Different approaches to using data-driven methods for subgrid-scale closure modeling of geophysical turbulence have emerged recently. Most of these approaches are data hungry and lack interpretability and out-of-distribution generalizability. Here, we use a hybrid approach that combines turbulence theory, physics-based modeling, and data-driven methods to overcome these challenges. Specifically, we address the parametric uncertainty of well-known physics-based large-eddy simulation (LES) closures: the Smagorinsky (Smag) and Leith eddy-viscosity models (one free parameter) and the Jansen-Held (JH) backscattering model (two free parameters). For various cases of two-dimensional turbulence, optimal parameters are first learned online from data via ensemble Kalman inversion (EKI), such that for each case, the LES energy spectrum matches that of direct numerical simulation (DNS). We quantify the uncertainties on these parameters using a modern machine-learning-accelerated Bayesian workflow, \", , \" Only a small training dataset is needed (to calculate the DNS spectra); i.e., the approach is data-efficient. We find the optimized parameter(s) and their associated uncertainty for each closure to be constant across broad flow regimes that differ in dominant length scales, eddy/jet structures, and dynamics, suggesting that these closures are generalizable. Next, we show that the online learned constants agree with the predictions of a recent semianalytical derivation, providing further interpretability. In both and tests that include examining the extreme events, LES with optimized closures, especially with JH, outperforms the baselines (LES with standard Smag, dynamic Smag, or Leith). This work shows the promise of combining advances in theory, physics-based modeling (e.g., JH), and data-driven modeling (e.g., online learning with EKI) to develop data-efficient frameworks for accurate, interpretable, and generalizable closures for geophysical turbulence, with ultimate applications in weather and climate prediction.
", "doi": "10.1103/mnbm-3g56", "issn": "2643-1564", "publisher": "American Physical Society", "publication": "Physical Review Research", "publication_date": "2026-05-27", "series_number": "2", "volume": "8", "issue": "2", "pages": "023215" }, { "id": "authors:t0fnh-pe364", "collection": "authors", "collection_id": "t0fnh-pe364", "cite_using_url": "https://authors.library.caltech.edu/records/t0fnh-pe364", "type": "article", "title": "Models for information propagation on graphs", "author": [ { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Elliott", "given_name": "Charles M." }, { "family_name": "Kreusser", "given_name": "Lisa Maria", "orcid": "0000-0002-1131-1125" } ], "abstract": "We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave, which emanates from a set of known nodes at an initial time, to all other unknown nodes at later times with an ordering determined by the arrival time of the information wave front. A second class of models is based on the notion of a travel time along paths between nodes. The time of information propagation from an initial known set of nodes to a node is defined as the minimum of a generalised travel time over subsets of all admissible paths. A final class is given by imposing a local equation of an eikonal form at each unknown node, with boundary conditions at the known nodes. The solution value of the local equation at a node is coupled to those of neighbouring nodes with lower values. We provide precise formulations of the model classes and prove equivalences between them. Finally, we apply the front propagation models on graphs to semi-supervised learning via label propagation and information propagation on trust networks.
", "doi": "10.1017/s0956792524000895", "issn": "0956-7925", "publisher": "Cambridge University Press (CUP)", "publication": "European Journal of Applied Mathematics", "publication_date": "2025-10", "series_number": "5", "volume": "36", "issue": "5", "pages": "1040-1061" }, { "id": "authors:9mnvk-fp456", "collection": "authors", "collection_id": "9mnvk-fp456", "cite_using_url": "https://authors.library.caltech.edu/records/9mnvk-fp456", "type": "article", "title": "Nesterov acceleration for ensemble Kalman inversion and variants", "author": [ { "family_name": "Vernon", "given_name": "Sydney", "clpid": "Vernon-Sydney" }, { "family_name": "Bach", "given_name": "Eviatar", "orcid": "0000-0002-9725-0203", "clpid": "Bach-Eviatar" }, { "family_name": "Dunbar", "given_name": "Oliver R.A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" } ], "abstract": "Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient descent. Here, we show that Nesterov acceleration is effective in speeding up the reduction of the EKI cost function on a variety of inverse problems. We also implement Nesterov acceleration for two EKI variants, unscented Kalman inversion and ensemble transform Kalman inversion. Our specific implementation takes the form of a particle-level nudge that is demonstrably simple to couple in a black-box fashion with any existing EKI variant algorithms, comes with no additional computational expense, and with no additional tuning hyperparameters. This work shows a pathway for future research to translate advances in gradient-based optimization into advances in gradient-free Kalman optimization.
