-
To construct various models and assess their prediction performances, various data are used. SST and T300 anomaly fields come from different datasets (Table 1). We used the Simple Ocean Data Assimilation (SODA) reanalysis products during 1871–1980 to formulate the POP model. For the ANN-based training process, we divided the predictors into pre-training and fine-training data. Because the observational period is still too short to meet the needs for having sufficiently large data, we additionally utilized data from 23 climate models during 1850−1980 that participated in the Coupled Model Intercomparison Project phase6 (CMIP6; Eyring et al., 2016; details in Table 2) to preliminarily train the CNN-LSTM and the hybrid models. Nevertheless, CMIP6 models have biases, which can affect the prediction accuracy of the constructed models. So, we used the SODA reanalysis products during 1871–1980 in transfer training (Pratt et al., 1991) to further calibrate the pre-trained models. Moreover, for the cross-validation analyses, the anomaly fields from Global Ocean Data Assimilation System (GODAS) reanalysis during 1994–2020 were used to evaluate prediction skills. In addition, we set an interval of more than ten years between the training and validation periods to eliminate the impact of the ocean's long-term memory on evaluation.
No. Reanalysis Data Set Institution Period 1 SODA University of Maryland Jan. 1871–Dec.1980 2 GODAS NCEP Jan. 1994–Dec. 2020 Table 1. Reanalysis data used in this study
No. CMIP6 Model
SourceModeling Group 1 AWI-CM-1-1-MR AWI 2 BCC_ESM1 BCC 3 CAMS_CSM1_0 CAMS 4 CanESM5 CCCma 5 CESM2_FV2 NCAR 6 CNRM_CM6_1 CNRM-CERFACS 7 E3SM_1_1 E3SM-Project RUBISCO 8 FGOALS-f3-L CAS 9 GFDL-CM4 NOAA-GFDL 10 GISS_E2_1_G NASA-GISS 11 HadGEM3-GC31-LL MOHC NERC 12 INM-CM4-8 INM 13 IPSL_CM6A_LR IPSL 14 MCM_UA_1_0 UA 15 MIROC_ES2L MIROC 16 MIROC6 MIROC 17 MPI_ESM1_2_HR MPI-M DWD DKRZ 18 MRI_ESM2_0 MRI 19 NESM3 NUIST 20 NorCPM1 NCC 21 NorESM2_LM NCC 22 SAM0_UNICOM SNU 23 UKESM1_0_LL MOHC NERC
NIMS-KMA NIWANotes: The variables of CMIP6 models used in pre-training are SST and T300 during Jan. 1850–Dec. 1980. Table 2. Details of the CMIP6 models used in this study.
ENSO was quantified by using Oceanic Niño Index (ONI; i.e., three-month running mean Niño-3.4 SST index), an area-averaged SST anomaly in the Niño-3.4 region). This index is the target of the predictand in models. In predictions, the ONI value is assigned to the last month within the considered averaging window; for example, the ONI in March is assigned to the mean of the January-February-March SST index. Its purpose is to prevent the prediction models from using any data in the future.
These data were used to configure a POP-based linear statistical model, an ANN model (CNN-LSTM), and their combined hybrid model (POP-Net). Various data were further used to make comparisons among predictions from different models.
-
The climate system and its variability are too complex to be clearly isolated and analyzed using traditional statistical methods. The POP analysis method was then developed to adequately extract periodically propagating or standing patterns from a multi-component system (Von Storch et al., 1988). In this section, we describe the POP approach briefly; more details can be found in Hasselmann (1988) and Von Storch et al. (1988).
Traditionally, EOF analyses are used to yield an optimal representation of anomaly covariance matrix to compress data freedom. The POP analyses are based on EOF analyses to further extract dominant oscillation patterns.
