Impact Statement

Climate studies heavily rely on simulated climate data from the Coupled Model Intercomparison Project Phase 6 (CMIP6) due to its significant contribution in addressing data gaps. Nevertheless, the computational demands of physics-based models within CMIP6 necessitate huge HPC resources. To overcome this challenge, the proposed Pix2Pix GAN model enables the generation of global maps of SST, similar to the CMIP6 model, on a comparatively low hardware-based system and in a reduced timeframe. By combining domain knowledge with cutting-edge machine learning, this work represents an important step towards the accessibility of climate modeling tools and datasets.

2. Literature survey

The coupled model intercomparison project (CMIP) was established in 1995 by the Joint Scientific Committee and CLIVAR (Core Project of the World Climate Research Programme) Working Group on Coupled Models to facilitate ensemble climate modeling. Now in its sixth iteration, CMIP6 enables coordinated simulations across complex physics-based models (Eyring et al. Reference Eyring, Bony and Meehl2016). CMIP outputs like SST are valuable real-world surrogates. The ocean and atmosphere are intrinsically linked (Gill, A. E. Reference Gill2016); hence simulated oceanic variables serve as predictors in diverse climate studies (Richter & Tokinaga Reference Richter and Tokinaga2020 and Rivera & Arnould (Reference Rivera and Arnould2020)). In particular, SSTs quantify various oceanic phenomena like Atlantic Multi-decadal Oscillation (Goswami et al. Reference Goswami, Chakraborty and Rajesh2022), El-Niño Southern Oscillation (Karoly, D. J. Reference Karoly1989), North Atlantic Nino (Yadav et al. Reference Yadav, Srinivas and Chowdary2018), and so forth They have a significant impact on the precipitation of East Africa (Yan et al. Reference Yan, Wu and Li2020, Yang et al. Reference Yang, Li and Yu2018, Stevenson et al. Reference Stevenson, Fox-Kemper and Jochum2012, Endris et al. Reference Endris, Lennard and Hewitson2019), Maritime continent (Power et al. Reference Power, Delage and Chung2013, Xu et al. Reference Xu, Tam and Zhu2017), Southern and Eastern parts of Asia (Goswami et al. Reference Goswami, Chakraborty and Rajesh2022, Wang et al. Reference Wang, Luo and Liu2020, Yang et al. Reference Yang, Li and Yu2018), North America (Fasullo et al. Reference Fasullo, Otto-Bliesner and Stevenson2018, Yang et al. Reference Yang, Li and Yu2018) and so forth Hence CMIP6’s 165-year (1850–2014) SST simulations have various utilities in the climate studies of various continental regions (Krishnamurthy & Krishnamurthy Reference Krishnamurthy and Krishnamurthy2014).

Meanwhile, ML and deep learning (DL) offer versatile utilities for geoscientists and climatologists. It includes the prediction of rainfall (Endalie et al. Reference Endalie, Haile and Taye2022, Haq et al. Reference Haq, Novitasari and Hamid2021, Sharma et al. Reference Sharma, Das and Chakraborty2023), extreme events (Yan et al. Reference Yan, Wang and Li2022), and streamflow (Singh et al. Reference Singh, Vardhan and Sahu2023); downscaling of data (Niazkar et al. Reference Niazkar, Goodarzi and Fatehifar2023, Sharma et al. Reference Sharma and Mitra2022) and so forth Apart from these prediction models, generative models are also used in climate studies. In recent years various variants of GAN have started to be used to model turbulent climate dynamics (Gupta et al. Reference Gupta, Mustafa and Kashinath2020), flood frequency estimation (Ji et al. Reference Ji, Mirzaei and Lai2024), tipping point discovery (Sleeman et al. Reference Sleeman, Chung and Gnanadesikan2023) and so forth However, there is a lot to explore in this field where GAN can come up with more effective solutions compared to the traditional models.

Motivated thus, we develop a GAN architecture to generate CMIP6-like global SST fields based solely on observational data. This model has the potential to increase the accessibility of simulated data by replacing the physics-based model with a statistical model, hence reducing the hardware requirement.