", "doi": "10.1016/j.jcp.2025.114063", "issn": "0021-9991", "publisher": "Elsevier", "publication": "Journal of Computational Physics", "publication_date": "2025-08-15", "volume": "535", "pages": "114063" }, { "id": "authors:anyvf-6j324", "collection": "authors", "collection_id": "anyvf-6j324", "cite_using_url": "https://authors.library.caltech.edu/records/anyvf-6j324", "type": "article", "title": "Hyperparameter optimization for randomized algorithms: a case study on random features", "author": [ { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Nelsen", "given_name": "Nicholas H.", "orcid": "0000-0002-8328-1199", "clpid": "Nelsen-Nicholas-Hao" }, { "family_name": "Mutic", "given_name": "Maya", "clpid": "Mutic-Maya" } ], "abstract": "Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random neural network whose hidden weights and biases are sampled from a probability distribution. Only the final output layer is fit to data. In randomized algorithms like RFR, the hyperparameters that characterize the sampling distribution greatly impact performance, yet are not directly accessible from samples. This makes optimization of hyperparameters via standard (gradient-based) optimization tools inapplicable. Inspired by Bayesian ideas from GPR, this paper introduces a random objective function that is tailored for hyperparameter tuning of vector-valued random features. The objective is minimized with ensemble Kalman inversion (EKI). EKI is a gradient-free particle-based optimizer that is scalable to high-dimensions and robust to randomness in objective functions. A numerical study showcases the new black-box methodology to learn hyperparameter distributions in several problems that are sensitive to the hyperparameter selection: two global sensitivity analyses, integrating a chaotic dynamical system, and solving a Bayesian inverse problem from atmospheric dynamics. The success of the proposed EKI-based algorithm for RFR suggests its potential for automated optimization of hyperparameters arising in other randomized algorithms.", "doi": "10.1007/s11222-025-10587-w", "issn": "0960-3174", "publisher": "Springer Science and Business Media LLC", "publication": "Statistics and Computing", "publication_date": "2025-02-25", "series_number": "3", "volume": "35", "issue": "3", "pages": "56" }, { "id": "authors:2x0kp-pkz30", "collection": "authors", "collection_id": "2x0kp-pkz30", "cite_using_url": "https://authors.library.caltech.edu/records/2x0kp-pkz30", "type": "article", "title": "Online Learning of Entrainment Closures in a Hybrid Machine Learning Parameterization", "author": [ { "family_name": "Christopoulos", "given_name": "Costa", "orcid": "0000-0002-8552-465X", "clpid": "Christopoulos-Costa" }, { "family_name": "Lopez\u2010Gomez", "given_name": "Ignacio", "orcid": "0000-0002-7255-5895", "clpid": "Lopez\u2010Gomez-Ignacio" }, { "family_name": "Beucler", "given_name": "Tom", "orcid": "0000-0002-5731-1040" }, { "family_name": "Cohen", "given_name": "Yair", "orcid": "0000-0002-9615-2476", "clpid": "Cohen-Yair" }, { "family_name": "Kawczynski", "given_name": "Charles", "clpid": "Kawczynski-Charles-N" }, { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" } ], "abstract": "This work integrates machine learning into an atmospheric parameterization to target uncertain mixing processes while maintaining interpretable, predictive, and well-established physical equations. We adopt an eddy-diffusivity mass-flux (EDMF) parameterization for the unified modeling of various convective and turbulent regimes. To avoid drift and instability that plague offline-trained machine learning parameterizations that are subsequently coupled with climate models, we frame learning as an inverse problem: Data-driven models are embedded within the EDMF parameterization and trained online in a one-dimensional vertical global climate model (GCM) column. Training is performed against output from large-eddy simulations (LES) forced with GCM-simulated large-scale conditions in the Pacific. Rather than optimizing subgrid-scale tendencies, our framework directly targets climate variables of interest, such as the vertical profiles of entropy and liquid water path. Specifically, we use ensemble Kalman inversion to simultaneously calibrate both the EDMF parameters and the parameters governing data-driven lateral mixing rates. The calibrated parameterization outperforms existing EDMF schemes, particularly in tropical and subtropical locations of the present climate, and maintains high fidelity in simulating shallow cumulus and stratocumulus regimes under increased sea surface temperatures from AMIP4K experiments. The results showcase the advantage of physically constraining data-driven models and directly targeting relevant variables through online learning to build robust and stable machine learning parameterizations.