Assuming the m-dimensional vector series composed of EOF-derived PCs is X(t), X(t) can be generated by a first-order multivariate Markov process:
Here, t is time and
${\boldsymbol{\xi}} $ is Gaussian white noise matrix, which is uncorrelated with X(t). Then constant matrix B can be obtained with lag-1 and lag-0 covariance matrices of X(t). The linear system's normal modes, called POPs [${\boldsymbol{P}}_{{k}}\text{ (}{k}\text{=1, 2, …,}\text{m}\text{)}$ ; k is mode index], are the eigenvectors of the matrix B, which are usually complex due to the asymmetric nature of B.In addition, the state vector X(t) can be uniquely represented in terms of eigenvectors:
where
$ {Z}_{k}\left(t\right) $ is the temporal coefficient of normal mode${\boldsymbol{P}}_{{k}}$ at time t . In the following, for brevity, we take the complex POP modes that are often used to describe propagating features in space as examples for analyses.When a complex POP mode pair is selected, the linear system X(t) can be reduced to a two-dimensional space spanned by the real and imaginary parts of the POP mode. Here,
${\tilde{\boldsymbol{X}}}_{{k}}\text{(}\text{t}\text{)}$ is defined as the part of system X(t) represented by the kth pair of POPs (${\boldsymbol{P}}_{k}={\boldsymbol{P}}_{\text{r,}{k}}\text{+i}{\boldsymbol{P}}_{\text{i,}{k}}$ ; i is a symbol representing the complex Pk consisting of its real and imaginary parts), and the corresponding temporal coefficients${{Z}}_{{k}}\left(t\right)$ [${{Z}}_{{k}}\text{(}\text{t}\text{)=}{{Z}}_{\text{r}{,k}}\text{(}\text{t}\text{)+i}{{Z}}_{\text{i,}{k}}\text{(}{t}\text{)}$ ]. Thus,${\tilde{\boldsymbol{X}}}_{{k}}\text{(}{t}\text{)}$ is written asTheoretically,
${\tilde{\boldsymbol{X}}}_{{k}}\text{(}{t}\text{)}$ tends to appear in sequences of the type:$\cdots\text{→}{\boldsymbol P}_{\text{i,}{k}}\text{→}{\boldsymbol P}_{\text{r,}{k}}\text{→}{-}{\boldsymbol P}_{\text{i,}{k}}\text{→}{-}{\boldsymbol P}_{\text{r,}{k}}\text{→}{\boldsymbol P}_{\text{i,}{k}}\text{→}\cdots$ . The corresponding coefficients${{Z}}_{\text{i,}{k}}\text{(}{t}\text{)}$ lead${{Z}}_{\text{r,}{k}}\text{(}{t}\text{)}$ by about one-quarter of the “POP period” (i.e., T), which is one of the characteristic fields estimated by the POP analyses, representing the average period of the full cycle in the sequence:${\boldsymbol{P}}_{\text{i,}{k}}\text{→} {\boldsymbol{P}}_{\text{r,}{k}}\text{→} $ $ {\rm{-}}{\boldsymbol{P}}_{\text{i,}{k}}\text{→}{\rm{-}}{\boldsymbol{P}}_{\text{r,}{k}}\text{→}{\boldsymbol{P}}_{\text{i,}{k}}$ .In general, the POP analyses provide a statistical technique to extract periodic oscillation patterns in a subspace spanned by POP modes (
${\boldsymbol{P}}_{{k}}$ ). The corresponding temporal coefficients,${{Z}}_{{k}}\text{(}{t}\text{)}$ , are the coordinates in this space, representing the state of POPs. In particular, the evolution of the POPs state is explicitly specified as a dynamical model defined in Eq. (1). This linear assumption and the oscillation evolution characteristics of modes are demonstrated reasonably for ENSO research (Xu, 1990). This is the main difference between the POP analyses and any other EOF technique, which maximizes variances from a simultaneous covariance matrix. According to the scientific problems studied, the POPs with particular periods can be selected for analyses. As will be seen below in the next section, we selected two ENSO-related POPs with periods of 2–7 years for analyses and predictions. -
We selected two POP modes to formulate the POP-based prediction model in this study. Firstly, SST and T300 anomaly fields from SODA dataset between 120°E–80°W and 30°S–30°N during 1871–1980 were interpolated onto a 2° × 2° grid with its linear trend and short time scale removed (less than 15 months). Next, as shown in Fig. 1, we performed combined EOF analyses using the SST and T300 fields to obtain the first fifteen combined EOFs and PCs, which explain more than 70% of the total variance. Then, POPs were computed on the matrix composed of the fifteen PCs. We selected the two dominant POPs with interannual periods to establish the prediction model because ENSO is characterized by 2–7 year quasi-periodical oscillation. The first ENSO-related POP mode (POP-1) has a period of 3.0 years, and the second one (POP-2) has a period of 8.1 years, respectively. These two modes account for over 45% and 21% of the total variance.
