Global Climate Model Bias Correction Using Deep Learning
Abhishek Pasula & Deepak N Subramani
Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru 560012, India. Divecha Center for Climate Change, Indian Institute of Science, Bengaluru 560012,
India. Abstract. Climate change affects ocean temperature, salinity and sea level, which in turn impacts monsoons and ocean productivity. Future projections by Global Climate Models (GCM) based on shared socioeconomic pathways (SSP) from the Coupled Model Intercomparison Project (CMIP) are widely used to understand the effects of climate change. However, CMIP models have significant bias compared to reanalysis in the Bay of Bengal for the time period when both projections and reanalysis are available. For example, there is a 1.5 [◦] C root mean square error (RMSE) in the sea surface temperature (SST) projections of the climate model CNRM-CM6 compared to the Ocean Reanalysis System. We develop a suite of data-driven deep learning models for bias correction of climate model projections and apply it to correct SST projections of the Bay of Bengal. We propose the use of three different deep neural network architectures: convolutional encoder-decoder UNet, Bidirectional LSTM and ConvLSTM. We also use a baseline linear regression model and the Equi-Distant Cumulative Density Function bias correction method for comparison and evaluating the impact of the new deep learning models. All bias correction models are trained using pairs of monthly CMIP6 projections and the corresponding month’s ORAS5 as input and output. Historical data and future projection data of CNRM-CM6 are used for training and validation, including hyperparameter tuning. Testing is performed on future projection data from 2021 to 2024. Detailed analysis of the three deep neural models has been completed. We found that the UNet architecture that is trained using a climatology-removed CNRM-CM6 projection as input and climatology-removed ORAS5 as output gives the best bias-corrected projections. Our novel deep learning-based method for correcting CNRM-CM6 data has a 15% reduction in RMSE compared to the widely used statistical correction technique, the Equidistant Cumulative Distribution Function (EDCDF).
1. Introduction
Climate change poses a growing and ongoing threat to social and economic well-being and has been characterized by the United Nations as one of the defining issues of our time. The ocean plays an important role in the dynamics of the Earth system, but climate change is modifying the physical and chemical properties of the ocean that have direct consequences for marine ecosystems and indirectly affect the land and atmosphere. The tropical sea surface temperature (SST) is particularly sensitive Global Climate Model Bias Correction Using Deep Learning 2
to climate change, with warming trends that disrupt the critical ocean-atmosphere interactions.
Quantifying the anthropogenic impact on climate change is a controversial subject that the climate research community must address rightly to adopt the correct climate policies. The World Climate Research Programme (WCRP) runs the Coupled Model Intercomparison Project (CMIP), whose data is used regularly by the Intergovernmental Panel on Climate Change (IPCC) in its assessment reports. Since the 1990s, the Coupled Model Intercomparison Project (CMIP) has facilitated the simulation of numerous Global Climate Models (GCMs) from a multitude of international institutes to enhance simulation accuracy and acquire precise scientific insights into the Earth’s future climate. The GCMs included in the CMIP Phase 6 have higher resolution compared to the GCMs of previous phases and use shared socioeconomic pathways (SSP) to offer projections for future climate change mitigation and adaptation efforts. The main demerit of GCMs is their potential for error, which can have significant implications for decision-making and policy making, with considerable biases in simulations that require correction methods to reduce model biases for impact studies. Several bias correction methods have been proposed in the literature for correcting GCM projections. The Equi-Distant Cumulative Distribution Function (EDCDF) method, a quantile-based mapping method for bias correction, is one of the most popular statistical bias correction methods used for the CMIP6 climate models.