3. Dataset and preprocessing

Our study uses two extensive datasets for model training and validation:

Observed Sea Surface Temperature (SST) data: Monthly global data spanning 1871–2010 was acquired from The Simple Oceanic Data Assimilation (SODA) v2.2.4 dataset (Giese et al. Reference Giese and Ray2011).

Simulated SST data: Ten ensembles from the Coupled Model Intercomparison Project Phase 6 (CMIP6) dataset for the EC-Earth3-CC and CMCC-CM2-SR5 models were selected, covering the same period.

Both datasets were preprocessed and resampled to a common spatial resolution of 3.75° × 2.5°, resulting in a data dimension of 144 × 48 towards longitude and latitude, respectively, for each month. Missing values were replaced with zeros, and observed data anomalies were calculated by subtracting the long-term mean.

For training, the first 130 years (1871–2000) of data were used. To match the dimensionality of the 10 CMIP6 ensembles, the observed data were replicated tenfold. This allowed training the model on each input data point separately for each ensemble. Validation was performed for the remaining 14 years (2001–2014). For each year, the mean of the 10 ensembles of the simulated data were used, ensuring the performance of the model was evaluated against the average ensemble behavior, instead of individual variations. This data processing and preparation strategy ensures thorough training on diverse simulated scenarios while evaluating the generalizability of the model against the average ensemble response.

4. Methodology

We develop a conditional generative adversarial network (cGAN) based on the Pix2pix architecture to generate simulated SST data based on the observed anomaly data as the condition. The cGAN contains two key components—a generator model to produce synthetic SST data, and a discriminator model to differentiate real versus generated SST.

4.1. Generator model

The generator is a convolutional neural network (CNN) that takes observed SST anomaly data as input and outputs corresponding simulated SST data. The Generator consists of a combination of a basic CNN block. As shown in Figure 1(a), the basic CNN block comprises convolutional (Conv2D) and transposed convolutional (ConvT2D) layers to down-scale (down) and up-scale (up) the spatial dimensions of the features, respectively. This layer is followed by batch normalization (BatchNorm2D) and ReLU activation.

Figure 1. The architecture of the generator model. (a) The basic convolutional neural network (CNN) block is used in the generator, (b) The full generator model, where the combination of the CNN block is used.

The input first undergoes initial feature extraction through two Conv2D and ReLU activation layers. The primary structure of the generator consists of four CNN blocks for downsampling features and an additional four blocks for upsampling. The final output layer is a ConvT2D layer to produce the simulated SST output. This architecture enables the generator to learn the spatial variability between input and output data. The full generator model is visually illustrated in Figure 1(b).

4.2. Discriminator model

The discriminator is a CNN that performs binary classification on SST data distinguishing between real and generated samples. As illustrated in Figure 2(a), it shares a similar CNN block structure as the generator, using Conv2D layers only to downsample the input.

Figure 2. Architecture of the discriminator model. (a) The basic convolutional neural network (CNN) block is used in the discriminator, (b) The full discriminator model, where the combination of the CNN block is used.

As in Figure 2(b), the discriminator takes both the input SST anomaly and either the real or generated SST data as input. These are concatenated and passed through initial Conv2D and ReLU layers, followed by five CNN blocks. The final Conv2D layer and sigmoid activation output the probability of the SST data being real or fake. By competing against the generator, the discriminator improves its ability to better differentiate between real and fake samples.

4.3. Adversarial learning

The generator and discriminator models are trained jointly through an adversarial learning approach. The objective of the generator is to synthesize increasingly realistic simulated SST data to fool the discriminator, while the discriminator aims to distinguish between real and generated SST. As the training progresses, both networks improve through this adversarial competition (Figure 3). Each input SST image is associated with 10 different ensemble members of simulated SST data. This aids the generator in learning to capture the variability across ensembles given the same input.

Figure 3. Architecture for adversarial learning for the proposed model.

Both models are optimized using the Adam optimizer with a learning rate of 0.00008. The discriminator loss is the binary cross-entropy between predictions and true labels for real–fake data. The generator loss combines binary cross-entropy for fooled predictions and Huber loss between generated and real SST. A batch size of 64 is used. To leverage multiple ensembles, we adopt a cyclic training strategy. Each epoch trains on a different ensemble of batch size 64, enabling the model to incrementally learn the distinct features of each. This mimics the transfer learning strategy to capture the inter-ensemble variability.

