ConvLSTM Based Temperature Forecast Modification Model for North China

Since the past century, weather forecasting has developed from the stage of forecasting based on experience and analogy to highly automated and high accuracy forecasting, thanks to the rapid development of atmospheric observation, more accurate description of atmospheric fluid mechanics and atmospheric physical processes, as well as the advances in digital computing (Benjamin et al. ^[1]; Shen et al. ^[2]). The development of high spatio-temporal resolution numerical weather forecast models and a new generation of Earth observation systems, including advanced operational remote sensing observations such as meteorological satellites and meteorological radar, has resulted in the amount of data generated every day far exceeding the ability of traditional data processing methods to extract, process and apply information (Agapiou ^[3]). In recent years, machine learning, especially deep learning (Lecun et al. ^[4]; Girshick ^[5]; Shan et al. ^[6]; Xia et al. ^[7]), has demonstrated a powerful ability to process big data. This method can effectively extract information from massive data and deal with nonlinear problems. It has been extensively studied in the fields of image processing and speech recognition, and has been widely applied in the detection and prediction of extreme events in the field of meteorology (Prabhat et al. ^[8]; Gao et al. ^[9]; Ham et al. ^[10]; Geng and Wang ^[11]), especially convective weather nowcasting (Shi et al. ^[12]; Shi et al. ^[13]; French et al. ^[14]; Geng et al. ^[15]).

Numerical weather prediction model is an important means of weather forecasting. It simulates atmospheric processes by solving a series of mathematical and physical equations. There are many uncertainties in the process of numerical simulation, such as inaccurate initial conditions and parameterization of physical process. Due to the chaotic characteristics of the atmosphere, inaccurate initial field and parameterization of physical process will lead to great uncertainty in model results (Huffman et al. ^[16]; Stevens and Bony ^[17]; Privé and Errico ^[18]; Bauer et al. ^[19]). In recent 20 years, the upgrading of observation technology, development of data assimilation techniques, advances in model parameterization of physical processes and the application of the model output statistics post-processing technology have effectively improved numerical weather prediction (Chen et al. ^[20]). Most post-processing methods correct the systematic bias in the original prediction system by establishing the functional relationship between the observed data and the predicted data, such as the model output statistics (MOS) method, which is widely used in model result correction based on the pioneering work of Glahn and Lowry ^[21]. But with the increase in the amount of observational data and model products, the limitations of conventional methods to deal with diversified data gradually emerge (Overpeck et al. ^[22]; Ma and Bao ^[23]). Deep learning technology provides a new way to solve the uncertainty of numerical weather prediction models and has achieved positive results. Post-processing can be viewed as a supervised learning task in machine learning. In the case of a large amount of data, deep learning can well fit complex functional relationships. For example, deep learning is used to replace traditional statistical post-processing to improve the forecasts by numerical weather prediction models (Glahn and Lowry^[21]; Overpeck et al. ^[22]).

A large number of deep learning algorithms have been studied in the field of atmospheric science at home and abroad, and some remarkable results have been achieved. In 2018, Rasp and Lerch ^[24] proposed a neural network-based correction method and conducted an experiment with the 2 m temperature prediction for ground stations in Germany. The experimental results show that the performance of the neural network method is significantly better than that of the traditional post-processing method, proving the feasibility of deep learning in this field. In 2019, Zhang et al. ^[25] integrated eight major meteorological parameters and simulated each parameter using long and short-term memory network (LSTM) to revise precipitation forecast in eastern China. In 2020, Grönquist et al. ^[26] proposed a hybrid model that combined the post-processing steps of convolutional neural networks and locally connected networks and applied it to global data, resulting in an increase of more than 14% in the continuous ranked probability score of the model. In 2020, Chen et al. ^[27] proposed an end-to-end post-processing method based on deep convolutional neural network, which effectively improved the prediction accuracy of 2 m temperature in Tianjin. In 2021, Kong et al. ^[28] proposed a deep spatio-temporal prediction model named DeepSTF for the post-processing of multi-station weather forecast based on spatio-temporal data.

In this paper, a deep learning model, encoder-decoder convolutional LSTM (ED-ConvLSTM), based on ConvLSTM and encoder-decoder structure is proposed for the error correction of the 2 m temperature forecast products by the European Centre for Medium-range Weather Forecasts (ECMWF) model. The capability of the deep learning model to correct 2 m temperature forecast at different time scales is tested. The model output statistics (MOS) (Glahn and Lowry ^[21]) method is used for comparison as it can process the original model output results by mining the relationship between meteorological observations and numerical forecasts. Meanwhile, a post-processing model based on convolutional neural network (CNN) is adopted to verify the superiority of ED-ConvLSTM in processing spatio-temporal information.

