1. Introduction

Climate models and simulations can generate future projection simulation data, with increasing spatial and temporal resolution as well as improving cloud-resolving radiative and microphysics models (Randall et al. 2007; Bador et al. 2020). Future computing power eventually allows global climate models to simulate low clouds at 10-m resolution until 2060 if computing power improves at a rate of Moore’s law (Schneider et al. 2017). At the same time, climate model simulation results are increasingly used for practical applications and more granular decision-making such as climate resilience assessments at specific sites or for specific issues. For example, the impact of climate change on soil and groundwater contamination has been studied recently, because extreme precipitation and/or shifts in precipitation/evapotranspiration regimes could remobilize contaminants and proliferate contaminated groundwater (Maco et al. 2018; Libera et al. 2019; Xu et al. 2022). This large volume of simulation outputs with high spatial–temporal resolution overwhelms the capacity of computing powers and resources when climate scientists and practitioners analyze trends and mechanisms under warming climate scenarios. Furthermore, the rapid evaluation of climate impact assessment may downturn due to the increasing volume of climate simulations with a variety of ensemble of models and scenarios.

Climate classification—or identifying similar climatic regions or zones—has been used to understand the spatial variability of climate across a large area or facilitate the assessment of the climate change impact. Such a classification essentially reduces the dimensionality of the vast climate simulation data into a set of zones. We can then understand the climate spatiotemporal patterns at a particular region or location without querying large climate datasets. Historically, there are multiple climate classifications available across the world (Köppen 1884; Peel et al. 2007; Cui et al. 2021a). For example, the most popular and accepted climate classification, Köppen–Geiger classification (KGC) (Köppen and Geiger 1936), well represents the empirical association with local vegetation and captures the long-term mean climatologies.

However, widely used climate classifications are often relied on deterministic definitions by human experts subjective based on prescribed thresholds (Köppen 1884; Peel et al. 2007; Beck et al. 2018; Cui et al. 2021a). The Köppen–Geiger schema and the updated versions identify five main categories and 30 subcategories based on the threshold values of temperature and precipitation. However, the schema is subjective to empirical biome distributions and thus difficult to scale when taking into account other variables (Beck et al. 2018; Cui et al. 2021a) for quantifying comprehensive similarities of climate patterns. In addition, there are some imperfections as different climate regions have been delineated based on the extent of plant species, rather than actual climatological parameters only temperature and precipitation (Triantafyllou and Tsonis 1994).

For validation and confidence needs, one must consider various uncertainties in the climate simulations: A simple average across ensembles of climate projections does not convey the modeling uncertainties with the underlying physics, thus oversimplifying across spatial and temporal transitions of the climate regimes (Ganguly et al. 2015). To address these limitations, it is important to develop a data-driven approach for climate zone delineation without subjective definitions. In particular, since climate change potentially alters these zones in the future, it is critical to develop objective and automated approaches for defining zones.

Machine learning (ML) techniques such as clustering have used new climate indices to better understand the complexity of weather and climate over the last decades. Clustering techniques are widely performed in Earth science to group various unique regional and global spaces based on weather/climate, hydroclimate, and ecohydrological patterns based on k-means clustering (Zhang and Yan 2014; Coe et al. 2021; Wainwright et al. 2022), hierarchical clustering (Metzger et al. 2013; Dechpichai et al. 2022), multitask learning (Papagiannopoulou et al. 2018), and principal component analysis (PCA) (Bueso et al. 2020). [Note that PCA is also known as empirical orthogonal function (EOF) in climate science, and we use PCA and EOF interchangeably in this study.] Many climate studies used PCA as a dimensionality reduction method (Coe et al. 2021; Chattopadhyay et al. 2020). This approach has some limitations as it is used to find only a few of the strongest signals and all the signals are orthogonal to each other, which leads to difficult physical interpretation. While these unsupervised ML approaches characterize global and local unique patterns in data-driven fashion, there needs to be an exponential demanding computing power when an application size to clustering analysis has increased despite available scalable clustering algorithms (Bahmani et al. 2012; Sumengen et al. 2021).

In recent times, artificial intelligence (AI) technologies, such as deep neural networks (DNNs), have transitioned from traditional rule-based methods to data-driven approaches. These advancements showcase remarkable capabilities in classification, pattern recognition, and object generation, particularly in the field of natural language processing (Devlin et al. 2018; Xu et al. 2019). For climate science applications, DNNs have been increasingly used to identify hidden patterns in climate studies from the large quantities of climate simulation datasets (Camps-Valls et al. 2021; Watson-Parris et al. 2022). For example, Liu et al. (2016) first introduce DNNs to detect extreme climate patterns from historical records. Chattopadhyay et al. (2020) leverage four layers of convolutional neural network (CNN) to predict climate patterns over North America based on predefined four clusters via k-means. Mittermeier et al. (2022) train DNNs with phase 6 of Coupled Model Intercomparison Project (CMIP6) large ensembles to classify 29 important circulation types over Europe. Autoencoders (AEs; Kramer 1991; Nair and Hinton 2010), a deep learning technique that leverages dimensionality reduction, show exploratory powers free from artificial assumptions to better represent underlying data structures (Racah et al. 2017; Kurihana et al. 2021). Tibau et al. (2021) argue that using autoencoders as a dimensionality reduction method addresses some problems the classical methods exhibit: first, finding the proper kernel to keep a nonlinear structure of data into a low-dimensional space, and second, creating understandable latent space (representation of original data in the lower-dimensional space) compared to the standard methods. Furthermore, as the typical dimensionality reduction approach usually involves summarizing climate model output information by calculating means and variances without maintaining information about extreme weather events, the advanced DNN approach may open up a new research approach to address this problem.