", "doi": "10.1029/2024ms004485", "issn": "1942-2466", "publisher": "American Geophysical Union", "publication": "Journal of Advances in Modeling Earth System (JAMES)", "publication_date": "2024-11", "series_number": "11", "volume": "16", "issue": "11", "pages": "e2024MS004485" }, { "id": "authors:sdv6s-rr183", "collection": "authors", "collection_id": "sdv6s-rr183", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220926-576391900.2", "type": "article", "title": "Ensemble-Based Experimental Design for Targeting Data Acquisition to Inform Climate Models", "author": [ { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Howland", "given_name": "Michael F.", "orcid": "0000-0002-2878-3874", "clpid": "Howland-Michael-F" }, { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" }, { "family_name": "Stuart", "given_name": "Andrew M.", "orcid": "0000-0001-9091-7266", "clpid": "Stuart-A-M" } ], "abstract": "Data required to calibrate uncertain general circulation model (GCM) parameterizations are often only available in limited regions or time periods, for example, observational data from field campaigns, or data generated in local high-resolution simulations. This raises the question of where and when to acquire additional data to be maximally informative about parameterizations in a GCM. Here we construct a new ensemble-based parallel algorithm to automatically target data acquisition to regions and times that maximize the uncertainty reduction, or information gain, about GCM parameters. The algorithm uses a Bayesian framework that exploits a quantified distribution of GCM parameters as a measure of uncertainty. This distribution is informed by time-averaged climate statistics restricted to local regions and times. The algorithm is embedded in the recently developed calibrate-emulate-sample framework, which performs efficient model calibration and uncertainty quantification with only O(10\u00b2) model evaluations, compared with O(10\u2075) evaluations typically needed for traditional approaches to Bayesian calibration. We demonstrate the algorithm with an idealized GCM, with which we generate surrogates of local data. In this perfect-model setting, we calibrate parameters and quantify uncertainties in a quasi-equilibrium convection scheme in the GCM. We consider targeted data that are (a) localized in space for statistically stationary simulations, and (b) localized in space and time for seasonally varying simulations. In these proof-of-concept applications, the calculated information gain reflects the reduction in parametric uncertainty obtained from Bayesian inference when harnessing a targeted sample of data. The largest information gain typically, but not always, results from regions near the intertropical convergence zone.", "doi": "10.1029/2022ms002997", "issn": "1942-2466", "publisher": "American Geophysical Union", "publication": "Journal of Advances in Modeling Earth Systems", "publication_date": "2022-09", "series_number": "9", "volume": "14", "issue": "9", "pages": "Art. No. e2022MS002997" }, { "id": "authors:1q6gn-mvc46", "collection": "authors", "collection_id": "1q6gn-mvc46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220810-402975000", "type": "article", "title": "Training physics\u2010based machine\u2010learning parameterizations with gradient\u2010free ensemble Kalman methods", "author": [ { "family_name": "Lopez-Gomez", "given_name": "Ignacio", "orcid": "0000-0002-7255-5895", "clpid": "Lopez-Gomez-Ignacio" }, { "family_name": "Christopoulos", "given_name": "Costa", "orcid": "0000-0002-8552-465X", "clpid": "Christopoulos-Costa-D" }, { "family_name": "Ervik", "given_name": "Haakon Ludvig Langeland", "orcid": "0000-0003-2912-5774", "clpid": "Ervik-Haakon-Ludvig-Langeland" }, { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Cohen", "given_name": "Yair", "orcid": "0000-0002-9615-2476", "clpid": "Cohen-Yair" }, { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" } ], "abstract": "Most machine learning applications in Earth system modeling currently rely on gradient-based supervised learning. This imposes stringent constraints on the nature of the data used for training (typically, residual time tendencies are needed), and it complicates learning about the interactions between