: y(x) n+1 )=y(x n )+hf(∈,y(∈))

[0153] Where: f(∈, y(∈)) is the interval (x... n ,x n+1 average slope on )

[0154] Take: x i+7 x i+m i∈1,2,3,...m>7

[0155] We get: y(x) i+m )=α(α(α(α(α(αy<∈<′(x i+1 )+βy′(x i+2 ))+βy′(x i+3 ))+βy′(x i+4 ))+βy′(x i+5 ))+βy′(x i+6 ))+βy′(x i+7 )

[0156] 4. Sea surface temperature forecast

[0157] The experiments in this project are mainly divided into two parts: model comparison experiments and factor forecasting experiments. Model comparison: The performance of the method is explored using experimental data from 1826 days (January 1, 2015 to December 31, 2019) in parts of the Pacific Ocean (0.95°S to 20°N, 135°W to 161.25°W). The satellite observation data used were from the NOAA best-interpolated sea surface temperature dataset (OISST version 2), which has a horizontal spatial resolution of 0.25° × 0.25° grid. The required daily downward solar shortwave radiation, daily upward solar shortwave radiation, daily downward solar longwave radiation, daily upward solar longwave radiation, daily sensible heat flux, daily latent heat flux, daily zonal seawater current velocity, and daily meridional seawater current velocity data were obtained from the in-analysis product data of the National Centers for Environmental Prediction - Department of Energy Reanalysis 2 (NECP-DOE R2). In this dataset, surface variables are stored in a global T62 Gaussian grid with a horizontal spatial resolution of 2.5° × 2.5°. The daily mixed layer thickness data and the sea surface temperature data used as the true values ​​were obtained from the Copernicus Marine Service (or Copernicus Marine Environment) of the Copernicus Programme of the European Union. The dataset uses global ocean reanalysis product data from MonitoringService, generated based on the NEMO model. Variable data is stored in an ORCA05 grid with a horizontal spatial resolution of 0.25° × 0.25°. 70% of the total data was used for training, 5% for validation, and the remaining 30% for testing. The spatial information of the grid with the lowest spatial resolution was used as the baseline grid points. The remaining variable data were interpolated and matched to these baseline grid points. Then, satellite observation data and reanalysis data were matched temporally to obtain a spatiotemporally matched dataset for use in this project. The input time step was fixed at 7, and sea surface temperature was predicted for the next m days. For spatiotemporal prediction tasks, missing values ​​in the selected experimental area needed to be imputed. Based on the distinction between land and ocean, the ocean portion still contained sea surface temperature data and other feature values ​​(such as solar radiation and sea surface velocity), while the land portion was set to 0. The feature selection method was a backward search algorithm without heuristics in the wrapper method (existing technology in this field).

[0158] To verify the performance of the proposed method, and without loss of generality, the following experiments were conducted: (1) The selected model was the 3D-CNN-ConvLSTM model, which currently performs best in the sea surface element time series prediction task; (2) The sea surface temperature prediction performance was compared by controlling the addition or absence of the physical information partial differential equation in the above model; (3) The performance of the two methods was compared by changing the prediction step size. In this way, the effect of adding or not adding the physical information partial differential equation on the element prediction was comprehensively measured.

[0159] In the model comparison experiment, a 3D-CNN-ConvLSTM model was selected for comparison. The prediction performance was compared with and without the addition of physical information partial differential equations to constrain the prediction effect. The "multi" steps in the multi-step prediction were updated synchronously. To ensure the fairness and reliability of the comparison results, model parameters were selected based on the prediction performance of the 3D-CNN-ConvLSTM model without constraints. The model parameters with the best prediction performance (i.e., the lowest root mean square error) in this experiment were selected as the model parameters for all comparison experiments. The processed data was input into the network. Each result is the average of five experiments. All parallel experiments used fixed random seeds of 1, 2, 3, 4, and 5 to ensure the reproducibility of the results. The root mean square error was used as the evaluation metric for all models, expressed in degrees Celsius (°C). The experimental results are shown in Table 1 and... Figure 4 , Figure 5 and Figure 6 As shown: CNN and CNN-ConvLSTM refer to multi-step sea surface temperature forecasting using traditional deep learning methods without physical constraints; finite element difference refers to the multi-step sea surface temperature forecasting results calculated using the traditional finite element difference method; SPNON-CNN and SPNON-CNN-ConvLSTM refer to the deep learning methods proposed in this invention that add physical constraints for multi-step sea surface temperature forecasting.