Figure 1. Schematic diagram showing the POP-based analysis procedure to extract principal oscillation modes from the SODA dataset during 1871−1980.
The spatial patterns of SST and T300 for the real and imaginary parts for POP-1 are shown in Figs. 2a–d. The evolution of the POP mode is
$\cdots\text{→}{\boldsymbol{P}}_{\text{r,1}}\text{→}{-}{\boldsymbol{P}}_{\text{i,1}}\text{→} {-}{\boldsymbol{P}}_{\text{r,1}}\text{→} {\boldsymbol{P}}_{\text{i,1}}\text{→} $ $ {\boldsymbol{P}}_{\text{r,1}}\text{→}\cdots$ , as shown for subplots in Figs. 2a through d. Obviously, spatial patterns in Figs. 2a and d represent the peak ENSO-like phase characterized by the centers of SST and T300 anomalies over the central and eastern tropical Pacific; those in Figs. 2b and c are the imaginary parts of POP-1 associated with the transition conditions with weak SST and T300 anomalies occurring in the eastern equatorial Pacific. According to the POP mode oscillatory behavior mentioned above, the${{-}\boldsymbol{P}}_{\text{i,1}}$ pattern gradually evolves and replaces the$ {\text{P}}_{\text{r,1}} $ pattern within a quarter of the POP-1 period, i.e., after about 9 months. This transition appears in space as a gradual migration of the negative sign of$ {\boldsymbol{P}}_{\text{r,1}} $ into the eastern Pacific. Similarly, after another quarter of the period, the${-}{\boldsymbol{P}}_{\text{r,1}}$ pattern evolves and replaces the${-}{\boldsymbol{P}}_{\text{i,1}}$ pattern with negative SST and T300 anomalies in the central and eastern Pacific, where the ocean-atmosphere state develops into a La Niña condition. Other evolutions are seen in a similar way.Figure 2. Spatial patterns of (a−d) sea surface temperature (SST; shading) and the oceanic heat content of the upper 300 m (T300; contours) for the first ENSO-related POP mode (POP mode-1; oscillation period: T = 3.0 yr), which is obtained using the first fifteen combined EOFs and principal component time series (PCs) of SST and T300 fields from the SODA dataset. The general evolution of the POP mode can be illustrated in a two-dimensional subspace spanned by the real and imaginary patterns: (a) and (d) are the real patterns associated with the peak ENSO-like phase; (b) and (c) are the imaginary patterns associated with the transition phase; (e) the corresponding real [
${\text{Z}}_{{r,1}}\text{(}{t}\text{)}$ ; red] and imaginary [${\text{Z}}_{{i,1}}\text{(}{t}\text{)}$ ; blue] POP coefficient time series. The ONI is indicated by the black line. The contour intervals are 0.2 for the T300 and SST anomalies are shown in color bar.The POP-1 temporal coefficients,
$ {{Z}}_{\text{r,1}}\text{(}t\text{)} $ and$ {{Z}}_{\text{i,1}}\text{(}t\text{)} $ , are shown in Fig. 2e together with ONI. As expected, the coefficient$ {{Z}}_{\text{r,1}}\text{(}t\text{)} $ and ONI change synchronously and display a high cross-correlation with each other. In addition,$ {{Z}}_{\text{i,1}}\text{(}t\text{)} $ , as the coefficient of the transition mode, leads$ {{Z}}_{\text{r,1}}\text{(}t\text{)} $ by about a quarter of the POP-1 period.The spatial patterns of SST and T300 for the real and imaginary parts for POP-2 are shown in Figs. 3a–d. Spatial patterns in Figs. 3a and d represent the peak phase, and those in Figs. 3b and c indicate the transition phase. Compared to the spatial patterns of POP-1 for the peak phase patterns, the SST and T300 anomaly centers of POP-2 are more concentrated in the central and northeast Pacific. This spatial pattern of SST is like the North Pacific meridional mode (NPMM), which exhibits significant periodicities of more than 5 years (You and Furtado, 2018). Moreover, the POP-2 temporal coefficients,
$ {{Z}}_{\text{r,2}}\text{(}t\text{)} $ and$ {{Z}}_{\text{i,2}}\text{(}t\text{)} $ , are shown in Fig. 3e together with ONI. The real part coefficient$ {{Z}}_{\text{r,2}}\text{(}t\text{)} $ is strongly correlated with ONI. The imaginary coefficient$ {{Z}}_{\text{i,2}}\text{(}t\text{)} $ leads$ {{Z}}_{\text{r,2}}\text{(}t\text{)} $ by a quarter of the POP-2 period, i.e., about 24 months.Figure 3. The same as in Fig. 2, but for the second ENSO-related POP mode (POP mode-2; oscillation period: T = 8.1 yr).
