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Abstract Due to differences between air and debris motions, debris centrifuging creates bias in wind estimates based on Doppler velocities and radar wind retrievals in tornadoes. Anomalous radial divergence, azimuthal wind underestimation, and vertical velocity bias associated with debris centrifuging can lead to erroneous interpretations of tornado intensity and structure from radar data. A novel spectral velocity correction technique is developed to reduce bias by identifying rain and debris motion in radar signals using dual-polarization spectral density estimation and fuzzy logic classification. This technique successfully improves Doppler velocity estimates in simulated S-band polarimetric time series data, although debris concentration modulates both the magnitude and correctability of velocity bias. Large bias magnitudes associated with high debris concentrations are the most difficult to fully correct using this technique, especially at low elevation angles and near the center of the tornado. However, the magnitudes of corrections applied are proportional to the original bias magnitudes, suggesting that the technique performs consistently across low and high debris concentrations. Spectral correction results in an overall 84% reduction in bias in simulations. The spectral correction technique is also applied to dual-polarization S-band radar observations of the 20 May 2013 Moore, Oklahoma tornado. Overall increases in Doppler velocity magnitudes, especially at lower elevation angles, imply that spectral correction can successfully reduce centrifuging bias in observed Doppler velocities. 

Simulating the time evolution of physical systems is pivotal in many scientific and engineering problems. An open challenge in simulating such systems is their multi-resolution dynamics: a small fraction of the system is extremely dynamic, and requires very fine-grained resolution, while a majority of the system is changing slowly and can be modeled by coarser spatial scales. Typical learning-based surrogate models use a uniform spatial scale, which needs to resolve to the finest required scale and can waste a huge compute to achieve required accuracy. We introduced Learning controllable Adaptive simulation for Multiresolution Physics (LAMP) as the first full deep learning-based surrogate model that jointly learns the evolution model and optimizes appropriate spatial resolutions that devote more compute to the highly dynamic regions. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNNbased actor-critic for learning the policy of spatial refinement and coarsening. We introduced learning techniques that optimize LAMP with weighted sum of error and computational cost as objective, allowing LAMP to adapt to varying relative importance of error vs. computation tradeoff at inference time. We evaluated our method in a 1D benchmark of nonlinear PDEs and a challenging 2D mesh-based simulation. We demonstrated that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error: it achieves an average of 33.7% error reduction for 1D nonlinear PDEs, and outperforms MeshGraphNets + classical Adaptive Mesh Refinement (AMR) in 2D mesh-based simulations. 

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems. However, both classical solvers and recent deep learning-based surrogate models are typically extremely computationally intensive, because of their local evolution: they need to update the state of each discretized cell at each time step during inference. Here we develop Latent Evolution of PDEs (LE-PDE), a simple, fast and scalable method to accelerate the simulation and inverse optimization of PDEs. LE-PDE learns a compact, global representation of the system and efficiently evolves it fully in the latent space with learned latent evolution models. LE-PDE achieves speedup by having a much smaller latent dimension to update during long rollout as compared to updating in the input space. We introduce new learning objectives to effectively learn such latent dynamics to ensure long-term stability. We further introduce techniques for speeding-up inverse optimization of boundary conditions for PDEs via backpropagation through time in latent space, and an annealing technique to address the non-differentiability and sparse interaction of boundary conditions. We test our method in a 1D benchmark of nonlinear PDEs, 2D Navier-Stokes flows into turbulent phase and an inverse optimization of boundary conditions in 2D Navier-Stokes flow. Compared to state-of-the-art deep learning-based surrogate models and other strong baselines, we demonstrate up to 128x reduction in the dimensions to update, and up to 15x improvement in speed, while achieving competitive accuracy. 

Abstract A simulated vortex within a large-eddy simulation is subjected to various surface terrain, implemented through the immersed boundary method, to analyze the effects of complex topography on vortex behavior. Thirty simulations, including a control with zero-height terrain, are grouped into four categories—2D sinusoidal hills, 3D hills, valleys, and ridges—with slight modifications within each category. A medium-swirl-ratio vortex is translated over shallow terrain, which is modest in size relative to the vortex core diameter and with no explicitly defined surface roughness. While domain size restricts results to the very near-field effects of terrain, vortex–terrain interaction yields notable results. Terrain influences act to increase the variability of the near-surface vortex, including a notable leftward (rightward) deflection, acceleration (deceleration), and an expansion (a contraction) of the vortex as it ascends (descends) the terrain owing to changes in the corner flow swirl ratio. Additionally, 10-m track analyses show stronger horizontal wind speeds are found 1) on upslope terrain, resulting from transient subvortices that are more intense compared to the control simulation, and 2) in between adjacent hills simultaneous with strong pressure perturbations that descend from aloft. Composite statistics confirm that the region in between adjacent hills has the strongest horizontal wind speeds, while upward motions are more intense during ascent. Overall, valley (ridge) simulations have the largest horizontal (vertically upward) wind speeds. Last, horizontal and vertical wind speeds are shown to be affected by other terrain properties such as slope steepness and two-dimensionality of the terrain. 

Abstract When a tornado lofts debris to the height of the radar beam, a signature known as the tornadic debris signature (TDS) can sometimes be observed on radar. The TDS is a useful signature for operational forecasters because it can confirm the presence of a tornado and provide information about the amount of damage occurring. Since real-time estimates of tornadic intensity do not have a high degree of accuracy, past studies have hypothesized that the TDS could also be an indicator of the strength of a tornado. However, few studies have related the tornadic wind field to TDS characteristics because of the difficulty of obtaining accurate, three-dimensional wind data in tornadoes from radar data. With this in mind, the goals of this study are twofold: 1) to investigate the relationships between polarimetric characteristics of TDSs and the three-dimensional tornadic winds, and 2) to define relationships between polarimetric radar variables and debris characteristics. Simulations are performed using a dual-polarization radar simulator called SimRadar; large-eddy simulations (LESs) of tornadoes; and a single-volume,-matrix-based emulator. Results show that for all simulated debris types increases in horizontal and vertical wind speeds are related to decreases in correlation coefficient and increases in TDS area and height and that, conversely, decreases in horizontal and vertical wind speeds are related to increases in correlation coefficient and decreases in TDS area and height. However, the range of correlation coefficient values varies with debris type, indicating that TDSs that are composed of similar debris types can appear remarkably different on radar in comparison with a TDS with diverse scatterers. Such findings confirm past observational hypotheses and can aid operational forecasters in tornado detection and potentially the categorization of damage severity using radar data.