[0160] A comparison of six different forecast durations shows that even for the best-performing model in the field, adding physical constraints can still comprehensively improve the model's forecast performance, indicating that this method has a certain degree of advancement.

[0161] In practical applications, not all tasks have sufficient data to train models and obtain the desired forecast results; data gaps and deficiencies are common problems in meteorological and oceanographic fields. To address this issue, this experiment selected data from 1-4 years (January 1, 2015 to December 31, 2018) to train the model and perform multi-step forecasts, aiming to measure the forecasting performance of the two methods under small data samples. To ensure fairness in the comparison, the same model parameters as in the previous experiment were selected and compared. The experimental results are shown in Table 1 below:

[0162] Table 1. Experimental results of multi-step sea surface temperature forecast using different experimental sample sizes.

[0163]

[0164] Small-sample experiments show that the addition of physical constraints can not only further improve the accuracy of the model when there is sufficient data, but also greatly improve the model's forecast results when there is insufficient data. This solves the problem of not being able to quickly and accurately obtain forecast elements due to insufficient data, which provides technical support for more accurate forecasting of sea surface temperature elements.

[0165] Element forecasting experiment

[0166] We used experimental data from parts of the Pacific Ocean over 1826 days (January 1, 2015 to December 31, 2019) to explore the performance of this method (0.95°S to 20°N, 135°W to 161.25°W). 70% of the dataset was selected for training, 5% for model validation, and the remaining 30% was used for testing and feature forecasting applications.

[0167] The beneficial effects of this invention are as follows:

[0168] 1) A machine learning multi-step forecasting method for regional grid mean sea surface temperature is proposed. Previous forecasting methods based on mean sea surface temperature were mostly targeted at specific buoy points, while the face-to-face regional forecasting method makes the forecast more valuable for application.

[0169] 2) With physical information constraints as the goal, the physical information of the mixed layer temperature heat budget equation is integrated into the neural network, and the sea surface temperature forecast results are made to conform to physical laws through iterative optimization.

[0170] 3) Based on the automatic differentiation function of neural networks, by first constructing a calculation graph of independent and dependent variables, and then solving the differentiation through neural networks, combined with the traditional difference method and Runge-Kutta method, a theoretical basis for multi-step sea surface temperature prediction based on physical information is constructed.

[0171] 4) 3D-CNN is used to pre-extract the feature elements of the input variables, and combined with the long-term series data processing capability of ConvLSTM, the input information is processed.

[0172] 5) The sea surface temperature data in the analysis data is used as the true value, and the network is optimized and iterated based on this. Combined with the multi-step forecast mathematical reasoning process, the multi-step forecast of sea surface temperature is completed and a good forecast effect is obtained.

[0173] As used herein, the term "preferred" is meant as an example, illustration, or illustration. Any aspect or design described herein as "preferred" need not be construed as being more advantageous than other aspects or designs. Rather, the use of the term "preferred" is intended to present the concept in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusionary "or." That is, unless otherwise specified or clear from the context, "X uses A or B" naturally includes either of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0174] Furthermore, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the aforementioned components (e.g., elements, etc.), the terminology used to describe such components is intended to correspond to any component (unless otherwise indicated) that performs the specified function of said component (e.g., is functionally equivalent to it), even if structurally not equivalent to the disclosed structure performing the functions in the exemplary implementations of this disclosure shown herein. Moreover, although specific features of this disclosure have been disclosed with respect to only one of several implementations, such features may be combined with one or more features of other implementations that may be desirable and advantageous for a given or particular application. Furthermore, with regard to the use of the terms “comprising,” “having,” “containing,” or variations thereof in the Detailed Description or claims, such terms are intended to be included in a manner similar to the term “including.”

[0175] The functional units in this invention embodiment can be integrated into a processing module, or each unit can exist physically separately, or multiple units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. The aforementioned devices or systems can execute the storage methods in the corresponding method embodiments.

