@article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/107459,
    title ="Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM",
    author = "Dunbar, Oliver R. A. and Garbuno-Inigo, Alfredo",
    
    
    
    
    month = "January",
    year = "2021",
    
    
    
    url = "https://resolver.caltech.edu/CaltechAUTHORS:20210113-143919927",
    note = "License: Attribution 4.0 International. \n\nPublished Online: Mon, 4 Jan 2021. \n\nThis work was supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by the Hopewell Fund, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS1835860). A.M.S. was also supported by the Office of Naval Research (award N00014-17-1-2079). We thank Emmet Cleary for his preliminary work underlying some of the results shown here. \n\nData Availability: All computer code used in this paper is open source. The code for the idealized GCM, the Julia code for the CES algorithm, the plot tools, and the slurm/bash\nscripts to run both GCM and CES are available at https://doi.org/10.5281/zenodo.4393029.",
    revision_no = "12",
    abstract = "Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes an 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(10⁵) model runs, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires only O(10²) model runs and can accommodate internal climate variability. The approach consists of three stages: (i) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (ii) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (iii) a sampling stage approximates the Bayesian posterior distributions by using the GP emulator and then samples using 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 data surrogates 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.",
}
@article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/106905,
    title ="An Improved Perturbation Pressure Closure for Eddy-Diffusivity Mass-Flux Schemes",
    author = "He, Jia and Cohen, Yair",
    
    
    
    
    month = "December",
    year = "2020",
    
    
    
    url = "https://resolver.caltech.edu/CaltechAUTHORS:20201204-110354763",
    note = "© 2020. California Institute of Technology. Government sponsorship acknowledged. \n\nThis research was made possible by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Earthrise Alliance, Mountain Philanthropies, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS-1835860). We would like to thank the Resnick Sustainability Institute at Caltech for fellowship support. Parts of the research were carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration and funded through the internal Research and Technology Development program. The PyCLES code used to generate LES results is available at climate-dynamics.org/software/#pycles. The SCM code is available at https://doi.org/10.5281/zenodo.4291143.",
    revision_no = "10",
    abstract = "Convection parameterizations such as eddy-diffusivity mass-flux (EDMF) schemes require a consistent closure formulation for the perturbation pressure, which arises in the equations for vertical momentum and turbulence kinetic energy (TKE). Here we derive an expression for the perturbation pressure from approximate analytical solutions for 2D and 3D rising thermal bubbles. The new closure combines a modified pressure drag and virtual mass effects with a new momentum advection term. This momentum advection is an important source in the lower half of the thermal bubble and at cloud base levels in convective systems. It represents the essential physics of the perturbation pressure, that is, to ensure the 3D non-divergent properties of the flow. Moreover, the new formulation modifies the pressure drag to be inversely proportional to updraft depth. This is found to significantly improve simulations of the diurnal cycle of deep convection, without compromising simulations of shallow convection. It is thus a key step toward a unified scheme for a range of convective motions. By assuming that the pressure only redistributes TKE between plumes and the environment, rather than vertically, a closure for the velocity pressure-gradient correlation is obtained from the perturbation pressure closure. This novel pressure closure is implemented in an extended EDMF scheme and is shown to successfully simulate a rising bubble test case as well as shallow and deep convection cases in a single column model.",
}
@article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/106265,
    title ="Top-of-atmosphere albedo bias from neglecting three-dimensional radiative transfer through clouds",
    author = "Singer, Clare E. and Lopez-Gomez, Ignacio",
    
    
    
    
    month = "October",
    year = "2020",
    
    
    
    url = "https://resolver.caltech.edu/CaltechAUTHORS:20201023-133020582",
    note = "Published Online: Fri, 16 Oct 2020. \n\nC.E.S. acknowledges support from NSF Graduate Research Fellowship under Grant No. DGE-1745301. I.L. is supported by a fellowship from the Resnick Sustainability Institute at Caltech. This research was additionally supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program and by Mountain Philanthropies. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. \n\nAll code or data used in this paper are freely available online. The LES were run using the PyCLES code (https://climate-dynamics.org/software/#pycles). The radiative transfer computations were done using the libRadtran code (http://www.libradtran.org). Post-processed LES 3D fields used as input files for libRadtran computations are available in Singer et al. (2020). The ISCCP data were downloaded from the GEWEX database (https://climserv.ipsl.polytechnique.fr/gewexca/).",
    revision_no = "12",
    abstract = "Clouds cover on average nearly 70% of Earth’s surface and are important for the global albedo. The magnitude of the shortwave reflection by clouds depends on their location, optical properties, and 3D structure. Earth system models are unable to perform 3D radiative transfer calculations and thus partially neglect the effect of cloud morphology on albedo. We show how the resulting radiative flux bias depends on cloud morphology and solar zenith angle. Using large-eddy simulations to produce 3D cloud fields, a Monte Carlo code for 3D radiative transfer, and observations of cloud climatology, we estimate the effect of this flux bias on global climate. The flux bias is largest at small zenith angles and for deeper clouds, while the albedo bias is largest (and negative) for large zenith angles. Globally, the radiative flux bias is estimated to be 1.6 W m⁻² and locally can be on the order of 5 W m⁻².",
}
@article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/106562,
    title ="Ensemble Kalman Inversion for Sparse Learning of Dynamical Systems from Time-Averaged Data",
    author = "Schneider, Tapio and Stuart, Andrew M.",
    journal = "arXiv",
    