However, this method is limited to addressing errors in the simulated frequency distributions in each cell of the grid individually and has other issues such as instability and overfitting. In recent years, deep learning has emerged as a prominent research methodology in various fields. This approach has penetrated almost every facet of our lives, offering intelligent solutions to challenges that were previously intractable or difficult to address. Today, machine learning technology has emerged as a powerful tool for solving difficult problems in climate science. A primary advantage of machine learning (ML) techniques is their ability to extract more pertinent information from multiscale datasets, thereby achieving a closer alignment with ground truth. Recent research has shown that machine learning is particularly effective in weather forecasting, predicting long-term climate trends, and filling in gaps in climate elements, with substantial advances being recorded. Deep neural networks from computer vision and image processing have been utilized effectively for a variety of tasks within the field of Earth system sciences, including weather forecasting. Recently, deep learning has been used to correct for bias in Tmin, Tmax, precipitation, and wind energy. The goal of the present paper is to explore the use of deep neural networks to perform bias correction in global climate models, with a focus on ocean surface properties. Specifically, we answer the following research questions. Global Climate Model Bias Correction Using Deep Learning 3
(i) Can bias correction of climate model projections be performed using deep neural operator learning? If so, what is the mathematical basis of this correction? (ii) What architecture is suitable for the task? How do the different architecture choices performin terms of figures of merit? (iii) How do deep models compare against a baseline of the linear model or the statistical Equi-Distant Cumulative Density Function (EDCDF) method? (iv) What data pre-processing strategies are essential for successful model development? We answer all the above questions and establish that the UNet architecture, a fully convolutional encoder-decoder operator network, is the best choice for climate model bias correction. Detailed ablation and architecture choice studies are completed with applications to correcting the sea surface temperature in the Bay of Bengal. The remainder of the paper is organized as follows. Section 2 describes the mathematical problem statement, describes the literature survey of bias correction methods, discusses the choice of neural architectures, and describes the data sets. The main UNet model is developed in Section 3 and the other architecture choices including linear models and statistical baselines are provided in Section 4. Section 5 document the comparison of difference bias corrections methods. Finally, a summary and future directions are given in Section 6. 2.
Method Development
2.1. Mathematical Problem Statement
Consider the spatio-temporal coordinates ( r, t ) in a domain r ∈ Ω ×
is the spatial domain. Within this framework, for a 2D spatial domain, we define U ( x, y, t ) as the climate projection generated by a General Circulation Model (GCM), while U [†] ( x, y, t ) represents the reanalysis data derived from observational measurements. We can conceptualize a bias-correcting mathematical operator G such that U [†] = G ( U ), which transforms the GCM projections into their bias-corrected counterparts. We propose to approximate this operator using a parameterized neural network N θ, trained on historical pairs of climate projections and their reanalysis datasets. Under the assumption that reanalysis data constitute the ground truth representation of the Earth system (specifically, oceanic conditions in our current study), the resulting neural operator effectively functions as a bias correction mechanism for climate projections. 2.2. Related Work
Bias correction of GCM projections could be classified into three types: (i) interpolation methods, (ii) dynamical downscaling, and (iii) machine learning methods. Global Climate Model Bias Correction Using Deep Learning 4
Interpolation methods Interpolation is a widely used bias correction method that adjusts mean and variance using projection and reanalysis (or observational) data. Some of the main interpolation-based statistical methods are as follows. The delta change approach uses observations as a basis that produces future time series with dynamics similar to current conditions. The linear scaling approach adjusts the monthly mean values and offers corrected data with a consistent variability with the observation data. Local Intensity Scaling (LOCI) combines the advantages of linear scaling with a correction of wet day frequencies (precipitation threshold). Although the linear scaling above accounts for a bias in the mean, it does not allow differences in the variance to be corrected. The power transformation is a nonlinear correction method in an exponential form to correct/adjust variance statistics. A similar exponential variance scaling method adjusts both the variance and the mean in a stepwise manner. Another method called distribution mapping corrects the distribution function of the model value so that it matches the data. The most widely used is the quantile mapping technique that adjusts the distributional properties of the model more closely to match those of the historical observations. There are different versions of quantile mapping methods available, of which the EquiDistant Cumulative Distribution Function (EDCDF) method is the most popular for bias correction of CMIP6 projections. Some studies have shown that EDCDF effectively reduces biases in GCM projections Sachindra et al.; Yang et al.; Mondal et al.. In this work, we have used EDCDF as the baseline for evaluating our neural model to correct the CMIP6 projections. Dynamical downscaling Dynamical downscaling, in contrast to interpolation and statistical downscaling, can generate dynamically consistent high-resolution climate data with a wide range of physical processes and their complex interactions within the Earth system. Traditional dynamical downscaling of future climate involves combining the initial and lateral boundary conditions of a general circulation model (GCM) with a regional climate model.
