Abstract: Extreme weather has devastating impacts on the American people, our communities, and our economy. All of us have seen the damage wrought by catastrophic wildfires in western states, by floods, and tropical cyclones on the Gulf Coast, and by recent severe tornados in southern and eastern states. Extreme weather also reduces property values, raises the costs of insurance, and poses national and global economic risks from supply chain disruptions and forced migrations. Today, climate change is changing the patterns and risks of extreme weather, including the frequency and severity of many hazards. The challenge of hurricanes and other severe storms, floods, and wildfires is gaining significant attention and the annual cost of climate and weather disasters has been rising. The National Oceanic and Atmospheric Administration (NOAA) has catalogued over $1 trillion of damages during the last seven years (2016-2022). Industry reports caution that by mid-century, insurance premiums in certain markets could rise substantially, straining U.S. households. Last year, the Office of Management and Budget (OMB) cited a potential federal revenue loss of $2 trillion per year from climate change at the end of the century, along with additional expenditures of $25 to $128 billion on selected insurance and disaster relief programs. In addition, there are deeper costs from loss of life, negative health impacts, and the destruction of communities. The Census Bureau recently estimated that in 2022 alone, 3.4 million Americans were displaced from their homes by extreme weather disasters. Moreover, lower-income households are often those at greatest risk from floods, storms, and wildfires. These households have fewer resources to take actions that will offset a rising risk of extreme weather. This PCAST report investigates how recent scientific and technical advances could be used to provide more accurate and actionable information to guide decision-making and policy at all levels. PCAST recommends federal actions to better quantify and disseminate current and future risks of extreme weather, including risks of human and financial losses caused by flood, fire, storms, and drought. PCAST also recommends actions to bolster the emerging private ecosystem providing climate risk information. Finally, PCAST recommends the development of a national adaptation plan to assist communities in preparing for and adapting to changing risks from extreme weather events. This report builds on the October 2021 White House report, A Roadmap to Build a Climate-Resilient Economy, outlining a multi-agency plan to implement Executive Order 14030 on climate-related financial risk. That plan addresses both the rising physical risks from extreme weather, and transition risks in moving toward a low-carbon economy. PCAST’s recommendations focus on how climate science and computing can provide significantly better information about the physical risks from extreme weather to empower households, communities, and companies and enable smart policy.

ID: CaltechAUTHORS:20230531-170532586

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Abstract: Microphysics methods for climate models typically track one, two, or three moments of a droplet size distribution for various categories of liquid, ice, and aerosol. Such methods rely on conversion parameters between these categories, which introduces uncertainty into predictions. While higher-resolution options such as bin and Lagrangian schemes exist, they require too many degrees of freedom for climate modeling applications and introduce numerical challenges. Here we introduce a flexible spectral microphysics method based on collocation of basis functions. This method generalizes to a linear bulk scheme at low resolution and a smoothed bin scheme at high resolution. Tested in an idealized box setting, the method improves spectral accuracy for droplet collision-coalescence and improves precipitation predictions relative to bulk methods; furthermore, it generalizes well to multimodal distributions with less complexity than a bin method. The potential to extend this collocation representation to multiple hydrometeor classes suggests a path forward to unify liquid, ice, and aerosol microphysics in a single, flexible, computational framework for climate modeling.

ID: CaltechAUTHORS:20220520-649616000

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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.

ID: CaltechAUTHORS:20220331-531674000

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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---the solution of Bayesian inference---is found through computationally expensive sampling methods, which require over O(10⁵) 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(10²). 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.

ID: CaltechAUTHORS:20220207-89642000

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Abstract: Targeted high-resolution simulations driven by a general circulation model (GCM) can be used to calibrate GCM parameterizations of processes that are globally unresolvable but can be resolved in limited-area simulations. This raises the question of where to place high-resolution simulations to be maximally informative about the uncertain parameterizations in the global model. Here we construct an ensemble-based parallel algorithm to locate regions that maximize the uncertainty reduction, or information gain, in the uncertainty quantification of GCM parameters with regional data. The algorithm is based on a Bayesian framework that exploits a quantified posterior distribution on GCM parameters as a measure of uncertainty. The algorithm is embedded in the recently developed calibrate-emulate-sample (CES) framework, which performs efficient model calibration and uncertainty quantification with only O(10²) forward model evaluations, compared with O(10⁵) forward model evaluations typically needed for traditional approaches to Bayesian calibration. We demonstrate the algorithm with an idealized GCM, with which we generate surrogates of high-resolution data. In this setting, we calibrate parameters and quantify uncertainties in a quasi-equilibrium convection scheme. We consider (i) localization in space for a statistically stationary problem, and (ii) localization in space and time for a seasonally varying problem. 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 results from regions near the intertropical convergence zone (ITCZ) and indeed the algorithm automatically targets these regions for data collection.

ID: CaltechAUTHORS:20220119-572479000

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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.

ID: CaltechAUTHORS:20201204-110354763

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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.

ID: CaltechAUTHORS:20201023-133020582

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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.

Publication: arXiv
ID: CaltechAUTHORS:20201109-141011032

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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.

Publication: arXiv
ID: CaltechAUTHORS:20201109-140955956

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