In this study, we present an unsupervised climate classification workflow to reduce the dimensionality of complex spatiotemporal climate simulation outputs and to identify and map distinct climatic zones relevant to hydrometeorology across the conterminous United States (CONUS) and their changes in the future. In particular, we leverage autoencoders to reduce the dimensionality of the extensive climate data on lower-dimensional space that captures essential climatological information. We also develop a clustering autoencoder for climate classification by integrating an online clustering algorithm to reduce exponentially increasing clustering time and increase the capacity of data for further generalization. Although this study focuses on the precipitation and evapotranspiration (ET) that are relevant to hydrological impacts such as droughts and groundwater assessments, the approach is general for any climate variables, supporting access to complex climate simulation outputs in a compact form by keeping the relevant climate information. All the workflow is based on the cloud platform such that we can assess the climate classification anywhere across the CONUS without downloading vast amounts of climate data.

The remainder of this article is as follows: Section 2 describes the GFDL-ESM2G and preprocessing steps used in our workflow. Section 3 describes the algorithms used for unsupervised climate data clustering: standard autoencoder that works with k-means clustering to perform dimensionality reduction and clustering in two different steps and clustering autoencoder that is capable of training and testing these two steps in an end-to-end fashion, and section 4 evaluates the cluster patterns geographically and in ET–precipitation (PR) space.

2. Data

Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G; Dunne et al. 2012, 2013) is one of the participated models in CMIP5 (Taylor et al. 2012) that provides a comprehensive ensemble simulation framework of global climate projections under different represented concentration pathway (RCP) scenarios. In this study, we use the downscaled monthly dataset (Maurer et al. 2007). The ocean dynamics of GFDL-ESM2G highlights the high fidelity of ocean carbon and heat content variability, resulting in a relatively shallow thermocline and weaker ENSO compared to observations. We select the GFDL-ESM2G to train and test our unsupervised learning approach due to the less bias for the precipitation and temperature (i.e., associated with evapotranspiration) projections (Karmalkar et al. 2019).

In particular, our study focuses on the CONUS region that covers a spatial extent from 25.5625° to 52.8125°N, −124.0625° to −67.0625°E. The dataset we used has the grid cells that contain mean-monthly climatic variables downscaled to a fine resolution of 0.125° using monthly bias-correction spatial disaggregation (BCSD) techniques (Bureau of Reclamation 2013). The covered area contains 219 × 457 grid cells. Used data are based on global climate projections from the World Climate Research Programme’s CMIP5. The BCSD procedure is done in two steps: First, global climate model (GCM) historical simulations are compared to observations in order to identify and remove biases from the projection dataset using quantile mapping [a recent bias-correction approach, popular in climate science (Thrasher et al. 2012)] constructed from daily GCM simulations and observation values. Second, the GCM projections of step 1 are spatially downscaled to the desired resolution. It is performed for the whole spatial domain on a specific time step basis. Finally, in this step, the historical climatology and spatially disaggregated changes in the given time step measured from that climatology are merged. The downscaled dataset is publicly available (Maurer et al. 2007).

Since precipitation and evapotranspiration have different ranges of values, we standardized data in order to provide an equal contribution of each variable to our cluster analyses (see step 2 in Fig. 1). Standardization is performed for each grid cell by removing the mean and dividing by the standard deviation. In general, a single or combination of climate variables is defined as the anomaly time series to accurately describe climate variability over large areas than the raw data would do. Moreover, the nature of climate variables is to contain recurrence patterns of seasonality, especially dominant in the midlatitude regions, leading to strong temporal autocorrelations. To get rid of the seasonal component, we removed the 3-month-running mean from the monthly data of both precipitation and ET. Finally, we applied area weighting for latitude to each grid cell for each monthly value to ensure that the value of each latitude and longitude location is treated equally. We achieve this by weighting each data by the cosine of the latitude. Given that the outputs of climate models are uncertain and the projected changes in precipitation events are not homogeneous in space and time, in this study, we incorporate all four representative concentration pathway (RCP) scenarios (i.e., RCP2.6, RCP4.5, RCP6.0, and RCP8.5) from GFDL-ESM2G that participates in the CMIP5.

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Illustration of our workflow of unsupervised climate data clustering. 1) Data collection: download CMIP5 GFDL-ESM2G simulation downscaled to a resolution of 0.125° over CONUS (Bureau of Reclamation 2013) between 1950 and 2099 from the downscaled CMIP3 and CMIP5 climate and hydrology projections. Select ET and PR (Precip) for data processing. 2) Deseasonalized and scaled: standardize the downloaded data by subtracting the mean and dividing by the standard deviation for each grid cell to scale different variables in the same range. Subtract the 3-month-running mean from the monthly data to remove the seasonal component. 3) Subdivide and patch: subdivide each snapshot of 219 × 457 grid cells into a smaller unit of 16 × 16 grid cells × 3 months, allowing efficient training of deep learning models. 4) Train: split the data between 1950 and 2022 into training and testing sets with 70% and 30%, respectively, leaving the data after 2021 for the evaluation step. 5) Clustering: train clustering algorithms (see section 3 in detail). 6) Cluster label prediction: evaluate cluster label predictions under future climate scenarios.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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After the transformation of data, we then handle each snapshot at 219 × 457 grid cells as image data to enable efficient learning of physical features by deep neural networks. We spatially subdivide 219 × 457 pixel “image” data into a 16 × 16 pixels × 3 month scale, ≈2° × 2° area, giving a smaller geographical and temporal unit, patch. The patch creation process (i.e., regrid of climate snapshot image) is performed by sliding every eight grids spatially with the extraction of large numbers of overlapping patches. This may provide an additional degree of translation invariance to our neural networks. We then split the patches into three windows: historical (1950–2020), midcentury (2021–60), and late century (2061–99). We only use 1 468 214 patches sampled from 70% of patches at the historical time window to train our neural networks and leave 30% for clustering and testing.