Coordinated Regional Climate Downscaling Experiment (CORDEX) is a global initiative of the World Climate Research Program (WCRP) focused on producing high-resolution climate change projections for different regions of the world. Machine learning methods Machine learning (ML) algorithms can make data-driven predictions using supervised learning that involves learning a mapping function between input and output variables. With the growing popularity and advances in machine learning, there has been an increase in the use of ML techniques with environmental data. These techniques are used to analyze and model complex ocean and atmospheric data, such as temperature, precipitation, salinity, and currents, to improve our understanding of the atmosphere and ocean dynamics and their impact on climate and weather patterns. Furthermore, ML is being used to develop more accurate and efficient model forecasting, which can have important implications for various sectors such as agriculture, energy, transportation, infrastructure planning, fishing, and offshore energy production. Deep neural networks, specifically convolutional and transformer models, have the potential to tackle spatio-temporal problems. Recently, deep learning has been used to correct for bias in Tmin, Tmax, precipitation, and wind energy. As far as we are aware, bias correction in CMIP6 has not been attempted using deep learning methods for the Bay of Bengal region. From the results cited above in other areas of Earth system modeling, the scope for machine learning for CMIP6 bias correction appears to be high. In this paper, we develop a suite of deep neural networks to correct errors in CMIP6 projections in the Bay of Bengal and identify the best architecture for this purpose. 2.3. Neural Architecture Choices
The selection of an appropriate neural network architecture N θ for bias correction of climate model projections presents a complex design challenge with multiple dimensions to consider. Several candidate architectures offer distinct advantages for handling spatiotemporal data patterns inherent in climate projections. These include Dense Neural Networks (DNNs), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), transformer models, and neural operators. DNNs offer simplicity and straightforward implementation, though traditional DNNs may struggle to capture the spatial dependencies crucial for climate field correction without significant feature engineering. CNNs excel at extracting spatial features through hierarchical pattern recognition, making them particularly suitable for processing gridded climate data where local patterns and spatial relationships are significant. RNNs, particularly architectures such as Long Short-Term Memory (LSTM) networks, specialize in temporal dependencies, potentially capturing seasonal patterns and long-term trends in climate model errors. With appropriate preprocessing strategies, RNNs can also handle spatial sequences by transforming gridded data into sequential representations through row-wise (latitude) or column-wise (longitude) scanning approaches. This versatility is further enhanced in Convolutional LSTM (ConvLSTM) architectures, which integrate convolutional operations within the LSTM framework, simultaneously capturing both spatial and temporal dependencies. Despite these advantages, training RNNs presents significant challenges, including vanishing and exploding gradients over long sequences, computational inefficiency with increasing sequence lengths, and difficulty in parallelizing the training process – all of which can impede effective learning of long-range climate patterns. Transformer models employ attention-based mechanisms that have demonstrated exceptional capabilities in modeling long-range dependencies, which could be valuable for capturing teleconnections and remote influences in climate systems. However, these models present significant Global Climate Model Bias Correction Using Deep Learning 6
implementation challenges for climate applications. Transformers typically require massive amounts of training data to achieve their potential, which can be problematic given the relatively limited historical climate records available (relative to the data available for language technology training). Their computational demands are exceptionally high, with quadratic scaling of memory and computation with respect to sequence length, making them resource-intensive for high-resolution climate fields. In addition, training stability issues often arise with transformers, requiring careful hyperparameter tuning, learning rate scheduling, and gradient clipping to achieve convergence. The positional encoding schemes that traditional transformers use may also need to be adjusted to irregular grids that are sometimes encountered in climate data. Neural operators such as Convolutional Neural Operators, Fourier Neural Operators, Geometric Neural Operators, and other architectures are sophisticated architectures designed to learn mappings between function spaces, enhancing bias correction generalization. Beyond architecture selection, the input-output configuration presents additional design considerations. Options include direct mapping from raw climate model outputs to corrected fields, inclusion of auxiliary variables as conditioning information, or embedding coordinate information to enhance spatial awareness.