This article is organized as follows. Section 2 describes the datasets used. Section 3 introduces three post-processing methods and scoring rules. Section 4 presents our main results and Section 5 provides a summary.

The numerical model products used in this paper are from The International Grand Global Ensemble (TIGGE), a public dataset provided by the ECMWF (Molteni et al. ^[29]; Palmer ^[30]). The TIGGE data center archives the integrated forecasting products of 12 numerical weather prediction centers worldwide, providing data of basic physical parameters such as wind speed, temperature, precipitation, and humidity, and basic weather phenomena that explain the state of the atmosphere. The initial time of ECMWF model integration is set to 0000 UTC with a horizontal resolution of 0.5°×0.5°.

In order to fully train our networks and evaluate their forecasting skills, we also need to obtain ground observational data at specific forecast times. ERA5 is the fifth generation ECMWF atmospheric reanalysis dataset of global climate. Reanalysis data combine model data with observations from across the world into a globally complete and consistent dataset that can be used as an approximate application of observational data. ERA5 has strong reference value and can be used as marker data for deep learning (Muñoz-Sabater et al. ^[31]). In this paper, we use ERA5 2 m temperature reanalysis data as the marker data of ECMWF. The selected data is from January 2007 to August 2015 for the area covering 32.5°N-42°N, 110.5°E-120°E, and the horizontal resolution is 0.5°×0.5°.

Dataset D₀ consists of two parts including model prediction data X₀ and ERA5 reanalysis data Y₀.

X₀ is the ECMWF model data from January 2007 to August 2015. The initial time of ECMWF model integration is set to 0000 UTC and the horizontal resolution is 0.5° × 0.5°. The ECMWF provides 6-360 hours medium range weather forecasts with a time interval of 6 hours.

In this paper, North China (32.5°N-42°N, 110.5°E-120° E) is selected as the area for research, and the corresponding lattice number of North China is 20×20 at the horizontal resolution of 0.5°×0.5°. The points on the grid can be represented as (m, n), where m = 1, 2, ···, 20, and n = 1, 2, ···, 20. The data of each day is taken as a sample S(S = 1, 2, ···, 3165). The ECMWF products contain 25 meteorological parameters. According to characteristic selection experiment of 2 m temperature in Tianjin by Chen et al.^[27], the 10 m V wind component (10V), 10 m U wind component (10U), 850 hPa temperature (T-850), 925 hPa temperature (T-925), visibility (VIS) and mean sea level pressure (MSL) have the highest correlation with 2 m air temperature. As Tianjin is in North China, the experiment of Chen et al. ^[27] has strong reference value. We selected these six parameters as auxiliary information of deep learning to correct 2 m temperature. Table 1 shows the names of seven types of meteorological parameters and their abbreviations. Therefore, each sample S contains 7 parameters C(C∈(10V, 10U, T-850, T-925, VIS, MSL, 2 m temperature)), and 60 time steps t(t = (6, 12, ..., 360)). Therefore, the five-dimensional (5D) tensor X₀ of 20 × 20 × 60 × 7 × 3165 can be written as:

where S is the sample, t is the time step, C is the meteorological parameter, and (m, n) is the lattice point.

Y₀ is the ERA5 land surface temperature 2 m temperature reanalysis data from January 2007 to August 2015 for North China, and the horizontal resolution is 0.5°×0.5°. North China is also selected as the area for study, and the corresponding lattice number is 20 × 20. The five-dimensional (5D) tensor Y₀ of 20 × 20 × 60 × 1 × 3165 can be expressed as:

where S is the sample (S = 1, 2, · · ·, 3165), t is the time step (t = 6, 12, ..., 360), C is the meteorological parameter (C∈ (2 m temperature)), and (m, n) is the lattice point (m = 1, 2, · · ·, 20, and n = 1, 2, · · ·, 20).

With year, season, and proportion considered, the whole dataset is divided into training period data (training set) and prediction period data (test set). The training period is for the first 84 months (January 2007 to December 2013) and the prediction period is for the rest 20 months (January 2014 to August 2015). The total 2532 samples in the training set are about 80% of the overall data, and the total 633 samples in the test set are about 20% of the overall data. Each sample is the model forecast for a certain day.