machine-learned parameterizations and other components of an Earth system model. Approaching learning about process-based parameterizations as an inverse problem resolves many of these issues, since it allows parameterizations to be trained with partial observations or statistics that directly relate to quantities of interest in long-term climate projections. Here we demonstrate the effectiveness of Kalman inversion methods in treating learning about parameterizations as an inverse problem. We consider two different algorithms: unscented and ensemble Kalman inversion. Both methods involve highly parallelizable forward model evaluations, converge exponentially fast, and do not require gradient computations. In addition, unscented Kalman inversion provides a measure of parameter uncertainty. We illustrate how training parameterizations can be posed as a regularized inverse problem and solved by ensemble Kalman methods through the calibration of an eddy-diffusivity mass-flux scheme for subgrid-scale turbulence and convection, using data generated by large-eddy simulations. We find the algorithms amenable to batching strategies, robust to noise and model failures, and efficient in the calibration of hybrid parameterizations that can include empirical closures and neural networks.", "doi": "10.1029/2022ms003105", "issn": "1942-2466", "publisher": "American Geophysical Union", "publication": "Journal of Advances in Modeling Earth Systems", "publication_date": "2022-08-11", "pages": "Art. No. e2022MS003105" }, { "id": "authors:s3q2y-tpm38", "collection": "authors", "collection_id": "s3q2y-tpm38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220815-504980000", "type": "article", "title": "An Efficient Bayesian Approach to Learning Droplet Collision Kernels: Proof of Concept Using \"Cloudy,\" a New n-Moment Bulk Microphysics Scheme", "author": [ { "family_name": "Bieli", "given_name": "Melanie", "orcid": "0000-0002-2056-9486", "clpid": "Bieli-Melanie" }, { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "De Jong", "given_name": "Emily K.", "orcid": "0000-0002-5310-4554", "clpid": "De-Jong-Emily-K" }, { "family_name": "Jaruga", "given_name": "Anna", "orcid": "0000-0003-3194-6440", "clpid": "Jaruga-Anna" }, { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" }, { "family_name": "Bischoff", "given_name": "Tobias", "orcid": "0000-0003-3930-2762", "clpid": "Bischoff-Tobias" } ], "abstract": "The small-scale microphysical processes governing the formation of precipitation particles cannot be resolved explicitly by cloud resolving and climate models. Instead, they are represented by microphysics schemes that are based on a combination of theoretical knowledge, statistical assumptions, and fitting to data (\"tuning\"). Historically, tuning was done in an ad hoc fashion, leading to parameter choices that are not explainable or repeatable. Recent work has treated it as an inverse problem that can be solved by Bayesian inference. The posterior distribution of the parameters given the data\u2014the solution of Bayesian inference\u2014is found through computationally expensive sampling methods, which require over O(10\u2075) evaluations of the forward model; this is prohibitive for many models. We present a proof of concept of Bayesian learning applied to a new bulk microphysics scheme named \"Cloudy,\" using the recently developed Calibrate-Emulate-Sample (CES) algorithm. Cloudy models collision-coalescence and collisional breakup of cloud droplets with an adjustable number of prognostic moments and with easily modifiable assumptions for the cloud droplet mass distribution and the collision kernel. The CES algorithm uses machine learning tools to accelerate Bayesian inference by reducing the number of forward evaluations needed to O(10\u00b2). It also exhibits a smoothing effect when forward evaluations are polluted by noise. In a suite of perfect-model experiments, we show that CES enables computationally efficient Bayesian inference of parameters in Cloudy from noisy observations of moments of the droplet mass distribution. In an additional imperfect-model experiment, a collision kernel parameter is successfully learned from output generated by a Lagrangian particle-based microphysics model.", "doi": "10.1029/2022ms002994", "issn": "1942-2466", "publisher": "American Geophysical Union", "publication": "Journal of Advances in Modeling Earth Systems", "publication_date": "2022-08", "series_number": "8", "volume": "14", "issue": "8", "pages": "Art. No. e2022MS002994" }, { "id": "authors:4xm8c-sh061", "collection": "authors", "collection_id": "4xm8c-sh061", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220325-220336231", "type": "article", "title": "Epidemic management and control through risk-dependent individual contact interventions", "author": [ { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" }, { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Wu", "given_name": "Jinlong", "orcid": "0000-0001-7438-4228", "clpid": "Wu-Jinlong" }, { "family_name": "B\u00f6ttcher", "given_name": "Lucas", "orcid": "0000-0003-1700-1897", "clpid": "B\u00f6ttcher-Lucas" }, { "family_name": "Burov", "given_name": "Dmitry", "orcid": "0000-0002-5060-6794", "clpid": "Burov-Dmitry" }, { "family_name": "Garbuno-I\u00f1igo", "given_name": "Alfredo", "orcid": "0000-0003-3279-619X", "clpid": "Garbuno-I\u00f1igo-Alfredo" }, { "family_name": "Wagner", "given_name": "Gregory L.", "orcid": "0000-0001-5317-2445", "clpid": "Wagner-Gregory-L" }, { "family_name": "Pei", "given_name": "Sen", "orcid": "0000-0002-7072-2995", "clpid": "Pei-Sen" }, { "family_name": "Daraio", "given_name": "Chiara", "orcid": "0000-0001-5296-4440", "clpid": "Daraio-C" }, { "family_name": "Ferrari", "given_name": "Raffaele", "orcid": "0000-0003-1895-4294", "clpid": "Ferrari-Raffaele" }, { "family_name": "Shaman", "given_name": "Jeffrey", "orcid": "0000-0002-7216-7809", "clpid": "Shaman-Jeffrey" } ], "abstract": "Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network. Network DA exploits diverse sources of health data together with the proximity data from mobile devices that exposure notification apps rely upon. It provides users with continuously assessed individual risks of exposure and infection, which can form the basis for targeting individual contact interventions. Simulations of the early COVID-19 epidemic in New York City are used to establish proof-of-concept. In the simulations, network DA identifies up to a factor 2 more infections than contact tracing when both harness the same contact data and diagnostic test data. This remains true even when only a relatively small fraction of the population uses network DA. When a sufficiently large fraction of the population (\u2273 75%) uses network DA and complies with individual contact interventions, targeting contact interventions with network DA reduces deaths by up to a factor 4 relative to TTI. Network DA can be implemented by expanding the computational backend of existing exposure notification apps, thus greatly enhancing their capabilities. Implemented at scale, it has the potential to precisely and effectively control future epidemics while minimizing economic disruption.", "doi": "10.1371/journal.pcbi.1010171", "pmcid": "PMC9223336", "issn": "1553-734X", "publisher": "Public Library of Science", "publication": "PLoS Computational Biology", "publication_date": "2022-06-23", "series_number": "6", "volume": "18", "issue": "6", "pages": "Art. No. e1010171" }, { "id": "authors:cx7ps-01463", "collection": "authors", "collection_id": "cx7ps-01463", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210412-121307581", "type": "article", "title": "Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods", "author": [ { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Duncan", "given_name": "Andrew B.", "clpid": "Duncan-Andrew-B" }, { "family_name": "Stuart", "given_name": "Andrew M.", "orcid": "0000-0001-9091-7266", "clpid": "Stuart-A-M" }, { "family_name": "Wolfram", "given_name": "Marie-Therese", "orcid": "0000-0003-1133-8253", "clpid": "Wolfram-Marie-Therese" } ], "abstract": "The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical, and social sciences. However, model complexity often leads to parameter-to-data maps which are expensive to evaluate and are only available through noisy approximations. This paper is concerned with the use of interacting particle systems for the solution of the resulting inverse problems for parameters. Of particular interest is the case where the available forward model evaluations are subject to rapid fluctuations, in parameter space, superimposed on the smoothly varying large-scale parametric structure of interest. A motivating example from climate science is presented, and ensemble Kalman methods (which do not use the derivative of the parameter-to-data map) are shown, empirically, to perform well. Multiscale analysis is then used to analyze the behavior of interacting particle system algorithms when rapid fluctuations, which we refer to as noise, pollute the large-scale parametric dependence of the parameter-to-data map. Ensemble Kalman methods and Langevin-based methods (the latter use the derivative of the parameter-to-data map) are compared in this light. The ensemble Kalman methods are shown to behave favorably in the presence of noise in the parameter-to-data map, whereas Langevin methods are adversely affected. On the other hand, Langevin methods have the correct equilibrium distribution in the setting of noise-free forward models, while ensemble Kalman methods only provide an uncontrolled approximation, except in the linear