The target output could range from complete field reconstruction to anomaly correction or adjustment of statistical parameters. The temporal resolution of the modeling approach represents another critical design choice. Given that most CMIP6 Global Climate Models provide monthly outputs, our neural model development naturally aligns with this discrete monthly timescale. This allows for capturing seasonal cycles and interannual variability while maintaining computational feasibility. Correction models could accept a sequence of several months of spatio-temporal projections or a single month as input and output a sequence of months or a single month. In our ablation study, we tried both options and present the
results. The combination of these architectural choices, input-output configurations, and temporal considerations creates avast design space of potential neural models. Our approach to navigating this space involves systematic experimentation with representative architectures, guided by physical understanding of climate processes and error patterns in the Bay of Bengal region. Specifically, we develop a convolutional encoder-decoder neural operator model, bidirectional LSTM model and ConvLSTM model. We also use simple baseline models, such as linear regression, to quantify the goodness of our bias correction method.
2.4. Data Sets
In this work, we selected the CNRM-CM6-1-HR Global Climate Model (GCM), which is a component of the CMIP6 suite, from the National Center for Meteorological Research (CNRM), France. Compared to earlier iterations, this model shows less bias in ocean Global Climate Model Bias Correction Using Deep Learning 7
temperature and salinity, and its predictions for ocean heat uptake closely resemble observed data. In addition to historical simulations from 1850 to 2014, CNRM-CM6 also provides future projections up to 2100 over four Shared Socioeconomic Pathways (SSPs)—SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5. These scenarios cover various routes for emissions, land usage, and energy use. The CNRM-CM6-1-HR has high spatial resolution with a 25 km ocean grid and a 50 km atmospheric grid, facilitating detailed simulations of atmospheric phenomena, regional flows, and ocean circulation. The training target for our bias correction model is reanalysis data. We selected Ocean Reanalysis System 5, developed by the European Center for MediumRange Weather Forecasts (ECMWF) in this work. ORAS5 is configured with the NEMO ocean model version 3.4.1 at a 25 km horizontal resolution and incorporates multiple observational datasets through a 3D-Var assimilation scheme with a 5-day cycle. The system assimilates sea surface temperature, subsurface temperature, salinity profiles, satellite sea level measurements, and sea ice concentration data. ORAS5 nudges the sea surface salinity to climatology. Historical CNRM-CM6-1-HR and ORAS5 employ an identical ocean model and span the same modeling period, but differ in initial and forcing conditions. CNRMCM6-1-HR considers observations about greenhouse gas concentrations, global gridded land use forcing, solar forcing, stratosphere aerosol data set, Atmospheric Model Intercomparison Project (AMIP) SST and sea ice concentration, ozone chemistry and aerosol forcing. ORAS5 uses initial conditions from ERA-40, ERA-Interim forcing fields, and different ocean observations assimilated in an operational ensemble reanalysis. Furthermore, CNRM-CM6 and ERA5 use different atmosphere models. ERA5 uses the Integrated Forecast System (IFS) model coupled with a land surface model (HTESSEL), while CNRM-CM6 uses the atmosphere-ocean general circulation model (AOGCM) with different initial conditions. ORAS5 includes freshwater discharge, while CNRM uses total runoff integration pathways to model river discharge. 2.5. Training, Validation and Testing
CNRM-CM6 historical data span from 1958 to 2014, and projections extend from 2015 to 2100. For training and validation, we utilized data from 1958 to 2020, dividing it into 768 months for training and 204 for validation. The test data set comprises data from 2021 to June 2024. The monthly climatology is derived from the ORAS5 reanalysis and subtracted from the input and target data. Our ablation study indicates that this anomaly correction produces optimal results. All monthly climatology-removed data from CNRM-CM6 and
ORAS5 were resized to 128 × 128 for our UNet model. This choice is to ensure that the dimensions have a power of 2 and that the original data resolution is not lost. ORAS5 is used as the target for all SSP scenarios. Global Climate Model Bias Correction Using Deep Learning 8
