Prediction of extreme events under climate change is challenging but essential for risk management of natural disasters. Although earth system models (ESMs) are arguably our best tool to predict climate extremes, their high computational cost restricts the application to project only a few future scenarios. Emulators, or reduced-complexity models, serve as a complement to ESMs that achieve a fast prediction of the local response to various climate change scenarios. Here we propose a data-driven framework to emulate the full statistics of spatially resolved climate extremes. The variable of interest is the near-surface daily maximum temperature. The spatial patterns of temperature variations are assumed to be independent of time and extracted using Empirical Orthogonal Functions (EOFs). The time dependence is encoded through the coefficients of leading EOFs which are decomposed into long-term seasonal variations and daily fluctuations. The former are assumed to be functions of the global mean temperature, while the latter are modelled as Gaussian stochastic processes with temporal correlation conditioned on the season. The emulator is trained and tested using the simulation data in CMIP6. By generating multiple realizations, the emulator shows significant performance in predicting the temporal evolution of the probability distribution of local daily maximum temperature. Furthermore, the uncertainty of the emulated statistics is quantified to account for the internal variability. The emulation accuracy in testing scenarios remains consistent with the training datasets. The performance of the emulator suggests that the proposed framework can be generalized to other climate extremes and more complicated scenarios of climate change.

A document by Simone Silvestri. Click on the document to view its contents.

Current eddy-permitting and eddy-resolving ocean models require dissipation to prevent a spurious accumulation of enstrophy at the grid scale. We introduce a new numerical scheme for momentum advection in large-scale ocean models that involves upwinding through a weighted essentially non-oscillatory (WENO) reconstruction. The new scheme provides implicit dissipation and thereby avoids the need for an additional explicit dissipation that may require calibration of unknown parameters. This approach uses the rotational, "vector invariant" formulation of the momentum advection operator that is widely employed by global general circulation models. A novel formulation of the WENO "smoothness indicators" is key for avoiding excessive numerical dissipation of kinetic energy and enstrophy at grid-resolved scales. We test the new advection scheme against a standard approach that combines explicit dissipation with a dispersive discretization of the rotational advection operator in two scenarios: (i) two-dimensional turbulence and (ii) three-dimensional baroclinic equilibration. In both cases, the solutions are stable, free from dispersive artifacts, and achieve increased "effective" resolution compared to other approaches commonly used in ocean models.

We describe CATKE, a parameterization for ocean microturbulence with scales between 1 and 100 meters. CATKE is a one-equation model that predicts diffusive turbulent vertical fluxes a prognostic turbulent kinetic energy (TKE) and a diagnostic mixing length that features a dynamic model for convective adjustment (CA). With its convective mixing length, CATKE predicts not just the depth range where microturbulence acts but also the timescale over which mixing occurs, an important aspect of turbulent convection not captured by convective adjustment schemes. As a result, CATKE can describe the competition between convection and other processes such as baroclinic restractification or biogeochemical production-destruction. We estimate CATKE’s free parameters with a posteriori calibration to eighteen large eddy simulations of the ocean surface boundary layer, and validate CATKE against twelve additional large eddy simulations with stronger and weaker forcing than used during calibration. We find that a CATKE-parameterized single column model accurately predicts the depth structure of buoyancy and momentum at vertical resolutions between 2 and 16 meters and with time steps of 10-20 minutes. We propose directions for future model development, and future efforts to recalibrate CATKE’s parameters against more comprehensive and realistic datasets.

We describe CATKE, a parameterization for fluxes associated with small-scale or “microscale’ ocean turbulent mixing on scales between 1 and 100 meters. CATKE uses a downgradient formulation that depends on a prognostic turbulent kinetic energy (TKE) variable and a diagnostic mixing length scale that includes a dynamic convective adjustment (CA) component. With its dynamic convective mixing length, CATKE predicts not just the depth spanned by convective plumes but also the characteristic convective mixing timescale, an important aspect of turbulent convection not captured by simpler static convective adjustment schemes. As a result, CATKE can describe the competition between convection and other processes such as shear-driven mixing and baroclinic restratification. To calibrate CATKE, we use Ensemble Kalman Inversion to minimize the error between 21~large eddy simulations (LES) and predictions of the LES data by CATKE-parameterized single column simulations at three different vertical resolutions. We find that CATKE makes accurate predictions of both idealized and realistic LES compared to microscale turbulence parameterizations commonly used in climate models.

Fast emulators of comprehensive climate models are used to explore the impact of anthropogenic emissions in future climate. A new approach to emulators is introduced that predicts distributions of coarse-grained monthly averaged variables as a multivariate Gaussian distribution. The emulator is trained with a state-of-the-art climate model and serves as a good first-order representation for many statistics of future climates. The emulator is applied to statistics of surface temperature and relative humidity for illustrative purposes, but the approach can be applied to any other variable of interest as long the multivariate Gaussian approximation captures the bulk of the distribution. Importantly the emulator accounts for the internal variability of the system, allowing one to examine shifts in distributions of climate variables. In this sense the work can be considered as an extension of pattern scaling emulators that focus on the evolution of the mean rather than the distribution of climate variables.

Parameterizations of unresolved turbulent processes often compromise the fidelity of large-scale ocean models. In this work, we argue for a Bayesian approach to the refinement and evaluation of turbulence parameterizations. Using an ensemble of large eddy simulations of turbulent penetrative convection in the surface boundary layer, we demonstrate the method by estimating the uncertainty of parameters in the convective limit of the popular ‘K-Profile Parameterization’. We uncover structural deficiencies and propose an alternative scaling that overcomes them.

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the limitations of traditional neural networks (NNs) in fluid dynamical applications in that they can readily incorporate conservation laws and boundary conditions and are stable when integrated over time. We advocate a method that employs a ‘residual’ approach, in which the NN is used to improve upon an existing parameterization through the representation of residual fluxes which are not captured by the base parameterization. This reduces the amount of training required and providing a method for capturing up-gradient and nonlocal fluxes. As an illustrative example, we consider the parameterization of free convection of the oceanic boundary layer triggered by buoyancy loss at the surface. We demonstrate that a simple parameterization of the process — convective adjustment — can be improved upon by training a NDE against highly resolved explicit models, to capture entrainment fluxes at the base of the well-mixed layer, fluxes that convective adjustment itself cannot represent. The augmented parameterization outperforms existing commonly used parameterizations such as the K-Profile Parameterization (KPP). We showcase that the NDE performs well independent of the time-stepper and that an online training approach using differentiable simulation via the Julia scientific machine learning software stack improves accuracy by an order-of-magnitude. We conclude that NDEs provide an exciting route forward to the development of representations of sub-grid-scale processes for climate science, opening up myriad new opportunities.