In addition to the climate variables, we also consider elevation data at 4-km spatial resolution from the PRISM dataset and regridded to 14 km (PRISM Climate Group 2014) to compare resulting cluster patterns from autoencoder and clustering. Figure 2 visualizes long-term monthly mean (Figs. 2a–c) for precipitation, ET, and recharge (difference between precipitation and ET), as well as elevation data. We add elevation to our evaluation because it is roughly associated with precipitation and temperature variables (see Fig. A1) used by the KGC scheme (Köppen 1884).

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Four variables used for training and testing unsupervised climate clustering. (a) PR and (b) ET are monthly averaged over from 1950 to 2099 from GFDL-ESM2G; (c) recharge ratio is calculated based on the subtraction of the monthly ET from the monthly PR and then takes the average from 1950 to 2099; (d) elevation over CONUS uses PRISM 4-km resolution dataset (PRISM Climate Group 2014).

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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Figure 3 presents the probability density functions (PDFs) of precipitation (Figs. 3a,b) and ET (Figs. 3c,d) for RCP2.6 (left column) and RCP8.5 (right column) to investigate differences between two RCP scenarios for the entire dataset. We highlight the lowest and highest radiative forcing scenarios used in the Fifth Intergovernmental Panel on Climate Change Assessment Report. Each plot shows distributions of monthly spatial averaged data across the CONUS. There is a historical PDF marked in blue against midcentury or late-century PDFs in orange and red, respectively. We also calculated the mean-monthly precipitation and ET for each future time window. Different mean-monthly values are noticeable between the 3 time periods.

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PDF for the spatial averaged monthly PR and ET values of RCP2.6 and RCP8.5 scenarios from GFDL-ESM2G simulation over the entire CONUS area. We show the distribution from midcentury and late century to be overlaid to that of historical data.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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As shown in Fig. 3, the distributions of precipitation and ET in the mid- and late century shift toward higher values than the values in historical time and become the long tail in extreme events. The value of mean precipitation during the midcentury ranges between 65.13 and 68.63 mm month⁻¹ for RCP2.6 and RCP8.5, respectively, and ranges between 66.78 and 68.27 mm month⁻¹ during the late century. Similarly, the value of mean ET increases from 45.56 and 47.28 mm month⁻¹ to 46.15 and 48.16 during the late century for RCP2.6 and RCP8.5. Moreover, it is important to notice that the most differences between the analyzed models leaned toward extreme weather events. As it is known, extreme events are expected to be more severe in the future due to climate change which will have significant impacts on buildings and infrastructure, as well as groundwater flow and contamination transport. Since the PDFs indicate more frequent extreme events in future projections, we expect that our resulting clusters via autoencoders (see section 3) may capture different patterns and frequencies.

3. Unsupervised climate data clustering

Unsupervised climate data clustering shown in Fig. 1 serves to reduce the dimensionality of climate simulation outputs by convolutional autoencoders and to group the lower-dimensional representation (i.e., latent representation) into similar climate patterns by clustering techniques. The resulting 512 dimensions at the latent representation can approximate a 666 176 × reduction in comprehensive climate information at 219 × 457 grid cells × 71 years from 1950 to 2020 × 4 RCP scenarios. Our workflow is composed of five elements: 1) Download CMIP5 simulation data as a source of historical and future projection products, from which we extract downscaled precipitation and evapotranspiration variables that determine the net flow of the groundwater system over CONUS; 2) transform the downloaded data through deseasonalizing and scaling; 3) subdivide data and patch creation to generate a smaller geographical unit of data to be efficient learning (see section 2 for steps 1–3); 4) train the convolutional autoencoders to reduce the dimensionality and then to produce the latent representation; 5) apply clustering to the latent representation for grouping the pixels into similar types of climate patterns. In particular, we develop and compare the two types of autoencoders: (i) Train standard convolutional autoencoders and the k-means algorithm separately, naming standard autoencoder, and (ii) develop a joint loss function to train convolutional autoencoders and the online clustering algorithm simultaneously, giving clustering autoencoder. This clustering autoencoder combines steps 4 and 5 in the same training process to be more scalable for a larger set of data in assigning clusters. We describe our two algorithms in turn; and 6) the cluster label prediction step finally assigns cluster labels to all future climate projection data so that we can evaluate trends in the distribution of different climate patterns.

a. Standard autoencoder

The autoencoder (Kramer 1991; Nair and Hinton 2010) is a commonly accepted unsupervised learning algorithm to map important information in input images x into latent representations z through dimensionality reduction and then reconstructs the original input image from the representations as the output. Training of autoencoder minimizes differences between the input images and their output images through the encoder E and decoder D.

