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Understanding Perturbed Parameter Ensemble Sensitivities Using A Contrastive Learning Approach
Da Fan, David John Gagne II, Gregory S Elsaesser, Brian Medeiros, Addisu G Semie, Qingyuan Yang, Akila Sampath, Subashree Venkatasubramanian
TL;DR
Interpreting parameter sensitivities in multivariate, spatially structured climate outputs remains challenging. This paper trains a contrastive learning model on two CAM6 PPEs to compare simulations and observations in a shared representation space. The representations preserve seasonal and ensemble variability, distinguish the schemes, and connect model-observation differences to physical variables, regions, and parameters.
Problem
Interpreting PPE differences is challenging because outputs are high-dimensional, spatially structured, and seasonal, and differences can reflect several sources of uncertainty or bias.
Source: §1 · p. 3Method
The study trains a self-supervised contrastive learning framework on monthly cloud and radiation fields from two CAM6 PPEs and observations to compare them in a shared embedding space.
Source: §3.2 · p. 7, §5 · p. 20Results
The embeddings separate TAU-ML and KK2000 while preserving seasonal variability and ensemble spread; TAU-ML is generally closer to observations, and attribution highlights cloud and radiation variables and key cloud, storm-track, and convection regions.
Source: §5 · p. 20Takeaways & Limitations
Contrastive representations combined with integrated gradients provide a compact, physically explainable diagnostic for identifying which variables and regions account for differences among simulations and observations.
Source: §5 · p. 21
Abstract
from arXiv · showhide
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.
Plain Language Summary
The study uses machine learning to organize cloud and radiation fields from climate simulations and compare them with observations. The learned organization distinguishes rain-formation methods while preserving parameter-driven variability and helps identify where model differences arise.
Method
- The method organizes monthly cloud-water and radiation fields from two simulation groups that differ in their representation of rain formation.The groups use the same uncertain parameter values.Source: Plain Language Summary · p. 2
Results
- The learned organization preserves seasonal cycles and parameter-driven ensemble spread while distinguishing the two rain-formation methods.Both simulation groups differ more from observations than from each other, although the more detailed rain representation is generally closer.Source: Plain Language Summary · p. 2
Interpretation
- Cloud liquid water and reflected sunlight explain most differences, especially over marine low-cloud regions and midlatitude storm tracks.The method also connects regional differences to parameters controlling cloud formation, atmospheric turbulence, and deep convection.Source: Plain Language Summary · p. 2
1 Introduction
Climate-model parameter choices and structural assumptions create uncertainties that are difficult to diagnose using scalar metrics or direct comparisons of high-dimensional fields. The paper proposes contrastive learning as a compact, physically meaningful way to compare simulations and observations while identifying the variables, regions, seasons, and parameters associated with differences.
1 Introduction
- Scalar climate metrics can miss structural deficiencies because different parameter combinations may yield similar mean states or compensate for errors across fields, regions, and seasons.Hand tuning is time-consuming, subjective, and harder as parameters, outputs, and observational constraints increase.Source: §1 · p. 3
- PPE interpretation is difficult because high-dimensional, spatially structured, seasonal differences can reflect parameter uncertainty, structural error, internal variability, observational uncertainty, or compensating biases.PPEs systematically perturb parameters and can support calibrated physics ensembles.Source: §1 · p. 3
- The proposed diagnostic should preserve regional and seasonal structure, represent variable interactions, distinguish configurations, quantify discrepancies, and identify controlling variables, regions, and parameters.This is especially relevant to calibration, which seeks to assess whether cloud and radiation processes improve alongside scalar error metrics.Source: §1 · p. 3
- Contrastive learning places similar samples closer and dissimilar samples farther apart in a compact embedding space, which can provide data-driven similarity measures for climate states.The introduction notes that such representations may encode seasonal variability, ensemble spread, and configuration differences.Source: §1 · p. 3
- The study applies contrastive learning to CAM6 PPEs that share parameter settings but use different warm-rain schemes, KK2000 and TAU-ML.It asks whether the representation captures seasonal variability, parameter uncertainty, and structural differences, and whether its distances and attributions reveal controlling variables, regions, and parameters.Source: §1 · p. 4
2 Data
The study uses CAM6 simulations and monthly observational climatologies to compare two warm-rain microphysics schemes. Its data cover five cloud and radiation variables, with ensemble parameter settings and geographic context specified for the simulations.