3. UNet: Fully Convolutional Encoder-Decoder Architecture
Figure 1 shows the UNet neural network architecture that we developed for bias correction of the climate model projections. This architecture was selected to combine the global context with local high-resolution features, making it particularly effective for our application, where fine details are as important as the overall structure. The input to the neural model is the pre-processed climate model projection, and the output is the bias corrected projection. During training, the target is supplied with the ORAS5 fields corresponding to the input climate model projections. The UNet architecture takes as input a 128 × 128 time slice of the monthly projection by CNRM-CM6. The CNRM-CM6 and ORAS5 data are available with a resolution of 85 × 85 in the Bay of Bengal study domain. These fields are bilinearly interpolated to 128 × 128. The processing is done by using a fully convolutional encoder-decoder structure. The encoder path comprises five downsampling stages using 3 × 3 convolutional layers with tanh activation and dropout, followed by 2 × 2 max pooling, with the number of filters doubling at each stage. The bottleneck contains two 3 × 3 convolutions with 1024 filters. The decoder mirrors this structure with five upsampling stages using 2 × 2 transposed convolutions, where each stage combines the upsampled features with the corresponding encoder features through skip connections (concatenate operation). Each decoder block includes two 3 × 3 transpose convolutional layers with tanh activation, and the final output is produced by a 1 × 1 convolution. The exact choice of the number of filters at each stage was reached during hyperparameter tuning on the validation data. We implement Python-based data processing tools and a UNet neural network implementation for bias correction of CNRM-CM6 SST and make our code available on GitHub ‡ . Figure 1. Schematic of the UNet fully convolutional encoder-decoder architecture for bias correction of CNRM-CM6. ‡ https://github.com/AbhiPasula/Climate-Model-SST-Bias-Correction-Toolkit Global Climate Model Bias Correction Using Deep Learning 9
3.1. Data Pre-processing
Through extensive experimentation we found out that pre-processing the input climate projections and output ORAS5 reanalysis using the monthly climatology from ORAS5 achieves the best bias correction results. Using ORAS5 data from 1958 to 2014, we calculate the mean of each month. Then, this calculated mean is removed from the climate model projections for each month and the corresponding ORAS5 target. During inference, the monthly climatology is added back to the output of our UNet model. We hypothesize that using climatology-removed data for training and inference allows the neural model to better learn the distribution of data.
4.1. BiLSTM
The BiLSTM model takes monthly CNRM-CM6 projections as input and gives a corrected field as the output. During training, ORAS5 is used as the ground truth Global Climate Model Bias Correction Using Deep Learning 10
target. The BiLSTM model treats ocean variables in a row-major and column-major format and applies 1D convolutional layers to extract their features. A BiLSTM layer with these encoded spatial representations is then used to estimate the bias-corrected fields. Figure 2 shows a schematic of the architecture. We performed ablations with only row-major and column-major data pre-processing and found that using both as two channels in the BiLSTM architecture is the best model.
Figure 2. Schematic of the BiLSTM architecture for bias correction of CNRM-CM6. 4.2. ConvLSTM
The ConvLSTM model is a spatio-temporal model that applies convolutions on spatial 2D data to obtain representations on which LSTM architecture is applied pixel-bypixel. This model can be used to accept any sequence length as input and output. During training, the CNRM-CM6 and ORAS5 data must be prepared appropriately. We performed ablations with multiple input and output sequence lengths. We found that the ConvLSTM model takes 4 month input sequences, each with dimensions of 85 × 85 pixels, and a 1 month output was the best. Figure 3 illustrates the architecture scheme of the ConvLSTM model. The ConvLSTM layers begin by enhancing the feature representation from 8 filters using a 7 × 7 kernel to 48 filters with a 3 × 3 kernel, before symmetrically reducing back to 8 filters. The final layer uses a Conv3D operation with a 3 × 3 × 3 kernel to reconstruct the output sequence.