Given a set of input images X = {x₁, …, x_n} that are encoded with encoder as Z = E(X), their reconstructed images are $\widehat{X}=D(Z)=D[E(X)]$. Loss function $\mathcal{L}(\theta )$ quantifies the difference between X and $\widehat{X}$ as follows:

$\mathcal{L}(\theta ,\varphi )={\displaystyle \sum _{x\in S}{\Vert x-D_{\theta }[E_{\varphi }(x)]\Vert }_p^p},$(1)

where S is a set of training images; (ϕ, θ) represents trainable parameters in encoder and decoder, respectively, and ${\Vert \cdot \Vert }_p^p$ is the pth power of the p norm of the inputs and restorations. We specify p = 2 to calculate the L₂ loss throughout this study. That is, the optimization of Eq. (1) minimizes the difference between input and output images so that the autoencoder eventually generates high-fidelity reconstructions.

The performance of image recognition improves with multiple layers of convolutional filters (Simonyan and Zisserman 2014) by extracting useful representations through the stack of these nonlinear filters. Therefore, we integrate convolutional layers into blocks, each incorporating the same size of two convolutional layers, and design a symmetric encoder–decoder structure (see Fig. 4a and architecture in the appendix). Each block has the same size of kernel but decreases the size from 5, 3, and then 2 based on our hyperparameter search. We add batch normalization (Ioffe and Szegedy 2015) to enable a stable and faster training process. We train different autoencoders for precipitation and ET, respectively, on 1 468 214 patches because our empirical evaluation shows better training performance gains during the training of autoencoder for each variable separately rather than training both variables as one input image.

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Diagrams illustrating two AEs and the clustering steps: (a) Standard AE conducts clustering in a separate step versus (b) clustering AE trains clustering partitions during training AE. In both diagrams, Z denotes the latent representation from the encoder. (a) Standard AE applies k-means to create centroids μ after the AE training. (b) Clustering AE simultaneously predicts clusters from Z to match clusters q using online clustering algorithms during the AE training. Both AEs use the same architecture, consisting of 520 thousand parameters. (a) Standard AEs. (b) Clustering AE.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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Having a trained standard autoencoder, we cluster the latent representation to identify unique climate patterns. We apply k-means++ (Arthur and Vassilvitskii 2006) as known for the probabilistic initialization to find an initial seed of k number of clusters, and the approach outperforms the native k-means algorithm. In implementation, we use k-means++ application programming interface (API) provided by scikit-learn Python package (Pedregosa et al. 2011) to 630 166 historical patches unseen in training of autoencoders. We separate the dataset for clustering from the training dataset because k-means++ has a memory limitation to fit all our training patches. We then obtain a set of k cluster centroids, μ = {μ₁, …, μ_k}. We determine the optimal number of clusters via the elbow method (Bholowalia and Kumar 2014), a heuristic approach used in determining the optimal number of clusters. See section 4a for the result.

4. Results

To evaluate differences in how climate patterns change through time, note again that we split the data into three windows: historical (1950–2020), midcentury (2021–60), and late century (2061–99). Such time windows are necessary to quantify the changes over this century because the interannual variability is quite large compared to the overall trend over the 100 years.

While our primary target is precipitation and ET, we examine the difference in resulting climate patterns from recharge rate, which subtracts ET values from precipitation (i.e., a net intake flow to the groundwater system). These two quantities are critical for water resource-related questions including soil and groundwater contamination. In addition, we used elevation as an indicator of topography and a proxy of air temperature variable and temperature as well, which are often associated with both precipitation and ET to quantify the influence from different combinations of variables. Thus, for the climate classification process, we group the results from the autoencoder into four parts:

• Train autoencoders and clustering separately on precipitation and ET.

• Train autoencoder and clustering on recharge rate.

• Train autoencoder and clustering on recharge and elevation.

• Train a clustering autoencoder on precipitation and ET values.

For all analyses in this section, we work with 1 476 425 test patches that have not been included in the training stage.

a. Optimal number of clusters

First, we determine an optimal number of clusters. In this study, we test a range of k ∈ {2, …, 9} and the elbow method indicates that five clusters are our optimal number of clusters, which is a pivot point in our study where the sum of square distance among latent representations resulting from patches in the historical time window (see Fig. 5). The results suggest that at least five clusters need to characterize the representative patterns in the dataset. We left the discussion of the physically optimal number of clusters for future work. For the rest of our study, we present clustering results working with five clusters.

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We plot the sum of squared distances between patches used in k-means clustering and resulting centroids as a function of the number of clusters. We observe that the sum of squared distance decreases almost linearly at five clusters, and for this reason, we choose five clusters as our optimal number of clusters.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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b. Runtime performance experiment

We perform a scaling experiment to examine the efficiency of the clustering process by clustering autoencoder against the k-means algorithm used for the clustering step in standard autoencoder, as described in section 3. The experiment setup is to measure the completion time of clustering runtime taken by each approach on a single CPU. We scale a range of sizes of patches ∈ {10, 100, 1000, 10 000, 100 000, 100 000, 500 000, 1 000 000}. This study defines clustering runtime as k-means process time for standard autoencoder and a neural network prediction time for clustering autoencoder.

The scaling experiment result is shown in Fig. 6. We observe that the completion time by k-means clustering exponentially increases with the number of application sizes, whereas the execution time by clustering autoencoder linearly increases, and the highest performance result by clustering autoencoder gains 9.23 times faster for a case of 1 000 000 patches. The result emphasizes that the clustering autoencoder can show significant scalability when applied to larger sizes of climate datasets.