Standardization before input of neural network training data can be very effective to improve the convergence speed and effect (Ioffe and Szegedy ^[32]). Since the units and magnitude of different meteorological parameters are inconsistent, it is necessary to standardize each layer of meteorological parameters separately after the datasets are created. In this paper, the Z-score standardization method is adopted to normalize different features of the original dataset to the dataset with 0 mean and 1 variance respectively. The normalization formula is as follows:

where μ is the mean of all sample data and σ is the standard deviation of all sample data.

In this paper, ED-ConvLSTM is used to revise the ECMWF temperature forecast, and the MOS method is adopted for comparison. Meanwhile, the CNN model is used to verify the spatial and temporal information processing capability of ED-ConvLSTM. The training index of the model is the root mean square error (RMSE) between the predicted value and the observed value.

The convolutional neural network is generally composed of input layer, convolutional layer, pooling layer, full connection layer and output layer. In the convolution layer, the convolution kernel is a weight matrix (such as a 3 × 3 matrix for a two-dimensional plane), which acts on the original input matrix step by step in a fixed order, and then generates a new matrix. The elements of the new matrix are:

where x is the element of the original matrix, S is the element of the new matrix, w is the weight of the convolution kernel, and (m, n) are the number of columns and rows of the convolution kernel, respectively. The convolution layer extracts features such as exponential linear unit and rectified linear unit through convolution operation and activation processing. The convolution layer at the bottom is used to extract low-level features, and the higher-level convolution layer extracts higher-level features by combining low-level features. To help the model develop certain generalization ability, we add the pooling layer immediately after the convolutional layer, and the resolution is further reduced by taking the maximum or average value. Such operation can make the recognition of the convolutional neural network obtain translation invariance. After multiple computations at the convolution layer and pooling layer, the intermediate variable enters the full connection layer, which can integrate the high-dimensional information with category differentiation and output the final result.

The grid field of physical quantity predicted by model has many similarities with common image data: the horizontal spatial distribution of physical quantity is like the pixel matrix of image, and the types and levels of physical quantity appear to be analogous to the concept of"channel"in image data. The revised model can make full use of the great advantages of convolutional neural network in the field of recognition to mine the possible mapping between numerical model prediction and observational data.

However, because the convolutional neural network cannot grasp the temporal information changes in the samples, the performance of the 2 m temperature correction is mediocre. Therefore, the ConvLSTM model based on the encoder-decoder structure is adopted to solve the problem of the poor performance of the convolutional neural network in the spatio-temporal task, especially in long time series. Encoder-decoder model is a typical sequence-to-sequence model (Lian et al. ^[33]). Originally developed for natural language processing, this model has been widely used in the field of spatio-temporal prediction in recent years. For example, Nguyen et al. ^[34] use genetic algorithm-based feature selection and encoder-decoder model to predict PM_2.5 concentration, and its prediction accuracy is higher than that of traditional models. The model consists of two independent structures: encoder and decoder. The former extracts the spatio-temporal features of the input data and sends the output signal of the encoding process to the decoder module. In the end, the predictive value of the decoder output can be obtained. To better extract the temporal and spatial features of model weather forecast data, we use ConvLSTM unit (Shi et al. ^[12]) to construct encoders and decoders.

LSTM (Graves et al. ^[35]; Smagulova and James ^[36]; Graves and Schmidhuber ^[37]) is a variant of recurrent neural network (Williams et al. ^[38]; Sherstinsky ^[39]), which is widely used in data sequential relationship mining, especially in dealing with long time series. An LSTM unit consists of memory cells, forgetting gates, input gates and output gates, etc. Output information is determined by the status of gating switches. ConvLSTM network is based on LSTM and convolution operation, so it is more effective for image feature extraction. LSTM gate structure is adopted to control information flow, and the expressions of input gate, cell state, forgetting gate and output gate are similar. LSTM differs from ConvLSTM in that the information input in each gate structure is replaced by the dot product with the convolution operation, and the dot product of cell state update remains unchanged. Part of the weight goes into the convolution kernel, and the rest goes into the loop kernel of the loop layer. The relationship between the parts can be expressed as:

where ∘ is the Hadamard product, xi represents the input at t time, xt represents the state retention probability of the output gate, f_t represents the state retention probability of the forgetting gate, c_t represents the state of the unit at time t, o_t represents the output probability of the output gate at time t, h_t represents the output of the hidden layer at time t, W_i and b_i respectively represent the weight and threshold of the input gate, W_f and b_f respectively represent the weight and threshold of the forgetting gate, W_c and b_c respectively represent the weight and threshold of the status gate, and W_o and b_o respectivelyrepresent the weight and threshold of the output gate.