Training continues for 400 epochs(as after that overfitting starts), with model weights being saved at every 20 epochs. The best weights are selected by evaluating the temporal correlation, spatial correlation, and discriminator accuracy on the validation set.

5. Experimental results

To evaluate model generalization, we have trained and validated our model on mutually exclusive training and validation datasets. Training ensemble members and validating the ensemble mean also test the generalization ability across the ensembles.

Figures 4 and 6 show the evolution of the training data generation for the EC-Earth3-CC and CMCC-CM2-SR5 models till epoch numbers 320 and 260, respectively, as our GAN model shows the highest correlation in these epochs. Here, mean maps are calculated by taking the grid-wise mean of all the individual SST maps. The correlation maps are generated by calculating the grid-wise Pearson correlation coefficient between the generated and original maps, while the mean squared error (MSE) maps are generated by calculating the MSE for each grid cell between the generated and original maps. As shown in Tables 1 and 2, metric values are calculated by averaging the values across all grid cells of the respective metric maps. In contrast, the spatial metric values are computed by considering the correlation and MSE between the mean generated and original maps, effectively evaluating the overall spatial patterns. According to the tables, in early epochs, the generated SST exhibits a low correlation with real data, as evident from the high values of the MSE between the generated and the original maps. This can also be understood visually by observing the sample-wise correlation and MSE maps. The random initialization of the weights improves substantially by epoch 80 although as per the correlation map, the prediction of the equatorial and polar regions remains challenging. This is because, in the equatorial region, all the waves of the tropical regions come together because of the Inter Tropical Convergence Zone (ITCZ; Schneider et. al. (Reference Schneider, Bischoff and Haug2014)) varying the characteristics of that region from the other regions of the ocean. For the polar regions, very low SST makes the region hard to predict. The magnitude differences also decrease drastically. By epoch 320 (for EC-Earth3-CC) and 260 (for CMCC-CM2-SR5), when the model peaks at the correlations 0.542 (0.577) and 0.998 (0.999), even these difficult regions achieve the correlation value nearly to 0.5. The grid-wise magnitude differences also come down to almost 0 in most of the grid locations, making the average MSEs 0.420 (0.263) and 0.485 (0.295), respectively.

Figure 4. Evolution of the generator on training data for the EC-Earth3-CC GCM model.

Table 1. Epoch-wise updation of the correlations and mean squared error (approximated till 3 decimal places) for training and validation dataset for EC-Earth3-CC GCM model (the highest values for each column have been highlighted in bold)

Table 2. Epoch-wise updation of the correlations and mean squared error (approximated till 3 decimal places) for training and validation dataset for the CMCC-CM2-SR5 model

The evolution of the validation set in Figures 5 and 7 follow a similar trajectory, with temporal and spatial correlation improving from 0.306 (0.527) and 0.70 (0.974) at epoch 0 to 0.612 (0.615) and 0.999 (0.999) at epochs 320 and 260 respectively. Even the MSE maps have also followed the same by improving the temporal and spatial values. Unlike the training set, in the validation set the equatorial and polar correlations reach a value of more than 0.5 by the best epochs, indicating the ability of the model to learn the capture ensemble variability. We have also shown some sample SST maps (January, February, and March months of the year 2001) from the EC-Earth3-CC model and our proposed GAN-based model in Figure 8.

Figure 5. Evolution of the generator on validation data for the EC-Earth3-CC GCM model.

Figure 6. Evolution of the generator on training data for CMCC-CM2-SR5 GCM model.

Figure 7. Evolution of the generator on validation data CMCC-CM2-SR5 GCM model.

Figure 8. Sample outputs from EC-Earth3-CC GCM model at epoch 320.

In summary, adversarial training enables the model to incrementally generate increasingly realistic SST data over epochs, as quantified by the improved values of spatial and temporal/sample-wise correlation and MSEs (Tables 1 and 2). Validating on an unseen time period and the ensemble mean demonstrates the ability of the model to generalize across both time and ensembles. The proposed training strategy effectively captures ensemble variability in simulated SST generation.