4.3. Baseline Models
Linear Regression As a simple baseline, we develop a linear regression model. We implemented a pixel-wise linear regression, training for each individual pixel of the ocean field. Linear regression takes the flattened vector of the ocean field as input and predicts the corrected field for that specific pixel location. Global Climate Model Bias Correction Using Deep Learning 11
Figure 3. Schematic of the ConvLSTM architecture for bias correction of CNRM CM6. EDCDF Statistical Method The Equi Distant Cumulative Density Function (EDCDF) method is a statistical bias correction method popularly used for correcting climate model projections. EDCDF corrects the projections of the model by comparing the output of the model with observations in the historical period. This allows for bias correction of the CMIP6 fields by using the resulting CDFs to correct discrepancies between the model and observations. The bias-corrected CMIP6 field can be expressed as follows. x m−p ~~a~~ djusted = x m−p + F o [−] − c [[] [F] [m][−][p] [(] [x] [m][−][p] [)]] [ −] [F] m [ −] − c [[] [F] [m][−][p] [(] [x] [m][−][p] [)]] [,]
where x m−p ~~a~~ djusted represents the bias-corrected results, x m−p denotes the raw model projections, Fm−p is the CDF of the CMIP6 model simulations min the projection period p, F o [−] − c [and] [ F] m [ −] − c [stands for the corresponding quantile functions for observations] [ o] [ and] model simulations min the historical training period c, respectively. The EDCDFmethod assumes that the statistical relationship between observations and GCM projections during the training period remains valid for future projections at a given percentile. Its application to the CNRM-CM6 SST correction results in relatively higher RMSE, as shown in the results. 5. Results and Analysis
We trained our UNet architecture and all other architecture choices and present significant results here. First, we compare the RMSE for the test years of SST in the Bay of Bengal in Section 5.1, followed by a long-term analysis of the trend of SST in Section 5.2. Next, we show the monthly projections of CNRM-CM6 and the corresponding corrected projections in Section 5.3. 5.1. Comparison of models in test period
The RMSE of SST projections in the Bay of Bengal for the test years is shown in Table 1. The raw CNRM-CM6 climate model shows the highest RMSE values. The RMSE comparison across different GCM correction methods reveals UNet’s superior performance in all tested scenarios. UNet consistently achieves the lowest Global Climate Model Bias Correction Using Deep Learning 12
RMSE values, ranging from 0.4920 for SSP5 to 0.5018 for SSP1, indicating more accurate temperature predictions than other methods. Linear regression shows considerably higher RMSE values than EDCDF, highlighting the limitations of simple statistical approaches for complex climate patterns. BiLSTM and ConvLSTM demonstrate comparable error metrics, but fall short of UNet’s accuracy. These quantitative results provide strong evidence that UNet offers the most reliable approach to correcting climate model errors in the Bay of Bengal region.
5.2. Comparison of models in future projections
The long term annual sea surface temperature (SST) projections for the BoB from 1958 to 2100 for four different SSPs, SSP1, SSP2, SSP3, and SSP5, are shown in Fig. 4. Historical CNRM-CM6 consistently underestimates the temperatures compared to ORAS5 reanalysis. The longterm trend of SST shows significant variations between different correction methods and SSP scenarios. SST projections indicate substantial warming, with the UNet-corrected SSP5 scenario projecting increases of 3-4 [◦] C by 2100, while the more conservative SSP1 scenario suggests modest warming of 1-1.5 [◦] C. Despite their varying intensities, the consistent upward trend across all scenarios strongly suggests continued ocean warming through the twentieth century, with the magnitude of warming heavily dependent on future greenhouse gas emissions and climate policy decisions. Comparison between SSP scenarios reveals distinct warming trajectories that reflect their underlying socioeconomic and emission assumptions. SSP5-8.5 demonstrates the most dramatic warming, with temperatures reaching approximately 33 [o] C by 2100), SSP3-7.0 follows a similar but slightly moderated pattern, with end-century temperatures around 32 [o] C), SSP2-4.5 shows an intermediate warming path with temperatures approaching 31 [o] C by 2100), SSP1-2.6, representing stringent mitigation measures, shows the least warming with temperatures stabilizing around 30 [o] C after 2060). The magnitude of warming indicated by the UNet-corrected projections is less severe than that indicated by the EDCDF-corrected SST projections. The BiLSTM correction fails to effectively capture the variability in annual mean projections, producing overly smoothed temperature trends. ConvLSTM projections align more closely with EDCDF-corrected projections. UNet captures both the magnitude and variability of SST changes in the GCM bias correction, suggesting that future warming in the Bay of Bengal may differ from previous projections, with implications for regional climate patterns, monsoon behavior, and marine ecosystems. Overall, we see that the UNet correction has the lowest RMSE and captures the variability accurately. 5.3. Analysis of UNet Corrected CNRM-CM6 SSP2-4.5 SST Projections in 2021
Figures 5 and 6 display the monthly SST for 2021 from the reanalysis, raw projections CNRM-CM6 SSP2-4.5, projections corrected for UNet (UNet), EDCDF corrected SST (EDCDF), BiLSTM corrected SST (BiLSTM) and Global Climate Model Bias Correction Using Deep Learning 13
Figure 4. Annual mean SST from CNRM-CM6 projections, corrected projections from EDCDF, UNet, BiLSTM, and ConvLSTM. Table 1. RMSE in SST projections of test years obtained by different CNRM-CM6 correction methods.