[0176] In summary, the above embodiments are one implementation of the present invention, but the implementation of the present invention is not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made that deviate from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A deep neural network method for predicting average sea surface temperature, characterized in that, Includes the following steps: S1: Select satellite observation data and reanalysis grid data as model data samples; S2: Interpolation calculation: Using the linear interpolation method, daily mixed layer thickness data, daily sea surface zonal velocity data, daily sea surface zonal velocity data at a depth of 108m, daily sea surface meridional velocity data, daily sea surface meridional velocity data at a depth of 108m, daily sea surface temperature data, and daily sea temperature data at 108m are used to calculate the daily sea flow velocity data and daily sea temperature data at a depth of 10m in the mixed layer. S3: Data matching. In order to match the satellite observation data with the reanalysis grid data, the spatial information of the grid data with the lowest spatial resolution is first selected as the reference grid point. The remaining variable data are interpolated and matched to the reference grid point. Then, the satellite observation data and the reanalysis data are matched on the time scale, and finally the two data are matched in space and time. S4: Construct a training set for sea surface temperature forecasting; The satellite-observed sea surface temperature data and the reanalysis grid data are used as training sample features, and the sea surface temperature data in the reanalysis data are used as sample labels. S5: Construct a multi-layer network structure for a deep neural network model for predicting mean sea surface temperature that integrates numerical solutions for spatial partial derivatives. This model consists of the following three parts: The first part uses a 3D-CNN convolutional layer as a data feature extraction module to obtain the feature matrix data after feature dimensionality reduction as input; The second part is a 3D-CNN convolutional neural network, which uses spatial convolutional layers and employs a two-layer spatial convolutional module. Temporally, it selects the matrix obtained by fusing and reducing the spatiotemporal features of satellite observation data and reanalysis data as input. The third part is the spatiotemporal convolutional neural network 3D-CNN-ConvLSTM, which includes the following: The spatiotemporal convolutional LSTM layer uses a 3-layer spatiotemporal convolutional LSTM module, and the input is the matrix obtained by fusing the spatiotemporal features of satellite observation data and reanalysis data after dimensionality reduction. The physical information partial differential equation fusion layer incorporates the partial differential terms from the mixed layer temperature heat budget equation into the network for solution. The obtained partial differential terms are then calculated with the element variables. Combined with the difference calculation method in the traditional solution, the forecast output for the next time step is obtained. The multi-step prediction layer, based on the Runge-Kutta method, calculates the average slope of the prediction output at time i and the prediction output at time i+1. The average slope obtained is then used to calculate the average slope of the prediction output at time i+2, and so on, to obtain the result of the multi-step prediction. The formula for calculating sea surface temperature is as follows: in This represents the average daily sea surface temperature. Geographic information representing latitude, Geographic information representing longitude, Represents the zonal current velocity at the sea surface. Represents the meridional velocity of seawater. Represents the thickness of the hybrid layer. The density of seawater is represented by 1025. , The specific heat of seawater is 4000. R represents the bias term. Represents the net heat flux over the sea surface. This represents the net shortwave solar radiation flux absorbed by the sea surface. This represents the net longwave solar radiation flux absorbed by the sea surface. For latent heat flux, For sensible heat flux, the direction in which the ocean absorbs heat is considered positive; This represents the seawater temperature 10m below the mixing layer. The water flow velocity at a depth of 10m in the mixed layer is given by [reference to a specific point], both of which were calculated using interpolation. T represents the depth of the seawater. 0.5 The seawater temperature at 0.5m below the mixing layer, v 0.5 The seawater flow velocity at 0.5m below the mixed layer, T i The seawater temperature at depth i meters below the mixing layer. This is the trend term for temperature change over time. Based on this term and the Runge-Kutta method, multi-step temperature forecasting is achieved. Based on the Runge-Kutta method and combined with the traditional middle-difference method, satellite observation data from 7 days ago and reanalysis data corresponding to the remaining 11 variables required by the equation are used as time-series data inputs. Loss calculations are performed with the actual data from day (7+i) to obtain the forecast model for day i. The mathematical process is as follows: set up: , make: We can obtain: in: For interval average slope on ) Pick: have to: in, and These represent the current input and the future predicted value, respectively. For the differential trend term, For algebraic calculations on the input data, The differential relationship between input variables is expressed by a neural network. This is the weighting coefficient of the current value to the predicted value, set to 0.