2.1 CAM6 model description
- CAM6 is the atmospheric component of CESM2 and includes cloud microphysics, moist turbulence, aerosols, deep convection, and radiation schemes.The described model includes prognostic cloud liquid, cloud ice, rain, and snow mass and number concentrations.Source: §2.1 · p. 4
2.2 PPE simulations
- The two 100-member PPEs differ only in warm-rain microphysics: KK2000 represents rain formation through autoconversion and accretion rates fitted to large-eddy simulations.The parameter table gives perturbed parameter names, descriptions, default values, ranges, and units.Source: §2.2 · p. 5, Table 1 · p. 5
- TAU-ML emulates the TAU bin microphysics model, replacing KK2000 autoconversion and accretion rates with a neural-network emulation of stochastic collection.The PPEs use 34 parameters spanning turbulence, cloud microphysics, aerosols, and deep convection; the accretion parameter is inactive in TAU-ML.Source: §2.2 · pp. 5–6
2.3 Observations
- Monthly observational climatologies provide LWCF, SWCF, FLUT, FSNT, and TLWP for evaluating the PPE outputs.The study does not account for observational uncertainty, which it says will be incorporated in future calibration work; Table 2 lists the monthly climatological observational products.Source: §2.3 · p. 6, Table 2 · p. 6
3 Methods
The methods prepare monthly PPE and observational fields, train a shared contrastive representation of the two microphysics ensembles, and use Integrated Gradients to attribute embedding distances to geographic regions.
3.1 Data Processing
- PPE and observational samples use standardized monthly anomalies of five climate variables and four static fields, with polar regions excluded.PPE members are split by ensemble member into training, validation, and testing subsets.Source: §3.1 · pp. 6–7
3.2 Contrastive Learning framework
- A shared encoder and projection head map climate inputs into a common embedding space, trained to bring same-scheme adjacent-month pairs together and distinguish cross-scheme pairs.The inputs are paired across corresponding ensemble members with the same perturbed parameters; training uses the NT-Xent loss.Source: §3.2 · pp. 7–8
3.3 Explainable AI
- Integrated Gradients attributes cosine distances between embeddings to geographic regions using normalized heatmaps averaged across ensemble members and months.The resulting maps are used to highlight structural differences among datasets.Source: Figure 1 · p. 7, §3.3 · p. 9
4 Results
The learned embeddings distinguish the two PPEs while retaining seasonal and ensemble variability, and place observations on a comparable low-dimensional manifold. Distances and attributions reveal seasonal model–observation differences concentrated in cloud-related regions and associated with microphysics, turbulence, and convection parameters.
4.1 Embedding evaluation
- Embedding-based classification exceeds 0.94 accuracy across network layers, with the highest skill at dense2 and the lowest at dense3.Even conv1 performs well; dense3 compression may discard some discriminative information while retaining features that better preserve embedding similarity.Source: Figure 2 · p. 9, §4.1 · p. 10
- Encoder and projection-head embeddings place observations on the PPEs’ low-dimensional manifold, while scheme separation and overlap vary across principal components.Encoder projections show within-season ensemble spread and generally separated schemes; dense3 embeddings mix schemes near the center but retain separation in PC3, which explains only 0.23% of variance.Source: §4.1 · p. 10, Figure 3 · p. 11, Figure 4 · p. 12
- Monthly encoder projections preserve seasonal clusters and ensemble spread, with observations displaced from model clusters especially in March, April, September, and October.The monthly clusters rotate with the seasonal cycle, while within-cluster spread reflects parameter perturbations.Source: §4.1 · pp. 11–12, Figure 5 · p. 13
4.2 Embedding distance analysis
- TAU-ML–observation cosine distances are consistently lower than KK2000–observation distances, while distances between the two PPEs are generally smaller than either model’s distance to observations.KK2000–observation distances peak in spring and autumn, and their larger ensemble spread indicates greater parameter sensitivity than for TAU-ML.Source: §4.2 · pp. 12–13, Figure 6 · p. 13
- The leading parameters differ by distance comparison: accretion enhancement ranks highest for PPE separation and KK2000–observation distance, while ice fall speed scaling ranks highest for TAU-ML–observation distance.Other top-three parameters include deep-convection triggers for PPE separation, liquid-water variance damping for KK2000–observation distance, and cloud-ice autoconversion threshold for both observation comparisons.Source: §4.2 · p. 14, Figure 7 · p. 14