In short, the POP-1 and POP-2 modes are two interannual-to-quasi-decadal modes related to ENSO. The real parts of temporal coefficients are highly correlated with the ONI, but the spatial patterns differ substantially. The POP-1 is the traditional ENSO-like mode, but the POP-2 is more like the NPMM pattern. These decomposed results are similar to those obtained using other Hadley Centre Sea Ice and Sea Surface Temperature data set (HadISST) and Ocean Reanalysis System 5 (ORAS5) dataset from ECMWF (not shown). As seen in their space-time evolution, both modes are critically important for ENSO evolution and prediction, which therefore are used for our POP-based prediction model formulation in the next section.
-
For a particular POP (
${\boldsymbol{P}}_{{k}}\text{=}{\boldsymbol{P}}_{\text{r,}{k}}\text{+i}{\boldsymbol{P}}_{\text{i,}{k}}$ ), its condition at certain time$ {{t}}_{\text{0}} $ is determined by the temporal coefficient${{Z}}_{{k}}\text{(}{{t}}_{\text{0}}\text{)}$ [${{Z}}_{{k}}\text{(}{{t}}_{\text{0}}\text{)=}{{Z}}_{\text{r,}{k}}\left({{t}}_{\text{0}}\right)\text{+}{\text{i}{Z}}_{\text{i,}{k}}\text{(}{{t}}_{\text{0}}\text{)}$ ]. Then, the state at future time${{t}}_{\text{0}}{+}\tau$ can be calculated fromHere,
${{ \lambda }}_{{k}}$ is the corresponding eigenvalue of the POP. Thus, the prediction problem becomes one of estimating the POP coefficient${{Z}}_{{k}}\text{(}{{t}}_{\text{0}}\text{)}$ instead.As described in section 2.2.1, the SODA analysis fields of interest were decomposed into individual modes during 1871–1980 using EOF and POP analyses, including the first 15 EOFs, PCs, and two ENSO-related POP modes. Next, we formulated the POP prediction model based on these results and evaluated the prediction performance using GODAS dataset. Specifically, SST and T300 anomaly fields at time
$ {t}_{0} $ from the GODAS dataset were projected onto the first 15 EOFs calculated from the SODA dataset to obtain the corresponding PCs. Then, the dot product between the vector PCs and the adjoint eigenvector D [${\boldsymbol{D}}_{{k}}\text{=}{({\boldsymbol{P}}_{{k}}^{{-1}})}$ ⊺] calculated from the SODA dataset was performed to obtain the POP coefficient${{Z}}_{{k}}\text{(}{{t}}_{\text{0}}\text{)}$ . Accordingly, we calculated the POP coefficient${{Z}}_{{k}}\left({{t}}_{\text{0}}{+}\tau\right)$ at any lead time$ \tau $ using Eq. (4). Finally, by combining the coefficient${{Z}}_{{k}}\left({{t}}_{\text{0}}{+}\tau\right)$ with POP spatial patterns, we obtained the predicted SST fields at time$ {{t}}_{\text{0}}\text{+}\text{τ} $ , including the Niño-3.4 index. Further, we could evaluate the prediction skills from the POP-based model. -
ENSO prediction is a multivariate problem, which requires us to consider spatiotemporal information. Therefore, we formulated an ANN model, named as CNN-LSTM, by combining CNN with long short-term memory (LSTM) arithmetic (Hochreiter and Schmidhuber, 1997), which was used both as an independent model to predict ENSO and as part of the subsequent construction of the hybrid model in the next section. As is well known, CNN can detect the essential features automatically without any human supervision. The LSTM is well-suited to process sequential information, as it has a versatile potential for managing critical information with long periods and time delays. Several studies have demonstrated the effectiveness of LSTM in capturing the El Niño index non-stationarity (Guo et al., 2020; Wang et al., 2021). Following this reasoning, as shown in Fig. 4, we formulated a space-information extraction module (SEM) and a sequence analysis module (SAM) based on CNN and LSTM algorithms, respectively.