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Scaling results in terms of completion time (second) with clustering by clustering AE (blue) and k-means clustering to latent representations from each AE. The dots represent the completion time as a function of the number of patches being clustered by both algorithms. We test the size of a set of patches from 10 to 1 000 000. Clustering AE shows significant advantages to reduce computation time for clustering in particular for the larger size of applications, indicating that the algorithms can scale efficiently to work with a larger amount of climate simulation datasets.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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c. Learned representation

We conduct a qualitative test of latent representations to assess their structure and quality because our climate clusters are derived from clustering results applied to them. We use t-distributed stochastic neighbor embedding (t-SNE) (van der Maaten and Hinton 2008), which projects higher-dimensional data onto a 2D map mostly used for visualization of a high-dimensional data structure, to examine whether the spatial structure of latent representations produced from our two autoencoders captures meaningful association with physical variables. t-SNE keeps the structure of data in a high-dimensional space at a projected space (often 2D) in such a way that a pair of similar representations of data is projected near to each other, while dissimilar pairs are in distant positions.

We then apply t-SNE to the latent representations from both autoencoders for 2000 patches sampled at random from the test dataset. Figure 7 visualizes 2D t-SNE projections where each color represents cluster numbers (leftmost column), patch-mean precipitation (left column), patch-mean ET (right column), and patch-center longitude values (rightmost column) for standard autoencoder at upper panels and for clustering autoencoder at lower panels, respectively. Note that we assign cluster numbers based on within-cluster mean precipitation in descending order. We see in Figs. 7a and 7e that patches in the same cluster locate coherently and those in different clusters are put far away, suggesting that autoencoders achieve learning separable latent representation among dissimilar patches. We also observe that the latent structure from the clustering autoencoder shows clearer intercluster segregation, indicating that the training does not fall into a trivial solution (i.e., all latent representations become identical) during optimizing the additional cross-entropy term 3. t-SNE panels colored by precipitation and ET highlight that similar physical properties are adjacent in the projected maps. Because our autoencoders work with precipitation and evapotranspiration data that exhibit a longitudinal subdivision in Fig. 2, the resulting latent representations in Figs. 7d and 7h capture the association with longitudinal values. These results suggest that our network learns underlying patterns within input data. In summary, we conclude that our autoencoder can capture nonlinear physical relationships and then generate nontrivial latent representations.

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t-SNE visualization of the latent representation of 2000 test patches from (a) to (d) standard AE in Fig. 4a and (e)–(h) clustering AE in Fig. 4b. Patches are randomly selected from a set of test patches unseen in the training stage. Each patch is colored by (a) and (e) cluster assignments (see section 4 for determining an optimal number of clusters), (b) and (f) patch-wise mean PR values, (c) and (g) patch-wise mean ET values, and (d) and (h) longitude values. We label cluster numbers in the order of within-cluster mean PR value in descending order (i.e., 1 has the highest PR mean; in contrast, 5 has the lowest PR mean). We observe that the structure of latent representations, cluster assignments, and physical variables are not randomly projected on the map, indicating that the latent representations generated from both standard and clustering AEs capture meaningful aspects of physical properties.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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d. Physical regimes

We first evaluate whether climate clusters produced by our two autoencoder algorithms have reasonable physical associations. That is, resulting clusters should identify unique physical regimes among clusters on a two-dimensional joint ET–precipitation histogram. We calculate the relative frequency of occurrence (RFO) of clusters from one of five clusters (see section 4a) whose average ET and precipitation fall at a bin defined by every 4 mm month⁻¹ in ET and every 10 mm month⁻¹ in precipitation across the same two-dimensional ET–precipitation space. Thus, 100% of RFO means that a bin is only classified into one of five clusters. We plot the RFOs of patches from each cluster on the ET–precipitation space (Fig. 8) for RCP8.5. Note that, we sort the numbers on the within-cluster mean precipitation in assigning cluster labels. Since the clustering algorithm assigns cluster number labels at random, we sort the cluster numbers in descending order of the mean precipitation values: The smallest number, 1, has the largest value of mean precipitation (wettest), and in contrast, 5 has the least value of mean precipitation (driest).

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Heatmap histograms of the RFO on a joint histogram of ET–PR space to the distribution of patches in RCP8.5 from (a) standard AE (Fig. 4a) and (b) clustering AE (Fig. 4b). (a) and (b) The within-patch-mean ET and PR values in bins of 4 mm month⁻¹ in ET and 10 mm month⁻¹ in PR. Both AEs generate a clear cluster partition, where 1 is dominant in domains at approximately ET < 80 mm month⁻¹ and PR > 100 mm month⁻¹, 2 is dominant in higher ET and PR, and 5 is dominant in domains at ET > 40 mm month⁻¹ and PR < 100 mm month⁻¹. The results suggest that AEs capture distinct physical features and reflect them into latent representations, giving unique climate clusters in the physical space.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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We see distinct unique physical regimes in clusters from both autoencoder approaches. Figure 8 shows that, for both autoencoders, 1 is a combination of high precipitation (200–400 mm month⁻¹) and low ET (20–60 mm month⁻¹), while 1 from clustering autoencoder could contain even large ET (80–150 mm month⁻¹) values and medium precipitation (70–250 mm month⁻¹). Similarly, 2 (Figs. 8b,g) from both autoencoders represents the identical physical regime that is distributed at relatively high precipitation (200–300 mm month⁻¹) and high ET (60–160 mm month⁻¹). In contrast, cluster 5 is characterized by either extremely low precipitation in a combination with all ranges of ET values or low ET with the combination of all ranges of precipitation values for both autoencoders. Cluster 5 from standard autoencoder (Fig. 8e) has the L-shaped distribution that puts together the two different climate situations in one regime, whereas 5 from clustering autoencoder (Fig. 8f) mainly helps to group data with ET ranging from 40 to over 160 mm month⁻¹ under conditions of low precipitation. This allows for the separation of situations with extremely low ET and a wide range of precipitation by merging them into cluster 4 because Fig. 7 explains that the additional loss term in Eq. (2) for clustering autoencoder encourages latent representation to generate clearer boundaries among similar data. The other clusters 3 and 4 from both autoencoders fill in the intermediate physical regimes. As will be shown later, 4 of the standard autoencoder spatially overlaps with 3 of the clustering autoencoder. Interestingly, the main physical regimes, which are commonly seen from both autoencoders, indicate that features extracted by autoencoder may capture representative patterns in climate data, and differences seen among the five regimes account for the combination of a loss function and clustering techniques. In summary, our five clusters are physically reasonable by distinguishing different physical regimes among clusters, supporting that a data-driven approach can provide rich information on climate patterns rather than performing a simple threshold approach.