    
    
    month = "July",
    year = "2020",
    
    
    
    url = "https://resolver.caltech.edu/CaltechAUTHORS:20201109-141011032",
    note = "We thank Melanie Bieli, Tobias Bischoff and Anna Jaruga for sharing their formulation of the moment-based coalescence equation, and for discussions about it. All authors are supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Earthrise Alliance, Mountain Philanthropies, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS1835860). A.M.S. is also supported by NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079).",
    revision_no = "10",
    abstract = "Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but also to the time derivative. In many applications, the data are available only in the form of time-averages such as moments and autocorrelation functions. We propose a sparse learning methodology to discover the vector fields defining a (possibly stochastic or partial) differential equation, using only time-averaged statistics. Such a formulation of sparse learning naturally leads to a nonlinear inverse problem to which we apply the methodology of ensemble Kalman inversion (EKI). EKI is chosen because it may be formulated in terms of the iterative solution of quadratic optimization problems; sparsity is then easily imposed. We then apply the EKI-based sparse learning methodology to various examples governed by stochastic differential equations (a noisy Lorenz 63 system), ordinary differential equations (Lorenz 96 system and coalescence equations), and a partial differential equation (the Kuramoto-Sivashinsky equation). The results demonstrate that time-averaged statistics can be used for data-driven discovery of differential equations using sparse EKI. The proposed sparse learning methodology extends the scope of data-driven discovery of differential equations to previously challenging applications and data-acquisition scenarios.",
}
@article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/106301,
    title ="Seasonal cycle of idealized polar clouds: large eddy simulations driven by a GCM",
    author = "Zhang, Xiyue and Schneider, Tapio",
    
    
    
    
    month = "June",
    year = "2020",
    
    
    
    url = "https://resolver.caltech.edu/CaltechAUTHORS:20201027-125955966",
    note = "License: Attribution-NonCommercial-NoDerivatives 4.0 International. \n\nPublished Online: Tue, 9 Jun 2020. \n\nX.Z. is supported by an Advanced Study Program postdoctoral fellowship from the National Center for Atmospheric Research. Part of this material is based upon work supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement No. 1852977. \n\nPart of this research was supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Mountain Philanthropies, and by the National Science Foundation (NSF grant AGS-1835860). Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The simulations were performed on Caltech's High Performing Cluster, which is partially supported by a grant from the Gordon and Betty Moore Foundation. The GCM and LES codes are available online at http://climate-dynamics.org/software. GCM forcing and LES output files are\navailable online at https://data.caltech.edu/records/1429.",
    revision_no = "9",
    abstract = "The uncertainty in polar cloud feedbacks calls for process understanding of the cloud response to climate warming. As an initial step, we investigate the seasonal cycle of polar clouds in the current climate by adopting a novel modeling framework using large eddy simulations (LES), which explicitly resolve cloud dynamics. Resolved horizontal and vertical advection of heat and moisture from an idealized GCM are prescribed as forcing in the LES. The LES are also forced with prescribed sea ice thickness, but surface temperature, atmospheric temperature, and moisture evolve freely without nudging. A semigray radiative transfer scheme, without water vapor or cloud feedbacks, allows the GCM and LES to achieve closed energy budgets more easily than would be possible with more complex schemes; this allows the mean states in the two models to be consistently compared, without the added complications from interaction with more comprehensive radiation. We show that the LES closely follow the GCM seasonal cycle, and the seasonal cycle of low clouds in the LES resembles observations: maximum cloud liquid occurs in late summer and early autumn, and winter clouds are dominated by ice in the upper troposphere. Large-scale advection of moisture provides the main source of water vapor for the liquid clouds in summer, while a temperature advection peak in winter makes the atmosphere relatively dry and reduces cloud condensate. The framework we develop and employ can be used broadly for studying cloud processes and the response of polar clouds to climate warming.",
}
@article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/106558,
    title ="Learning Stochastic Closures Using Ensemble Kalman Inversion",
    author = "Schneider, Tapio and Stuart, Andrew M.",
    journal = "arXiv",
    
    
    
    month = "April",
    year = "2020",
    
    
    
    url = "https://resolver.caltech.edu/CaltechAUTHORS:20201109-140955956",
    note = "The authors thank Dr. Yvo Pokern at University College London for providing the butane dihedral angle data. All authors are supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Earthrise Alliance, Mountain Philanthropies, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS1835860). A.M.S. is also supported by NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079).",
    revision_no = "10",
    abstract = "Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions within the first principles description. Therefore researchers often seek simpler descriptions that describe complex phenomena without numerically resolving all the interacting components. Stochastic differential equations (SDEs) arise naturally as models in this context. The growth in data acquisition provides an opportunity for the systematic derivation of SDE models in many disciplines. However, inconsistencies between SDEs and real data at small time scales often cause problems, when standard statistical methodology is applied to parameter estimation. The incompatibility between SDEs and real data can be addressed by deriving sufficient statistics from the time-series data and learning parameters of SDEs based on these. Following this approach, we formulate the fitting of SDEs to sufficient statistics from real data as an inverse problem and demonstrate that this inverse problem can be solved by using ensemble Kalman inversion (EKI). Furthermore, we create a framework for non-parametric learning of drift and diffusion terms by introducing hierarchical, refineable parameterizations of unknown functions, using Gaussian process regression. We demonstrate the proposed methodology for the fitting of SDE models, first in a simulation study with a noisy Lorenz 63 model, and then in other applications, including dimension reduction starting from various deterministic chaotic systems arising in the atmospheric sciences, large-scale pattern modeling in climate dynamics, and simplified models for key observables arising in molecular dynamics. The results confirm that the proposed methodology provides a robust and systematic approach to fitting SDE models to real data.",
}