The best values are highlighted in bold text. Linear Scenario CNRM EDCDF UNet ConvLSTM BiLSTM Regression
SSP1 1.2264 0.7723 0.6871 0.5018 0.5830 0.5210
SSP2 1.3480 0. 7483 0.6352 0.5091 0.5573 0.5340
SSP3 1.3494 0.8053 0.6255 0.5092 0.6968 0.5261
SSP5 1.2368 0.8253 0.7898 0.4920 0.5906 0.5046
ConvLSTM corrected SST (ConvLSTM) in the Bay of Bengal. Henceforth, we discuss only the SSP2-4.5 scenario and present the analysis for other SSP scenarios in the supplementary material. Winter The winter period (December-February) exhibits a pronounced north-south temperature gradient in the Bay of Bengal. The ORAS5 reanalysis shows temperatures of 26-27 [o] C in the northern bay, gradually increasing to 28-29 [o] C in the southern regions. CNRM-CM6 shows a significant cold bias during this period, with temperatures 1-2 [o] C lower than in the reanalysis, particularly in the northern and central regions where temperatures fall below 26 [o] C. In contrast, the UNet corrections substantially improve Global Climate Model Bias Correction Using Deep Learning 14
Figure 5. Monthly sea surface temperature (SST) in the BoB during 2021 Dec to May, comparing ORAS5 reanalysis data, raw CNRM-CM6 model projections, UNet-corrected SST (UNet), EDCDF corrected SST (EDCDF), BiLSTM corrected SST (BiLSTM), ConvLSTM corrected SST (ConvLSTM). these patterns, closely matching the ORAS5 reanalysis in both spatial distribution and temperature values. EDCDF correction tends to overestimate temperatures in the northern bay, particularly in December and January, failing to accurately capture the gradient intensity. BiLSTM performs similarly to EDCDF, with corrections showing excessive warming in the northern regions while maintaining reasonable patterns in the south.
ConvLSTM correction reproduces the general gradient, but misses the finer circulation features, particularly along the eastern boundary and in regions influenced by the WMC. Global Climate Model Bias Correction Using Deep Learning 15
Pre-monsoon The pre-monsoon season (March-May) demonstrates progressive warming across the basin. March initiates this warming phase, with temperatures beginning to increase, particularly in the eastern bay. April shows substantial warming and the ORAS5 reanalysis shows temperatures reaching 30 [o] C in the central and eastern regions, marking the development of the warm pool. May represents peak pre-monsoon conditions with temperatures exceeding 31 [o] C in parts of the central and northern bay. Throughout this period, CNRM-CM6 consistently underestimates temperatures by 12 [o] C and fails to adequately capture the formation of this warm pool. UNet corrections significantly improve these representations, accurately depicting both the spatial extent and intensity of the warming patterns, particularly in the critical central and eastern regions. EDCDF overestimates temperatures in the northern and western regions in March but shows improved patterns in April and May. BiLSTM correction generates a more uniform temperature field, albeit at the expense of mesoscale features in the eastern bay.