As a typical spatio-temporal data processing model, ConvLSTM has been applied to weather prediction, such as sea ice concentration prediction, El Niño prediction and ocean temperature prediction (Liu et al. ^[40]; Wang et al. ^[41]; Zhang et al. ^[42]). This paper attempts to use ConvLSTM as the basic unit of codec to extract the spatio-temporal features of observational data. After repeated experiments to balance training efficiency and model correction effect, ED-ConvLSTM is finally selected to contain four hidden layers, each of which has 128 nodes, and each features a convolutional channel. Fig. 1 shows the detailed network structure of ED-ConvLSTM.

Figure 1.  The base framework of ED-ConvLSTM. The output length of both encoder and decoder is t. X_i, X_i+1, …, and X_i+t-1 are the input data, which consist of t time steps corresponding to historical selection features from i to i + t - 1. In this model, t = 60. Y_i, Y_i+1, …, Y_i+t-1 are the correction results of t time step from i to i + t - 1.

The network consists of an encoder and a decoder. The encoder consists of three layers of ConvLSTM. The first ConvLSTM receives a sample from the input sequence, encodes it and outputs the hidden state (H) and cell state (C). The last ConvLSTM cell transmits H and C to the decoder. Like the encoder, the decoder is also composed of three layers of ConvLSTM units, each of which accepts the hidden state (h) and cell state (c) of the previous unit as input and predicts the output of y_t at time t.

The method of model output statistics can establish a statistical relationship between the forecast products of numerical weather prediction models and the forecast objects of corresponding time. In this paper, the prediction field of 2 m temperature and its corresponding analysis field of ECMWF numerical forecast model in a certain forecast time are used to establish a linear regression equation:

where S_i is the regression set value at the ith moment, F_i is the model forecast value at the moment, a is the constant term, and b is the regression coefficient (solved by the least square method) (de Souza and Junqueira ^[43]). The forecast value S_{m, n, t} for different time tand space (m, n) is calculated by its corresponding a, b, and F_i.

To verify the prediction accuracy of different models, we test the results of these algorithms using root mean square error (RMSE) and temperature prediction accuracy (Acc) to evaluate the impact of these methods on prediction. RMSE is a general evaluation index for solving regression problems. The RMSE of temperature is expressed by the following:

where f is the deep learning regression model, K is the total number of dataset samples, x_k is the input, and y_k is the label. In addition to RMSE, temperature prediction accuracy T_Acc is used to ensure evaluation quality:

where N_p is the percentage of temperature forecast with absolute deviation no more than 2℃, and N_n is the percentage of temperature forecast with absolute deviation more than 2℃.

In order to analyze the effect of several post-processing models on the correction of ECMWF model forecasts in different forecasting timeliness, we select the data from the forecast period (January 2014 to August 2015). We use RMSE and Acc to evaluate the correction results of the ECMWF, MOS, CNN and ED-ConvLSTM. RMSE is negatively correlated with prediction accuracy. The lower the RMSE, the better the correction effect. Acc is positively correlated with prediction accuracy. The higher the Acc, the better the correction effect.

There are 633 samples in the test set, and the prediction time of each sample is 6 h-360 h in the next 15 days (the time interval is 6 h). The grid point of each time step is 20 × 20, and each grid point is used as a prediction result. Therefore, we first calculate all the test samples S(S=1, 2, ..., 633). We calculate RMSE and Acc of all grid points (m, n) for all test samples S(S=1, 2, ..., 633) and all prediction timescales t(t=6, 1, 2, ..., 360). Table 2 shows the average of all grid evaluation metrics for the test dataset. We also use the ERA5 reanalysis data to calculate the accuracy of the 2 m temperature directly predicted by the ECMWF and the modified 2 m temperature by MOS, CNN, ED-ConvlSTM post-processing models respectively. It can be seen from Table 2 that the direct prediction of 2 m temperature by the ECMWF has obvious errors. Several post-processing models can effectively correct 2 m temperature prediction by the ECMWF, and the fitting effect of the two deep learning models is more obvious.