Figure 4. Architecture of the CNN-LSTM model configured for the Niño-3.4 index prediction. The CNN-LSTM model consists of one input layer (the predictor as indicated by SST and T300), one space information extraction module (SEM) based on convolutional neural network (CNN) technique, one sequence analysis module (SAM) based on long short-term memory (LSTM) technique, and finally one output layer (the predictand). The input variables include SST and T300 anomaly fields between 0°–5°W and 50°S–50°N, from
$ {t}_{0}-11 $ months to the time$ {t}_{0} $ , in which$ {t}_{0} $ is the start month for the predictions. The ONI for the targeted prediction month is used as a variable for the output layer.The training process of the model was divided into pre-training and fine-training processes, where CMIP6 data were used in pre-training and SODA data were used in fine-training process. The model processing procedures are identical for different inputs. Detailed processes are described as follows. The CNN-LSTM model used SST and T300 anomaly fields over (0°–5°W, 50°S–50°N) for twelve consecutive months as predictors, and the Niño-3.4 index was the targeted predictand as an output. Firstly, all predictors were interpolated to a 5° × 5° grid and then, as an input, fed to the SEM, which contained two parallel paths that extracted the important spatial features from SST and T300 fields, respectively. Each path of SEM had two convolutional layers whose convolutional filter number was 12 and size of 5 × 3. The outputs of the SEM were reshaped and spliced into a feature map, which was then incorporated as input to the SAM consisting of two LSTM layers meant to capture the overall information of the sequence. The second LSTM layer of the SAM was linked to a fully connected layer that contained 64 neurons and links to the final output layer. In addition, we trained the CNN-LSTM model with four different initialization parameters while keeping the model framework fixed. Finally, the predicted Niño-3.4 indexes from the four calculations were averaged to obtain the final values.
-
So far, we have reviewed the POP analysis method, which can adequately extract propagating or standing patterns with specific periods from a complex system. Also, we constructed an ANN model, CNN-LSTM, for Niño-3.4 index prediction. We explored the combination of the two techniques to see whether a more effective ENSO prediction framework could be configurated. Consequently, we developed a hybrid model, named as POP-Net, which was composed of a CNN-LSTM module and a time-information extraction module (TEM; see Fig. 5). To facilitate the comparison, we set the CNN-LSTM module in POP-Net to have the same structure as the CNN-LSTM model presented in section 2.3, containing the SEM and the SAM as well. In addition, the TEM contained three-POP modes calculated using SODA SST and T300 data between (30°S–30°N, 120°E–80°W) with 5° × 5° resolution during 1871–1980. The periods of these POPs are 1.8 yr, 4.0 yr, and 7.2 yr, respectively. Therefore, the TEM could extract the POP temporal coefficients at specific frequency bands from the anomaly fields. In these cases, the attributes of the POP-Net were derived from topological properties of the climate neural networks and knowledge of physical processes.
Figure 5. The same as in Fig. 4 but for architecture of the hybrid model developed for the Niño-3.4 index prediction (POP-Net). The POP-Net model is composed of the POP analysis part and the CNN-LSTM model, with the former being added in by a time information extraction module (TEM). More specifically, the TEM is used to extract POP temporal coefficients at different frequencies from input SST and T300 data. Meanwhile, the convolution kernels in the SEM extract the spatial information from the input data (SST and T300). Then, the output data through the TEM and SEM processing are combined together as an input into the SAM to get more predictable information.
In the actual operations, when SST and T300 data from CMIP6 dataset in pre-training or SODA dataset in fine-training for twelve consecutive months were used as an input, the SEM could extract spatial information from the SST and T300 fields; on the other hand, the TEM calculates periodic POP temporal coefficients from input fields. Next, by combining the SEM and TEM outputs into the SAM, we obtained the final Niño-3.4 index predictive results. Just as the training process of the CNN-LSTM model described in the last section, we also trained the POP-Net with four different initialization parameters while keeping the model framework fixed. The final prediction values were obtained by averaging the results from the four calculations. This ensemble prediction method leads to a slight systematic improvement in prediction skills by canceling out the uncertainty within the individual calculation.