e. Cluster patterns for precipitation and ET via standard autoencoder versus clustering autoencoder

In this section, we compare the results of spatial distributions of clusters from the standard autoencoder and clustering autoencoder for each of which we calculate the most frequent cluster as well as the relative frequency of occurrence of clusters at each patch location. To examine whether our climate clusters exhibit unique spatial patterns over CONUS, we analyze spatial patterns for different time windows. Note again that, in the training stage, autoencoders do not learn time and location information explicitly.

Figure 9 shows the distribution of clusters for the late-century time window via standard autoencoder and clustering autoencoder. Again, in both cases, we sort the cluster numbers in descending order of the mean precipitation values: The smallest cluster number, 1, has the largest value of mean precipitation, and in contrast, 5 has the least value of mean precipitation. We observe that the spatial patterns for both approaches do not excessively change over different times under the warming scenario among all three cases, while within-cluster mean precipitation increases compared to the values from 1950 to 2020 (see Fig. A2 for more details). The average percentage of five clusters over one of the 3-time windows alters at most 1% of patch locations, whereas the monthly change shows at most 8%—the 8% change can still not occur every month. The few minor transitions in cluster positions from both autoencoders appear at the boundaries of clusters in geographical space. For instance, we may notice that the few patches over southeast California and southern Nevada change cluster numbers from 5 to 4 from the historical to late-century time windows, meaning that the region is projected to get wetter by the end of the century, but a few patches over southwestern Oregon and northwestern California are changing cluster numbers from 1 to 4, meaning the region is projected to get drier by the end of the century. Similarly, clusters alter to wetter clusters in eastern Texas and western Louisiana as this region gets more precipitated over time. The results suggest that our climate clusters rather capture the consistent climatological distinctions over CONUS. It is interesting to note that both, standard and clustering autoencoders, give higher within-cluster precipitation mean during the midcentury than the means during the late-century cluster.

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Spatial distribution of the most frequent one of five clusters generated from (a) standard AE and k-means clustering and (b) clustering AE. Dot points represent the center of patch, 2° × 2° area. Patches are overlapped 1°, and dot points are 1° resolution. The cluster labels colored by cluster number are assigned in descending order of within-cluster mean PR, and the legend shows the mean values. Clusters in (a) and (b) show uniform geographical patterns within the same cluster but exclusive among different clusters, and those patterns are roughly matched with KGC’s five climate classes: 2 corresponds with C (temperate) climate as well as 4 and 5 correspond with B (dry) climate. Yet, standard and clustering AEs capture a unique climate pattern in 1, suggesting the exploratory power of a data-driven approach.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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As expected that two different autoencoders produce equivalent physical regimes in Fig. 8 at physical space, we also observe similar patterns of spatial distributions of clusters in Fig. 9: The driest and relatively drier clusters (5 and 4, respectively) are likely assigned at a Rocky Mountain region and the eastern part of the south and north Great Plains. In contrast, the wettest cluster (1) is located along the far West Coast of CONUS. Cluster 4 from the standard autoencoder and cluster 3 from the clustering autoencoder are qualitatively and quantitatively comparable by the location as well as by the means of precipitation (61.86 and 64.92 mm, respectively). We highlight the spatial similarity of individual clusters by investigating RFOs of each cluster at each patch location in Fig. 10 to determine whether clusters are spatially localized or widely spread. Spatial RFOs shown for each cluster are visually similar. Clusters 2 and 5 roughly match their spatial domain, 4 from standard autoencoder and 3 from clustering autoencoder overlap each other, and 1 is different between two autoencoders such that 1 in clustering autoencoder combines patterns seen 1 and 3 from standard autoencoder.

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As in Fig. 9, but plotting the spatial distribution of the RFO for each climate cluster at each patch location from (a) to (e) standard AE and from (f) to (j) clustering AE. Clusters are arranged in rows from (top) cluster 1 to (bottom) cluster 5. RFO of clusters indicates that cluster patterns occur in a specific location instead of distributing evenly. Clusters show unique geographic distinctions as well as similarities with known climate patterns: 1 overlaps with humid subtropical climate zone (Cfa) and humid continental climate zone (Dfa). Cluster 5 spatially aligns with semiarid (BS) and desert (BW).