4.3 Embedding distance explanation
- Integrated-gradient maps identify cloud processes, especially TLWP and SWCF, as major contributors to embedding distances, with signals in subtropical low-cloud and storm-track regions.Across comparisons, attributions are strongest over oceanic cloud regions; KK2000–observation TLWP signals also mark broad subtropical and storm-track biases.Source: §4.3 · pp. 14, 15, 17, 18, Figure 8 · p. 15
- Seasonal attributions link TAU-ML–KK2000 differences to subtropical low clouds and midlatitude storm-track TLWP, while observation comparisons show subtropical and tropical SWCF signals.TAU-ML has more subtropical low clouds than KK2000; TAU-ML–observation SWCF signals also occur in tropical convective regions, with seasonal changes across the Pacific and Indian Ocean.Source: §4.3 · pp. 15–17, Figure 9 · p. 16
4.4 Regional parameter importance
- Regional attribution correlations implicate microphysics, boundary-layer turbulence, and deep-convection parameters, with patterns varying by comparison and region.For TAU-ML–observation biases, autoconversion and accretion parameters correlate with storm-track and subtropical stratocumulus attributions, while convection parameters correlate with tropical-ocean signals; KK2000 shows a similar pattern but also sensitivity to its accretion enhancement parameter.Source: Figure 7 · p. 14, §4.4 · p. 19
5 Conclusions
The learned embedding space distinguishes the two CAM6 ensembles while retaining physically meaningful variability and enabling regional and parameter-level diagnosis of model–observation differences. TAU-ML is generally closer to observations than KK2000, though both retain substantial discrepancies.
5 Conclusions
- The framework trains on paired CAM6 PPEs that share perturbed parameter settings but use different warm-rain schemes, comparing KK2000, TAU-ML, and observations in a common embedding space.Inputs include monthly TLWP, SWCF, LWCF, FSNT, FLUT, and static geographic fields.Source: §5 · p. 20
- Embeddings separated TAU-ML and KK2000 while preserving seasonal variability and parameter-driven ensemble spread; observations occupied the same manifold but were displaced most in spring and autumn.Monthly samples formed seasonal clusters, with within-cluster spread reflecting ensemble variability.Source: §5 · p. 20
- TAU-ML is generally closer to observations than KK2000, while both retain substantial discrepancies, especially in spring and autumn; KK2000 biases are more parameter-sensitive.The KK2000–observation distance has a larger ensemble spread than the TAU-ML–observation distance.Source: §5 · p. 20
- Integrated Gradients attributed embedding distances mainly to TLWP and SWCF, with strongest signals over low-cloud and deep-convection regions and weaker contributions from FSNT, LWCF, and FLUT.Attributions varied seasonally with TLWP, SWCF, and low-cloud fraction.Source: §5 · p. 20
- TAU-ML–KK2000 differences center on low-cloud and storm-track regimes, whereas model–observation attributions are broader and include tropical convection.The broader biases may involve coupled low-cloud, storm-track, and deep-convective processes, not warm-rain microphysics alone.Source: §5 · p. 20
- Regional attributions correlate most with cloud microphysics, boundary-layer turbulence, and deep-convection parameters; aerosol-emission, solubility, and dust parameters show weaker, less systematic relationships.Accretion and deep-convection triggering parameters influence scheme separation, while model–observation attributions also relate to autoconversion, ice and snow processes, turbulence, and convective triggering.Source: §5 · p. 21
- Contrastive learning with integrated gradients provides a compact diagnostic space that connects model differences to the variables and regions responsible for separation.The framework captures seasonal variability, ensemble spread, structural differences between configurations, and model–observation discrepancies.Source: §5 · p. 21
- For calibration, embedding distance preserves spatial structure, seasonal dependence, and coupled cloud-radiation behavior beyond a scalar global error metric, while future work should address observational uncertainty.Attribution and parameter-correlation analyses identify implicated cloud regimes and process parameters.Source: §5 · p. 21
6 Data Availability Statement
The statement identifies Zenodo as the repository for the study datasets and names the sources of CERES EBAF and MAC-LWP data.
6 Data Availability Statement
- Study datasets are made available on Zenodo, with CERES EBAF from NASA Langley’s ordering tool and MAC-LWP from the MEASURES archive.The passage says the repository would be officially published with a permanent DOI upon manuscript acceptance.Source: §6 · p. 21