In contrast, the ConvLSTM correction demonstrates the least effective performance among correction techniques, failing to capture essential warming patterns in the central bay. Monsoon The monsoon season (June-September) shows distinctive SST patterns associated with monsoon circulation. June marks the onset of the monsoon, with ORAS5 showing temperatures of 29-30 [o] C in most of the bay and slightly cooler waters in regions affected by the monsoon. July and August demonstrate the established monsoon pattern with the Summer Monsoon Current (SMC) evident south of Sri Lanka and the Western Boundary Current (WBC) flowing northward along the Indian coast. September shows the beginning of monsoon withdrawal with slight warming in parts of the northern bay. CNRM-CM6 exhibits a cold bias throughout this period, particularly in the central bay, and fails to accurately represent the SMC’s thermal signature. UNet corrections substantially improve these representations, closely matching ORAS5’s depiction of basin-wide patterns and localized features associated with monsoon circulation. EDCDF correction shows slightly cooler temperatures than observed, particularly in the central bay. BiLSTM correction captures the general spatial pattern, but produces a more homogenized structure. ConvLSTM correction generates temperature patterns closer to CNRM-CM6 in August and September, particularly along the western boundary, failing to capture the influence of the EICC. Post-monsoon The post-monsoon period (October-November) transitions to winter conditions. October maintains relatively warm temperatures, with ORAS5 showing values around 29- 30 [o] C across much of the bay, while November displays the beginning of the winter cooling pattern with decreasing temperatures in the northern regions and the establishment of a north-south gradient. The East India Coastal Current (EICC) begins its seasonal reversal to southward flow during this period, influencing temperature patterns along the western boundary. CNRM-CM6 shows its most significant cold bias during this transition period, particularly in November, where the temperatures in the Global Climate Model Bias Correction Using Deep Learning 16
Figure 6. Monthly sea surface temperature (SST) in the BoB during 2021 June to Nov, comparing ORAS5 reanalysis data, raw CNRM-CM6 model projections, UNet-corrected SST (UNet), EDCDF corrected SST (EDCDF), BiLSTM corrected SST (BiLSTM), ConvLSTM corrected SST (ConvLSTM). northern bay are underestimated by more than 2 [o] C. UNet corrections demonstrate remarkable skill in reproducing the observed ORAS5 patterns, accurately capturing both the spatial distribution of temperatures and the onset of winter cooling, while accurately representing the thermal influence of the EICC along the western boundary. EDCDF correction shows excessive cooling in the northern bay in November. BiLSTM correction captures the general transition pattern, but does not capture important features, particularly along the western boundary. ConvLSTM correction fails to capture the development of the north-south gradient in November and misses the thermal signature of the EICC. Global Climate Model Bias Correction Using Deep Learning 17
The difference plots of each correction method on SSP2 with ORAS5 are shown in the supplementary information in section S3. Furthermore, similar analyses of the corrected projections of SSP1, SSP3, and SSP5 are also shown in the supplementary information sections S2, S4, and S5. 6. Conclusion
Our study demonstrates that deep neural operator learning can effectively correct biases in the climate projections by global climate models in the Bay of Bengal. We established that the U-Net architecture with an encoder-decoder structure and skip connections provides the mathematical foundation necessary to capture both spatial and temporal patterns in climate data. This approach significantly outperforms traditional methods and was trained on climatology-removed CNRM-CM6 inputs to focus on anomaly patterns and predict the corresponding corrected anomalies. Our experiments revealed that pre-processing the data by removing climatology is essential to obtain state-of-the art correction results. As a baseline, linear regression models and statistical EDCDFmethods were also evaluated. We found that baseline models provide basic correction capabilities but fail to capture the complex nonlinear relationships present in climate projections. Although ConvLSTM produced reasonable annual mean projections aligned with statistical methods, only the U-Net model consistently captured both spatial and temporal variability, outperforming all alternatives in reducing errors in the climate projections. This confirmed U-Net as the most suitable architecture for GCM error correction in the Bay of Bengal. Performance evaluation demonstrated a 15% reduction in root mean square error (RMSE) in SST projections compared to the widely used Equidistant Cumulative Distribution Function (EDCDF) method. This improvement highlights the ability of deep learning approaches to model complex, nonlinear, and spatially dependent bias structures inherent in global climate models. Looking ahead, the proposed framework offers promising opportunities for application in other ocean basins and climate variables, including ocean currents and atmospheric parameters. The bias correction capability of UNet could be extended to other dynamical variables such as Dynamic Sea Level and Salinity. The oceanographic implications of these corrected projections have also been explored in other papers. In the future, similar architecture development could be completed for atmospheric variables to get a complete picture of the future climate scenarios. Our work presents a structured approach and template for such future development. Data Availability
All the data used in this work is available for download from the respective data providers with links provided in the manuscript. Our code and data produced from this work are REFERENCES 18
available on GitHub § . Acknowledgment
We thank the Ministry of Earth Sciences and the Anusandhan National Research Foundation, Government of India, for their grants that allowed the purchase of the compute resources used in model training. The authors thank the members of the QUEST Lab at IISc for insightful discussion.