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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Finally, we compare the spatial structure of our cluster with known climate patterns from KGC (Cui et al. 2021b): We observe that 1 overlaps with the humid subtropical climate zone (Cfa) and humid continental climate zone (Dfa). Cluster 5 is spatially associated with their semiarid (BS) and desert (BW) climate types, suggesting that our clusters capture physically meaningful spatial patterns that identify similar climate areas tightly.

Overall, we conclude that the proposed clustering autoencoder generates physically meaningful and spatially comparable cluster patterns and dramatically reduces computational resources to those from standard autoencoder.

f. Cluster patterns for recharge and elevation via standard autoencoder

Our results have demonstrated that clusters based on precipitation and ET are largely unchanged over time, show strong geographical features, and group unique physical regimes on ET–PR space. We extend the analysis to investigate the difference in spatial cluster patterns via standard autoencoders that use recharge, and recharge and elevation data, respectively, in training. Here, we are motivated to analyze how different input variables alter the resulting climate patterns as our standard autoencoder results in having diverse spatial patterns.

As expected based on prior results, at a high level, Fig. 11 displays the common longitudinal structure where 1, a cluster with the highest recharge, only locates at the West Coast of CONUS, drier clusters (4 and 5) are mostly distributed at the central CONUS, and wetter clusters (2 and 3) are dominant at the east part of Midwest and South and East Coast of CONUS.

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As in Fig. 9, but standard AE and clustering AE are trained on (a) recharge rate and (b) recharge rate and elevation. Note that we assign cluster numbers based on within-cluster mean recharge values in descending order. A legend shows the mean recharge rate within cluster. We observe that training AE with multiple variables helps to produce spatially cohesive cluster patterns and to make clusters relatively insensitive to outliers from a long-tailed distribution, leading to percent sporadic spatial patterns seen in (a).

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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In comparison with the precipitation and ET cases, cluster patterns resulting solely from recharge values shown in Fig. 11 show different spatial structures where two dominant clusters, 3 22.01 mm month⁻¹) and 4 (12.26 mm month⁻¹), split the entire CONUS. Because the distribution of patch-mean recharge value is positively skewed and long tailed as the mode is 3.74 mm month⁻¹ but the mean is 15.95 mm month⁻¹, clusters that group patches around the mode and mean are spatially significant. Here, the resulting clusters tell how different autoencoders capture similar groups of lands depending on input variables over CONUS.

We now evaluate cluster patterns resulting from recharge and elevation (see Fig. 11b). The primary difference in spatial patterns is 5 (i.e., the least perceptible cluster), which clearly captures the topographical effect (see Fig. 2) at the Rocky Mountains. Figure 11 also shows that 3 smooths the spatial distribution of clusters at the east part of CONUS (95°–80°W) than clusters based on recharge-only case distribution, indicating that autoencoder reflects terrain information on the latent representation. That is, adding elevation data in the training data can prevent autoencoder from generating sporadic spatial patterns, which result from grouping outliers in a long-tailed distribution in recharge rate. The results suggest that the combination of multiple relevant variables may produce more spatially coherent and rich information in the purpose of unsupervised climate classification.

g. Comparison with conventional classification

In this section, we conduct a quantitative test to identify the similarities and unique patterns that the autoencoders capture with KGC climate classes. In Fig. 12, we examine the percentage of overlaps between two versions of future 30 KGC climate subcategories during the late century (Cui et al. 2021b; Beck et al. 2018). We define the percent of cluster per category as the sum of percent from our cluster 1 to cluster 5 is 100% at each subcategory. We note that since our patches overlap every 1°, we aggregate the most frequent KGC class every 1° if the dataset provides high-resolution (<1°) data. The results from comparing the future RCP8.5 projections of our analysis and analyses from two studies demonstrate that our five clusters from the clustering autoencoder have a diversity of cluster arrangements, whereas those from the standard autoencoder put most of the B (dry), C (temperate), and D (continental) subcategories into cluster 5.

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Comparison of (from top to bottom) our two clustering results with (from left to right) two updated versions of 30 KGC subcategories (B18; C21). The color scheme shows the percentage of one of five clusters overlapping on each KGC subcategory. The plots suggest that our approaches group unique climate zones regardless of conventional B, C, and D zones: Cluster 2 is composed of Cfa and Dfa; B, C, and D zones are grouped by cluster 4 and cluster 5; and high PR area at Csa and Csb is assigned to cluster 1.

Citation: Artificial Intelligence for the Earth Systems 3, 3; 10.1175/AIES-D-23-0035.1

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First, when considering the distribution of the KGC subcategories between cluster 1 and cluster 5, there is less distinctiveness within C subcategories. Specifically, based on the clustering autoencoder, for Csa, 36.4% belongs to cluster 1, 36.4% to cluster 4, and 27.3% to cluster 5 from the Cui et al. (2021b) dataset (hereafter C21) and 40.7% belongs to cluster 1, 18.5% to cluster 4, and 40.7% to cluster 5 from the Beck et al. (2018) dataset (hereafter B18). However, dissimilarities in Csb, which describes the region with cooler summer compared to Csa, arise from variations in the dataset and different criteria used to define subcategories in those two studies. For clustering, autoencoder based on B18 is predicted to be 100% in cluster 1, whereas results based on C21 are composed of 20% of cluster 1, 34.5% of cluster 4, and 45.5% of cluster 5. The analysis also reveals that cluster 1 predominantly overlaps with Csa and Csb subcategories from C21 and B18. Both subcategories are characterized by the same precipitation patterns throughout the year where more precipitation falls during the winter than during the summer. The lack of distinctiveness observed in the subcategories is associated with the inherent subtleties in subcategory delineations when transitioning from rule-based approaches to data-driven methodologies. This discrepancy could be attributed to the introduction of additional variables and an increase in the number of clusters.