1. The weighting coefficient of the previous value to the predicted value is set to 0.9; By combining the partial differential terms obtained from the neural network, the sea surface temperature data for day m is obtained.

2. The deep neural network method for predicting average sea surface temperature according to claim 1, characterized in that, The satellite observation data and reanalysis gridded data include daily downward solar shortwave radiation data, daily upward solar shortwave radiation data, daily downward solar longwave radiation data, daily upward solar longwave radiation data, daily sensible heat flux data, daily latent heat flux data, daily sea surface zonal current velocity data, daily sea surface meridional current velocity data, daily mixed layer thickness data, daily sea surface temperature data, daily temperature data 10m below the mixed layer, and daily current velocity data 10m below the mixed layer.

3. The deep neural network method for predicting average sea surface temperature according to claim 2, characterized in that, The constructed sea surface temperature (SST) forecast training set includes a dataset composed of 12 environmental variable elements spatiotemporally matched from satellite observation data and reanalysis gridded data. In addition, 12 temporally continuous 7-day environmental variable elements are used as the temporal features of the training set, and the latitude and longitude data of SST are constructed and added to the training set as temporal features. Finally, two spatially and temporally continuous image forms of data are obtained, including daily downward solar shortwave radiation data, daily upward solar shortwave radiation data, daily downward solar longwave radiation data, daily upward solar longwave radiation data, daily sensible heat flux data, daily latent heat flux data, daily seawater zonal current velocity data, daily seawater meridional current velocity data, daily mixed layer thickness, daily seawater current velocity data 10m below the mixed layer, and daily seawater temperature data 10m below the mixed layer. 3D-CNN adopts Feature extraction, dimensionality reduction, and fusion are performed using convolutional kernels of varying sizes in spatiotemporal convolutional LSTM. Spatial feature extraction is performed using convolutional kernels of different sizes, while the number of neurons in each layer of the 3-layer spatiotemporal convolutional LSTM is 64, 64, and 64, respectively; the number of neurons in each layer of the 3-layer spatial convolutional CNN is 16, 32, and 64, respectively.

4. The deep neural network method for predicting average sea surface temperature according to claim 1, characterized in that, Feature extraction from 3D-CNN layers yields fused feature data. Through inter-layer propagation and a gating mechanism, upper-layer memory information is adaptively updated, selectively transmitting information to avoid gradient explosion while capturing global spatiotemporal information. The input gate, forget gate, and memory gate mechanisms, combined with spatial information extraction during convolution, complete the partial differential equation calculation in the prediction process. The mathematical representation of the memory-update-output process is as follows: in, For the input data, p, q, and r are the sizes of the three convolutional kernels, respectively. Input gate pair at the current time The weight, Input gate pair at the current time The weight, This is the hidden state from the previous moment. Input gate pair at the current time The weight, This is the cell state update value from the previous time step. This is the bias information for the input gate. For the bias information of the forget gate, Forget the door pairing at the current moment The weight, Forget the door pairing at the current moment The weight, Forget the door pairing at the current moment The weight, For the current moment, remember the gate pair The weight, For the current moment, remember the gate pair The weight, This is the bias information for the memory gate. Output gate pair at the current moment The weight, Output gate pair at the current moment The weight, This provides the bias information for the output gate. For the Gate of Oblivion for, For input gate, For memory gate, The values ​​are obtained from the output gate and the cell state. To 3D convolution operations, For output gate, This is the unit state.

5. The deep neural network method for predicting average sea surface temperature according to claim 1, characterized in that, A computational graph between independent and dependent variables is constructed, and the automatic differentiation function of the neural network is used to solve the differential of the objective function. The difference between the physical equation before and after iteration is introduced into the loss function of the neural network. Based on the method of minimizing the loss function, the backpropagation mechanism of the neural network is used to iteratively optimize the differentiation result, so that the neural network can obtain the prediction result that satisfies the set physical law.

6. The deep neural network method for predicting average sea surface temperature according to claim 5, characterized in that, The feature selection method used in the 3D convolution process is the backward search algorithm without heuristics in the wrapper method.

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