In order to better visualize and analyze the overall effect and overall variation trend of several post-processing models as the forecast time increases, we use the mean RMSE and Acc of each day rather than each forecast time during the forecast period (January 2014 to August 2015). From the distribution of RMSE (Fig. 2), it can be seen that several revised models can significantly correct 2 m temperature forecast by the ECMWF. In the early stage of prediction, the correction effect of several post-processing models is not much different. On the first day, the RMSE of CNN is only 0.08℃ lower than that of MOS, and the RMSE of ED-ConvLSTM is 0.32℃ lower than that of MOS. With the increase of forecast time, the gap between CNN and MOS gradually increases and tends to be stable because CNN can effectively extract the complex spatial nonlinear relationship between 2 m temperature forecast and the labeled data. The RMSE of CNN is about 0.35℃ lower than that of MOS at every moment after the 7th day. It is about 0.85℃ lower than the ECMWF direct forecast. The ED-ConvLSTM can not only extract complex spatial nonlinearity, but also extract temporal information and capture temporal and spatial features of the data. This powerful ability to capture temporal and spatial features empowers ED-ConvLSTM with better fitting ability, and the longer the prediction time is, the more obvious the strength. On day 1, the RMSE of ED-ConvLSTM is 0.32℃ lower than that of MOS, and 1.02℃ lower than that of ECMWF. On day 15, the RMSE of ED-ConvLSTM becomes 0.73℃ lower than that of MOS and 1.22℃ lower than ECMWF forecast.

Figure 2.  RMSE of different post-processing methods for 2 m temperature at grid points in North China during from day 1 to day 15 on the test set.

In order to understand whether there are significant seasonal differences among several post-processing models, we use the data with a one-year forecast period (September 2014 to August 2015) to evaluate the RMSE distributions of temperature forecasts by the ECMWF, MOS, CNN, and ED-ConvLSTM in different seasons (Fig. 3). The RMSE of MOS, CNN and ED-ConvLSTM is significantly smaller than that of ECMWF, especially in November, December, January, February and March of the next year, indicating that the three methods improve the temperature forecast the most. In summer (June to August), the RMSE of the three methods and ECMWF forecast is very small, indicating that the error of summer forecast is small, and the correction effect is not obvious. However, in November, December and January, the RMSE of these four forecasting methods is high, and the error of winter forecast is large, but the correction effect is good. In general, the three post-processing methods can effectively improve the accuracy of ECMWF prediction. ED-ConvLSTM has the best correction effect with the RMSE of ED-ConvLSTM being 3.26℃, the RMSE of ECMWF is 2.21℃, while CNN and MOS have the RMSE of 2.51℃ and 2.86℃, respectively. In summer (June to August), the mean RMSE of ECMWF, MOS, CNN and ED-ConvLSTM are 2.85, 2.53℃, 2.31℃ and 2.20℃, respectively. In winter (December to January and February), the mean RMSE of ECMWF, MOS, CNN and ED-ConvLSTM are 3.31℃, 2.96℃, 2.511℃ and 2.14℃, respectively.

Figure 3.  RMSE of temperature forecast results of different post-treatment methods in different seasons at 2 m grid points in North China.

In this paper, an encoder-decoder ConvLSTM model named ED-ConvLSTM was developed to modify the 2 m temperature forecast of the ECMWF. MOS method was adopted for comparison. Meanwhile, the CNN model was used to verify the spatial and temporal information processing capability of ED-ConvLSTM. The results show that:

(1) Both ED-ConvLSTM and CNN deep learning post-processing methods can effectively correct ECMWF 2 m temperature forecast, and the correction effect is significantly better than that of the MOS method. The ED-ConvLSTM method can extract the spatio-temporal features of the data more effectively, and perform best in all time series.

(2) The deep learning model performs better in winter. This is because the prediction errors of numerical models are relatively larger in winter, and the post-processing model performs better in such scenarios.

The model proposed in this paper also has some limitations. Temperature changes are continuous, while other parameters such as precipitation usually have large abrupt changes. This paper only verifies the effectiveness of the model in modifying 2 m temperature forecast, and whether it is applicable to other parameters with large changes needs further study. The forecast time limit modified in this paper is 15 days, no more than 360 h. The application of deep learning for longer time scales (such as 10-30 d extension period), especially the correction of meteorological parameters for over 14 days, needs further study.