Cfa and Dfa show significant similarities in that they spread over all clusters, but the highest percentage is dominant by cluster 2. Cfa ranges from 42.5% to 69.4%, and Dfa ranges from 35.1% to 74.6% in cluster 2. The similarity accounts for the almost identical definitions of Cfa and Dfa in terms of precipitation. Cluster 2 mainly overlaps with the Cfa and Dfa from both, C21 and B18 datasets, and those are characterized by similar precipitation distribution with no dry seasons which is in agreement with our analysis where cluster 2 is associated as the cluster with the second wet conditions across the CONUS.

Furthermore, in analyzing how the area of cluster 3 overlaps with subcategories from C21 and B18, we may notice that there are lower values of Cfa and Dfa compared to cluster 2 including additional BSh, indicating a dryer climate.

Finally, despite the fact that Cfa and Dfa have common cluster percentages, we observe that Dfb exhibits more similarities with Csa, BSh, and Dsa. Figure 2 indicates that Dfb distributes on less precipitation and evapotranspiration areas across CONUS, indicating that dry-like subcategories are scattered among cluster 4 and cluster 5. More subcategories with the arid BW (desert) and BS (steppe) overlap with cluster 4, such as BWh, BWk, Cwa, and Cfb, while the area of cluster 5 mainly overlaps with BSh, BSk, Dsa, Dsb, and Dfb from C21 and B18 analyses. This shows us that we successfully identified the arid area across the CONUS as cluster 4 and cluster 5 are defined as the clusters with the driest conditions. Overall, these findings highlight the complexity of climate clusters generated by autoencoders against rule-based KGC categories.

5. Conclusions

We have presented our unsupervised climate classification approach that reduces the dimensionality of the vast climate simulation data to capture five unique climate patterns via autoencoder techniques and then provides lightweight climate pattern projections across the conterminous United States. Our two autoencoders, standard and clustering autoencoders, generate physically reasonable, homogeneous within-cluster, and distinct intercluster latent representations. We verify that our clusters show spatially stable climatological patterns along with future extreme precipitation events. The clusters also yield spatial climate patterns, some of which match known climate classes defined by human experts. Our results support the exploratory power of autoencoders and the benefits of extracting only relevant vast amounts of climate simulations compressing by a factor of 660 000.

Our five AI-generated climate clusters are based on a purely data-driven approach without reliance on location, time/seasons, predefined variables, and predesignated thresholds. The method addresses the limitations in complicated classification schemas (Köppen 1884; Peel et al. 2007) and artificial biases (Charles et al. 2018) by a comprehensive integration using deep neural networks and data selection. Cluster patterns via autoencoders can reflect the nonlinear combination of different physical features in inputs on the latent space and group distinct data physically and spatially. For example, a standard autoencoder trained on precipitation and ET groups patches into unique physical regimes on ET–PR space, whereas an identical architecture of autoencoder but trained on only recharge values, the difference between precipitation and ET, produces different spatial patterns than the results from precipitation and ET values. The comparison with KGC in particular based on results from clustering autoencoder suggests that they identify unique patterns grouping wet and dry patterns across the rule-based conventional subcategories. It should be noted that diverse models adhere to distinct model physics, as do observations. Consequently, the delineation of clustering boundaries and patterns reflects inherent variations in these models. We believe that incorporating further climate variables may introduce further complexity of physical information in our AI-generated climate zones.

Our clustering autoencoder shows potential advantages in increasing the capacity of data used for the clustering stage by reducing exponentially increasing clustering time via k-means (e.g., 9.23 times faster to clustering 1 000 000 patches). This leads to improving the generalization of results from data-driven climate classification algorithms by unleashing a larger amount of climate datasets to capture underlying patterns. The preliminary results are able to generate equivalent spatial patterns over CONUS and physical patterns on ET–PR space with clusters from standard autoencoder, whose results are one of the key baselines in unsupervised climate classification. However, we observe that the clustering autoencoder produced imbalanced or equal cluster partitions based on a choice of μ parameter in Eq. (3), which adjusts the regularization of cross entropy. Empirically, the online clustering approach may collapse to the same solution easily (Caron et al. 2020; Wu et al. 2021) based on regularization metrics, hyperparameters, and diverseness of minibatch. Thus, it will be important to introduce an appropriate evaluation metric for whether clusters produced from clustering autoencoder are physically reasonable. We leave a potential solution in future work.

Overall, we believe that a combination of an autoencoder and clustering approach can help the evaluation of climate patterns immediately without querying large climate datasets. The use of clustering in the latent space of autoencoders on climate data for building representative climate regions can be extended to other domains of applications (Wang et al. 2022; Xu et al. 2022), particularly in climate resilience assessment. We envision applying the unsupervised climate classification workflow under various uncertainties of future climate projections and eventually contributing to demands from stakeholders who need a fast evaluation tool that can handle many possible climate projections.

Data availability statement.

The code for deep learning and analysis is publicly available at https://github.com/ALTEMIS-DOE/climate-clustering (accessed on 21 April 2023). The training, testing, and result data can be found at https://console.cloud.google.com/storage/browser/us-digitaltwiner-pub-features/ai_generated_climate_dataset. The downscaled dataset is archived at https://gdo-dcp.ucllnl.org/downscaled_cmip_projections/dcpInterface.html.