We analyze the applicability of convolutional neural network (CNN) architectures for downscaling of short‐range forecasts of near‐surface winds on extended spatial domains. Short‐range wind forecasts (at the 100 m level) from European Centre for Medium Range Weather Forecasts ERA5 reanalysis initial conditions at 31 km horizontal resolution are downscaled to mimic high resolution (HRES) (deterministic) short‐range forecasts at 9 km resolution. We evaluate the downscaling quality of four exemplary CNN architectures and compare these against a multilinear regression model. We conduct a qualitative and quantitative comparison of model predictions and examine whether the predictive skill of CNNs can be enhanced by incorporating additional atmospheric variables, such as geopotential height and forecast surface roughness, or static high‐resolution fields, like land–sea mask and topography. We further propose DeepRU, a novel U‐Net‐based CNN architecture, which is able to infer situation‐dependent wind structures that cannot be reconstructed by other models. Inferring a target 9 km resolution wind field from the low‐resolution input fields over the Alpine area takes less than 10 ms on our graphics processing unit target architecture, which compares favorably to an overhead in simulation time of minutes or hours between low‐ and high‐resolution forecast simulations.

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here on the case of time series data that can ultimately be modelled as a spatially distributed system (e.g. a partial differential equation, PDE), but where we do not know the space in which this PDE should be formulated. Hence, even the spatial coordinates for the distributed system themselves need to be identified - to “emerge from”-the data mining process. We will first validate this “emergent space” reconstruction for time series sampled without space labels in known PDEs; this brings up the issue of observability of physical space from temporal observation data, and the transition from spatially resolved to lumped (order-parameter-based) representations by tuning the scale of the data mining kernels. We will then present actual emergent space “discovery” illustrations. Our illustrative examples include chimera states (states of coexisting coherent and incoherent dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics, arising in partial differential equations and/or in heterogeneous networks. We also discuss how data-driven “spatial” coordinates can be extracted in ways invariant to the nature of the measuring instrument. Such gauge-invariant data mining can go beyond the fusion of heterogeneous observations of the same system, to the possible matching of apparently different systems. For an older version of this article, including other examples, see https://arxiv.org/abs/1708.05406.

Oscillatory systems with long-range or global coupling offer promising insight into the interplay between high-dimensional (or microscopic) chaotic motion and collective interaction patterns. Within this paper, we use Lyapunov analysis to investigate whether chimera states in globally coupled Stuart-Landau (SL) oscillators exhibit collective degrees of freedom. We compare two types of chimera states, which emerge in SL ensembles with linear and nonlinear global coupling, respectively, the latter introducing a constraint that conserves the oscillation of the mean. Lyapunov spectra reveal that for both chimera states the Lyapunov exponents split into different groups with different convergence properties in the limit of large system size. Furthermore, in both cases the Lyapunov dimension is found to scale extensively and the localization properties of covariant Lypunov vectors manifest the presence of collective Lyapunov modes. Here, however, we find qualitative differences between the two types of chimera states: Whereas the ones in the system under nonlinear global coupling exhibit only slow collective modes corresponding to Lyapunov exponents equal or close to zero, those which experience the linear mean-field coupling exhibit also faster collective modes associated with Lyapunov exponents with large positive or negative values.

PT 462s ST-CVAE 210sPT 899s ST-CVAE 232sPT 1882s ST-CVAE 252sPT 3604s ST-CVAE 305sFigure 1: Subsurface scattering simulation for homogeneous media with varying density and high anisotropy (g = 0.875) using standard path-tracing (PT) vs. our approach -a sphere-tracing algorithm using data-driven learning of multiple-scattering statistics (ST-CVAE). 8000 light paths per pixel are simulated. Density doubles from left to right, increasing the number of scatter events during path-tracing. Our approach achieves improved performance by summarizing long scattering chains into a single sphere-tracing step.

<p>Numerical weather prediction models with high resolution (of order kms or less) can deliver very accurate low-level winds. The problem is that one cannot afford to run simulations at very high resolution over global or other large domains for long periods because the computational power needed is prohibitive.</p><p>Instead, we propose using neural networks to downscale low-resolution wind-field simulations (input) to high-resolution fields (targets) to try to match a high-resolution simulation. Based on short-range forecasts of wind fields (at the 100m level) from the ECMWF ERA5 reanalysis, at 31km resolution, and the HRES (deterministic) model version, at 9km resolution, we explore two complementary approaches, in an initial “proof-of-concept” study.</p><p>In a first step, we evaluate the ability of U-Net-type convolutional neural networks to learn a one-to-one mapping of low-resolution input data to high-resolution simulation results. By creating a compressed feature-space representation of the data, networks of this kind manage to encode important flow characteristics of the input fields and assimilate information from additional data sources. Next to wind vector fields, we use topographical information to inform the network, at low and high resolution, and include additional parameters that strongly influence wind-field prediction in simulations, such as vertical stability (via the simple, compact metric of boundary layer height) and the land-sea mask. We thus infer weather-situation and location-dependent wind structures that could not be retrieved otherwise.</p><p>In some situations, however, it will be inappropriate to deliver only a single estimate for the high-resolution wind field. Especially in regions where topographic complexity fosters the emergence of complex wind patterns, a variety of different high-resolution estimates may be equally compatible with the low-resolution input, and with physical reasoning. In a second step, we therefore extend the learning task from optimizing deterministic one-to-one mappings to modelling the distribution of physically reasonable high-resolution wind-vector fields, conditioned on the given low-resolution input. Using the framework of conditional variational autoencoders, we realize a generative model, based on convolutional neural networks, which is able to learn the conditional distributions from data. Sampling multiple estimates of the high-resolution wind vector fields from the model enables us to explore multimodalities in the data and to infer uncertainties in the predictand.</p><p>In a future customer-oriented extension of this proof-of-concept work, we would envisage using a target resolution higher than 9km - say in the 1-4km range - to deliver much better representivity for users. Ensembles of low resolution input data could also be used, to deliver as output an “ensemble of ensembles”, to condense into a meaningful probabilistic format for users. The many exciting applications of this work (e.g. for wind power management) will be highlighted.</p>