Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data

While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines MCMC with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM

Perturbation dynamics of a planktonic ecosystem

Planktonic ecosystems provide a key mechanism for the transfer of carbon from the atmosphere to the deep ocean via the so-called biological pump. Mathematical models of these ecosystems have been used to predict CO2 uptake in surface waters at particular locations, and more recently have been embedded in global climate models. While the equilibrium properties of these models are well studied, less attention has been paid to their response to external perturbations, despite the fact that as a result of the variability of environmental forcing such ecosystems are rarely, if ever, in equilibrium. In this study, linear theory is used to determine the structure of perturbations to state variables of an ecosystem model describing summertime conditions at Ocean Station P (50°N 145°W) that maximize either instantaneous or integrated export flux. As a result of the presence of both direct and indirect pathways to export in this model, these perturbations involve the dynamics of the entire ecosystem. For all optimal perturbations considered, it is found that the flux to higher trophic levels is the primary contributor to export flux, followed by sinking detritus. In contrast, the contribution of aggregation is negligible. In addition, small phytoplankton contribute significantly (comparable to large phytoplankton) to the export flux through indirect pathways, primarily through the microzooplankton, even following a bloom in only large phytoplankton. While the details of these results may be specific to the particular model under consideration, the optimal perturbation framework is general and can be used to probe the dynamics of any mechanistic ecosystem model

Teleconnected warm and cold extremes of North American wintertime temperatures

Current models for spatial extremes are concerned with the joint upper (or lower) tail of the distribution at two or more locations. Such models cannot account for teleconnection patterns of two-meter surface air temperature ($T_{2m}$) in North America, where very low temperatures in the contiguous Unites States (CONUS) may coincide with very high temperatures in Alaska in the wintertime. This dependence between warm and cold extremes motivates the need for a model with opposite-tail dependence in spatial extremes. This work develops a statistical modeling framework which has flexible behavior in all four pairings of high and low extremes at pairs of locations. In particular, we use a mixture of rotations of common Archimedean copulas to capture various combinations of four-corner tail dependence. We study teleconnected $T_{2m}$ extremes using ERA5 reanalysis of daily average two-meter temperature during the boreal winter. The estimated mixture model quantifies the strength of opposite-tail dependence between warm temperatures in Alaska and cold temperatures in the midlatitudes of North America, as well as the reverse pattern. These dependence patterns are shown to correspond to blocked and zonal patterns of mid-tropospheric flow. This analysis extends the classical notion of correlation-based teleconnections to considering dependence in higher quantiles

Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model

Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant structural assumptions that can limit their scalability. Machine learning models, including neural networks, are able to represent a wide range of distributions and build optimized mappings between a large number of inputs and sub-grid forcings. Recent research on machine learning parameterizations has focused only on deterministic parameterizations. In this study, we develop a stochastic parameterization using the generative adversarial network (GAN) machine learning framework. The GAN stochastic parameterization is trained and evaluated on output from the Lorenz '96 model, which is a common baseline model for evaluating both parameterization and data assimilation techniques. We evaluate different ways of characterizing the input noise for the model and perform model runs with the GAN parameterization at weather and climate timescales. Some of the GAN configurations perform better than a baseline bespoke parameterization at both timescales, and the networks closely reproduce the spatio-temporal correlations and regimes of the Lorenz '96 system. We also find that in general those models which produce skillful forecasts are also associated with the best climate simulations.Comment: Submitted to Journal of Advances in Modeling Earth Systems (JAMES