physics.ao-phSep 24, 2026

Understanding Perturbed Parameter Ensemble Sensitivities Using A Contrastive Learning Approach

Authors: Da Fan, David John Gagne, Gregory S Elsaesser, Brian Medeiros, Addisu G Semie, Qingyuan Yang, Akila Sampath, Subashree Venkatasubramanian

Organizations: Learning the Earth with Artificial Intelligence and Physics (LEAP) National Science Foundation (NSF) Science and Technology Center, Columbia University, New York, NY, USA · Department of Earth and Environmental Engineering, Columbia University, New York, NY, USA · NSF National Center for Atmospheric Research, Boulder, CO, USA · NASA Goddard Institute for Space Studies, NY, USA · 

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Perturbed parameter ensembles (PPEs) reveal how physics parameters affect climate simulations, but interpreting parameter sensitivities across multivariate, spatially structured outputs remains challenging, particularly when calibrating models against observations. We develop an explainable contrastive learning model that maps 5 monthly cloud and radiation fields into a shared representation space. We train the model on the fields of two 100-member Community Atmosphere Model version 6 (CAM6) PPEs, spanning 34 parameters, that only differ in the warm rain microphysics scheme: KK2000, the default bulk microphysics scheme, and TAU-ML, a neural network emulator of a bin microphysics scheme. The learned representations separates two PPEs with over 94% linear classification accuracy while preserving the seasonal variability and ensemble spread due to parameter perturbations. In the shared representation space, the representations of satellite observations occupy the same low-dimensional manifold as the PPEs but are displaced from them most strongly during boreal spring and autumn. TAU-ML PPE has a lower distance to observations compared to KK2000 in the representation space. Integrated Gradients attributions highlights the contributions in subtropical low-cloud regions, Northern and Southern Hemisphere storm track regions, and tropical convection regions to differences between PPEs and observations. Regional attributions correlate most strongly with parameters associated with cloud microphysics, boundary layer turbulence, and deep convection. These results demonstrate that explainable representations of climate fields can attribute model differences to specific variables, regions, seasons, and physical parameters.

Figures & tables

Table 1: Perturbed parameter names, descriptions, default values, rangesm and units for the 100 member PPE.
Table 2: Monthly climatological observational products used in this work.
Figure 1: Schematic of the contrastive learning framework and explainable AI workflow. (a) Contrastive learning architecture showing the training and inference pipelines and a visualization of the two-dimensional projections of the learned embeddings. The model uses five atmospheric variables and four static fields; only SWCF is shown for illustration. (b) Shared neural network encoder and projection head that map input from different data sources into a common embedding space. (c) Explainable AI workflow that uses the Integrated Gradient method to attributes cosine distances between embeddings to geographic regions of the input fields.
Figure 2: Linear (TAU-ML vs KK2000) classification evaluation of the learned embeddings from different layers of the contrastive learning model.
Figure 3: Pairwise two-dimensional (2D) PCA projections of the learned encoder (pool2) embeddings for TAU-ML, KK2000, and observations. Diagonal panels show distributions for each principal component (PC), while off-diagonal panels show pairwise projections among PC1, PC2, PC3, and PC4. Blue circles denote TAU-ML samples, red circles denote KK2000 samples, and yellow triangles denote observations.
Figure 4: Same as Fig 3 , but for the last layer (dense3) embeddings.
Figure 5: Monthly two-dimensional PCA projections of the learned encoder embeddings for TAU-ML, KK2000, and observations. Blue points represent TAU-ML outputs, red points represent KK2000 outputs, and yellow triangles represent observations. The colorbars indicate ensemble member index for TAU-ML and KK2000.
Figure 6: Monthly variation in mean cosine distance among encoder embeddings of monthly climatology for TAU-ML, KK2000, and observations. Shading represents standard deviation of the ensemble.
Figure 7: Top-15 parameter importance for latent distances of KK2000 a TAU-ML, KK2000 versus observations, and TAU-ML versus observations. Red bars indicate positive correlation while blue bars indicate negative correlation.
Figure 8: Mean integrated gradient attribution maps for embedding distances among TAU-ML, KK2000, and observations across months and members. Rows show (a) TAU-ML versus KK2000, (b) TAU-ML versus observations, and (c) KK2000 versus observations. Columns show TLWP, SWCF, FSNT, LWCF, and FLUT. Positive and negative values indicate regions where each input variable contributes to the latent distance between the datasets.
Figure 9: Seasonal integrated gradient attribution maps of SWCF and TLWP and differences of TLWP, SWCF, and low cloud fraction for the TAU-ML and KK2000 comparison. Columns show December-January-February (DJF), March-April-May (MAM), June-July-August (JJA), and September-October-November (SON). Rows show, from top to bottom, SWCF integrated gradient (IG) attribution, SWCF difference, TLWP IG attribution, TLWP difference, and low cloud fraction difference. The differences are calculated as TAU-ML minus KK2000. Positive and negative IG values indicate regions where each input variable contributes to the latent distance between the KK2000 and TAU-ML.
Figure 10: Same as Fig. 9 , but for TAU-ML and observations comparison
Figure 11: Same as Fig. 9 , but for TAU-ML and observations comparison
Figure 12: Pearson correlations between perturbed physics parameters and regional integrated gradient attributions for selected high-attribution variable and region pairs. Rows show selected regions for TLWP, SWCF, FSNT, LWCF, and FLUT, including marine stratocumulus, subtropical cloud-transition, ITCZ, and storm-track regions. Columns show perturbed parameters associated with cloud microphysics, CLUBB boundary layer turbulence and shallow convection, deep convection, cloud fraction, aerosol emissions, solubility, and aerosol microphysics. Panels show correlations for (a) TAU-ML versus KK2000, (b) TAU-ML versus observations, and (c) KK2000 versus observations. Colors indicate Pearson correlation coefficients between parameter values and regionally averaged integrated gradients. Open circles indicate statistically significant correlations over 0.3. Positive correlations indicate that increasing parameter values would increase the attribution in the region, while negative correlations indicate that increasing parameter values would decrease the attribution in the region.
More in this topic

Climate Modeling

Climate modeling uses physical simulations and data-driven methods to understand, predict, and project Earth’s climate and its response to external forces.

See all 69 papers

Explore similar work

CardsList

  1. Does Aurora Encode Atmospheric Structure? Latent Regime Analysis and Attribution

    Jun 24, 2026Emma Kasteleyn, Ana LucicWeather Forecasting

    University of Amsterdam

  2. Learning Hierarchical Causal Representations of the Effects of Forcings on Temperature in Climate Models

    Sep 25, 2026Shan Zhao, Ilija Trajkovic, Julia Kaltenborn +4Surrogate ModelingCausal Representation Learning

    Technical University of Munich Munich, Germany · Karlsruhe Institute of Technology Karlsruhe, Germany · McGill University & Mila Montreal, Canada +1

  3. Kernelized Parameter Sensitivity Atlases for Amortized Conditional Interpretability

    Oct 8, 2026Davide Wiest, Ahanaf Hasan Ariq, Abdul Monaf ChowdhuryNeural Network InterpretabilityGradient-Based Attribution

    Technische Universität Darmstadt · Daffodil International School · University of Dhaka