We used the AdaGrad optimizer (Duchi et al., 2011) to train the CNN-LSTM and the POP-Net models during 25 epochs, fix the learning rate to 5 × 10−3 for the pre-training process, and set the training epochs to 20 and the learning rate fixed to 5 × 10−5 for the transfer learning process. The CNN-LSTM and the POP-Net models were formulated separately for each targeted prediction month and lead time during the training process. As will be seen below, the POP-based analyses could be incorporated into an ANN-based model, transferring physical understanding and representation of ENSO processes into an improved prediction capability.
-
During the model validation process, we used the Pearson correlation coefficient (PCC), the root mean square error (RMSE), and the mean absolute error (MAE) between the predicted and observed ONI values to evaluate the prediction performance of the models. The PCC measures the linear correlation, and the RMSE and MAE measure the differences or errors between the predicted and observed ONI. The PCC, RMSE, and MAE are calculated as follows:
Here, n is the number of months during the validation period (1994–2020; taken as n=324);
${{Y}}_{{j}}$ and${{O}}_{{lj}}$ denote the observed and predicted ONI in the jth month at lead time of l month;$\overline{{Y}}$ and$\overline{{{O}}_{{l}}}$ are their averaged values. -
This paper focuses on the feasibility and effectiveness of the combined POP analyses and ANNs for ENSO prediction. In so doing, we first evaluate the prediction performance for the individual POP and CNN-LSTM models based on the GODAS dataset during 1994−2020; the validation results are shown in Fig. 6.
Figure 6. ENSO prediction performance assessed for the POP and CNN-LSTM models. (a) The all-season Pearson correlation coefficient (PCC; blue), root mean square error (RMSE; green), and mean absolute error (MAE; red) are used to quantify skill of the ONI as a function of the prediction lead month; the POP model is denoted by unmarked solid lines and CNN-LSTM model by solid lines with circular marks. The prediction skill of the ONI is also assessed by calculating the correlation coefficients as a calendar month in (b) the POP model and (c) the CNN-LSTM model. The contours highlight the correlation coefficients exceeding 0.5 in (b) and (c).
We calculated all-season PCC, RMSE, and MAE between the predicted and observed ONI values to assess the overall prediction performance. As shown in Fig. 6a, the POP model was able to make a valid prediction for only 6 months in advance (i.e., PCC>0.5). In contrast, the CNN-LSTM model is systematically superior to the POP model. The PCC skill of the ONI in the CNN-LSTM model is above 0.5 for a lead time of up to 15 months. Also, both RMSE and MAE are less than those in the POP model for all lead months. These results clearly indicate that the prediction error in the CNN-LSTM model is significantly smaller than that in the POP model. It is not surprising that such outcomes can be achieved, in practice, by using the complex ANNs such as the CNN-LSTM model, which can fit any nonlinear mapping given enough data theoretically (Scarselli and Tsoi, 1998). Many previous studies have also confirmed the advantages in using ANN models to make ENSO prediction over traditional linear statistical models (Tang and Hsieh, 2002; Wu et al., 2006; Guo et al., 2020).
Figure 6b shows the correlation between the POP-based predictions and observed ONI as a function of start months and lead times. The distribution indicates an obvious SPB phenomenon, with rapid decreases in correlation coefficients when the prediction is initialized from boreal spring, increasing notably to later months at longer lead times. For example, the predictions initialized from May were only able to achieve a successful prediction for the following three months. In contrast, the CNN-LSTM model shows higher prediction skills for almost all calendar months than the POP model (Figs. 6b, c). Furthermore, skillful Niño-3.4 index prediction could be made for lead times of one year when initiated prior to boreal spring. So, the CNN-LSTM model substantially alleviates the SPB problem, which increases effective prediction time to 14 months when the prediction is started from May. Nevertheless, there still exists a “gap” in the correlation distribution when the CNN-LSTM prediction is initiated in boreal spring with the lead times of 5−7 months.
In short, the POP model, as a simple linear statistical model, has limited prediction ability. The CNN-LSTM model benefits from its powerful nonlinear fitting ability, showing significantly better prediction performance than the POP model. Even without excessive training manipulations, the CNN-LSTM model produces skillful ENSO predictions for lead times of up to 15 months, which is already better than most linear statistical or dynamical models (Barnston et al., 2012; Tippett et al., 2012; Tang et al., 2018; Ham et al., 2019; Zhang et al., 2021).