case. Therefore a new class of algorithms, ensemble Gaussian process samplers, which combine the benefits of both ensemble Kalman and Langevin methods, are introduced and shown to perform favorably.", "doi": "10.1137/21M1410853", "issn": "1536-0040", "publisher": "Society for Industrial and Applied Mathematics", "publication": "SIAM Journal on Applied Dynamical Systems", "publication_date": "2022-06-21", "series_number": "2", "volume": "21", "issue": "2", "pages": "1539-1572" }, { "id": "authors:w8jdm-e8b55", "collection": "authors", "collection_id": "w8jdm-e8b55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210823-173258629", "type": "article", "title": "Parameter Uncertainty Quantification in an Idealized GCM With a Seasonal Cycle", "author": [ { "family_name": "Howland", "given_name": "Michael F.", "orcid": "0000-0002-2878-3874", "clpid": "Howland-Michael-F" }, { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" } ], "abstract": "Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top-of-atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and parameters. Bayesian calibration can estimate climate model parameters and their uncertainty using a larger fraction of the available data and automatically exploring the parameter space more broadly. In Bayesian learning, it is natural to exploit the seasonal cycle, which has large amplitude compared with anthropogenic climate change in many climate statistics. In this study, we develop methods for the calibration and uncertainty quantification (UQ) of model parameters exploiting the seasonal cycle, and we demonstrate a proof-of-concept with an idealized general circulation model (GCM). UQ is performed using the calibrate-emulate-sample approach, which combines stochastic optimization and machine learning emulation to speed up Bayesian learning. The methods are demonstrated in a perfect-model setting through the calibration and UQ of a convective parameterization in an idealized GCM with a seasonal cycle. Calibration and UQ based on seasonally averaged climate statistics, compared to annually averaged, reduces the calibration error by up to an order of magnitude and narrows the spread of the non-Gaussian posterior distributions by factors between two and five, depending on the variables used for UQ. The reduction in the spread of the parameter posterior distribution leads to a reduction in the uncertainty of climate model predictions.", "doi": "10.1029/2021MS002735", "issn": "1942-2466", "publisher": "American Geophysical Union", "publication": "Journal of Advances in Modelling Earth Systems", "publication_date": "2022-03", "series_number": "3", "volume": "14", "issue": "3", "pages": "Art. No. e2021MS002735" }, { "id": "authors:5x2v8-6ma54", "collection": "authors", "collection_id": "5x2v8-6ma54", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210113-143919927", "type": "article", "title": "Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM", "author": [ { "family_name": "Dunbar", "given_name": "Oliver R. A.", "orcid": "0000-0001-7374-0382", "clpid": "Dunbar-Oliver-R-A" }, { "family_name": "Garbuno-Inigo", "given_name": "Alfredo", "orcid": "0000-0003-3279-619X", "clpid": "Garbuno-Inigo-Alfredo" }, { "family_name": "Schneider", "given_name": "Tapio", "orcid": "0000-0001-5687-2287", "clpid": "Schneider-T" }, { "family_name": "Stuart", "given_name": "Andrew M.", "orcid": "0000-0001-9091-7266", "clpid": "Stuart-A-M" } ], "abstract": "Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically require O(10\u2075) model runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires only O(10\u00b2) model runs and can accommodate internal climate variability. The approach consists of three stages: (a) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (b) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (c) a sampling stage approximates the Bayesian posterior distributions by sampling the GP emulator with MCMC. We demonstrate the feasibility and computational efficiency of this calibrate-emulate-sample (CES) approach in a perfect-model setting. Using an idealized general circulation model, we estimate parameters in a simple convection scheme from synthetic data generated with the model. The CES approach generates probability distributions of the parameters that are good approximations of the Bayesian posteriors, at a fraction of the computational cost usually required to obtain them. Sampling from this approximate posterior allows the generation of climate predictions with quantified parametric uncertainties.", "doi": "10.1029/2020MS002454", "issn": "1942-2466", "publisher": "American Geophysical Union", "publication": "Journal of Advances in Modelling Earth Systems", "publication_date": "2021-09", "series_number": "9", "volume": "13", "issue": "9", "pages": "Art. No. e2020MS002454" } ]