-
In section 2.4, we combined the POP analyses with the CNN-LSTM arithmetic to formulate a hybrid model, POP-Net. The POP-Net model imposes additional constraint on the prediction process by incorporating the knowledge of characteristic ENSO space-time evolution patterns obtained from the TEM into the prediction. This combinational scheme not only reduces complexity of ANNs to extract helpful information from the input automatically, but practically improves the ENSO prediction performance. In this subsection, therefore, we will demonstrate the ENSO prediction performance using the POP-Net model.
The predicted Niño-3.4 index for 1–6 month lead times using the POP-Net model is shown in Fig. 7, together with the corresponding observed Niño-3.4 index. Here, only the predictions initiated from January of each year during 1994–2020 are shown. The results demonstrate that the POP-Net model can adequately predict the amplitude and variation of the Niño-3.4 index with at least 6-month lead times in advance.
Figure 7. Examples for the 6-month Niño-3.4 predictions in the POP-Net model (red) which are initialized from January of each year from 1994 to 2020; the observed Niño-3.4 index (black) is shown for comparison.
In addition, as expected, the hybrid model, POP-Net, further exhibits its ability to improve ENSO prediction skills, with correlation coefficients exceeding 0.5 up to a lead time of 17 months (Fig. 8a). Moreover, the POP-Net model further alleviates the SPB. As shown in Fig. 8b, the POP-Net model can make a valid prediction at least up to a lead time of 1 year when the predictions start from boreal spring, which is another significant improvement in prediction skill compared to the POP model and the CNN-LSTM model individually.
Figure 8. ENSO prediction skill in the POP-Net model. (a) The PCC (blue), RMSE (green), and MAE (red) between predicted and observed ONI as a function of different lead times; two experimental results are presented: solid lines indicate that the input variables in the POP-Net model include both SST and T300 fields, and the dotted lines indicate the input variable includes SST only. (b) The correlation coefficients between the POP-Net predicted and observed ONI as a function of lead months and start months. Contours highlight the correlation coefficients exceeding 0.5 in (b).
To compare the prediction performance with different models more clearly, Table 3 quantifies the prediction skills in terms of the PCC, RMSE, and MAE at lead times of 3, 6, 9, and 12 months, respectively. Evidently, the prediction skills of the POP-Net model are systematically superior to the other two models at different lead times. In addition, we conducted a sensitivity experiment to illustrate the effect of the input variables (SST and T300) on the model prediction skills. As shown by dashed lines in Fig. 8a, when the input variables are changed to include SST only, the ENSO prediction skill in the POP-Net model is significantly reduced. For example, the prediction has correlation coefficients exceeding 0.5 only up to a lead time of 12 months. Also, the prediction errors are larger than the experiment in which input fields include both SST and T300, indicating the vital role played by heat content in the long-term prediction of ENSO.
Model Metric Lead=3 month Lead=6 month Lead=9 month Lead=12 month POP PCC 0.76 0.52 0.27 0.16 RMSE 0.48 0.70 0.84 0.87 MAE 0.37 0.54 0.64 0.67 CNN-LSTM PCC 0.90 0.79 0.69 0.57 RMSE 0.41 0.55 0.64 0.73 MAE 0.33 0.44 0.51 0.57 POP-Net PCC 0.93 0.83 0.73 0.61 RMSE 0.35 0.51 0.62 0.70 MAE 0.28 0.40 0.48 0.55 Notes: Bold means the best results in multi-mode comparison. Table 3. Comparison among predictions made using POP, CNN-LSTM, and POP-Net models; here prediction validations are performed using GODAS dataset for 3-, 6-, 9-, and 12-month lead times. The input variables for all predictions made are SST and T300.
These results show that the inclusion of POP-based physical knowledge in the data-driven CNN-LSTM model does help improve the performance of ANN models. For example, the hybrid model can extend the effective lead time to 17 months, and further reduce the prediction errors, including significantly improved spring-time prediction skills (i.e., the alleviation of SPB). The combination of the POP analyses with ANN models is thus an effective method for predicting ENSO.
No. | Reanalysis Data Set | Institution | Period |
1 | SODA | University of Maryland | Jan. 1871–Dec.1980 |
2 | GODAS | NCEP | Jan. 1994–Dec. 2020 |