arXiv subjects

Karl Lapo

Publications and source records attributed to Karl Lapo.

7 recordsLinked to original sources

arXiv2026

Multiscale Decomposition Reveals Predictable Interannual Variability and Climate Trends in Antarctic Sea Ice Loss

Antarctic sea ice has undergone unprecedented changes in recent years, raising questions about how this key geophysical system is responding to climate change. Decades of slow expansion were replaced by a precipitous decline in 2014-2017, a subsequent apparent recovery, and a renewed collapse from 2022 to the present. We diagnosed sea ice concentration (SIC) from satellite observations with a hierarchical decomposition method based on Dynamic Mode Decomposition (DMD) that finds coherent spatiotemporal modes. We find that the 2014-2017 decline and apparent recovery are the result of interacting interannual modes and that a climate change signal emerges in 2012, which becomes unambiguous by 2022 when it dominates over interannual variability. These rapid changes underscore the need for seasonal-to-annual forecasts of SIC. However, existing forecasts are subject to limited prediction horizons combined with high computational costs. Our predictive DMD model (IceDMD) is regularised to prioritize the stationary spatiotemporal modes found by the decomposition. The predictive model can forecast SIC anomalies in 2023-2024 up to two years in advance, outperforming all existing approaches with the additional benefits of physical interpretability and extremely cheap computational cost. Finally, this framework for regularising predictive DMD models can be generalized to a range of multi-scale systems.

physics.ao-ph↗

arXiv2026

An Interpretable Data-Driven Model of the Flight Dynamics of Hawks

Despite significant analysis of bird flight, generative physics models for flight dynamics do not currently exist. Yet the underlying mechanisms responsible for various flight manoeuvres are important for understanding how agile flight can be accomplished. Even in a simple flight, multiple objectives are at play, complicating analysis of the overall flight mechanism. Using the data-driven method of dynamic mode decomposition (DMD) on motion capture recordings of hawks, we show that multiple behavioral states such as flapping, turning, landing, and gliding, can be modeled by simple and interpretable modal structures (i.e. the underlying wing-tail shape) which can be linearly combined to reproduce the experimental flight observations. Moreover, the DMD model can be used to extrapolate naturalistic flapping. Flight is highly individual, with differences in style across the hawks, but we find they share a common set of dynamic modes. The DMD model is a direct fit to data, unlike traditional models constructed from physics principles which can rarely be tested on real data and whose assumptions are typically invalid in real flight. The DMD approach gives a highly accurate reconstruction of the flight dynamics with only three parameters needed to characterize flapping, and a fourth to integrate turning manoeuvres. The DMD analysis further shows that the underlying mechanism of flight, much like simplest walking models, displays a parametric coupling between dominant modes suggesting efficiency for locomotion.

q-bio.QM↗

arXiv2025

Phasor notation of Dynamic Mode Decomposition

Dynamic Mode Decomposition (DMD) is a powerful, data-driven method for diagnosing complex dynamics. Various DMD algorithms allow one to fit data with a low-rank model that decomposes it into a sum of coherent spatiotemporal patterns. Nominally, each rank of the DMD model is interpreted as a complex, stationary spatial mode modulated by a single set of complex time dynamics (consisting of exponential growth/decay and oscillation), and an amplitude. However, the specifics of how these DMD components are interpreted do not appear to be consistent with the information actually present in the DMD decomposition or the underlying data. While there is a clear physical interpretation for the complex time dynamics, there is practically no guidance on the complex spatial modes. To resolve these issues, we introduce the phasor notation of the DMD model for conjugate pair DMD modes, which results in a strictly positive and real spatial pattern as well as spatiotemporal waveform. The phasor notation terms result in an interpretable DMD model that provides a more complete diagnoses of the model components, as demonstrated on a toy model. This DMD interpretation needs to be adjusted for DMD variants which alter the relationship between the DMD model and the data, such as those that window data in time. We derive the phasor notation terms for one such method, multi-resolution Coherent Spatiotemporal Scale-separation, and demonstrate the new terms by interpreting a multi-scale data set.

math.DS↗

arXiv2025

Revealing the drivers of turbulence anisotropy over flat and complex terrain: an interpretable machine learning approach

Turbulence anisotropy was recently integrated into Monin-Obukhov Similarity Theory (MOST), extending its applicability to complex terrain and diverse surface conditions. Implementing this generalized MOST in numerical models, however, requires understanding the key drivers of turbulence anisotropy across various terrain conditions. This study therefore employs random forest models trained on measurement data from both flat and complex terrain and including upstream terrain features, to predict turbulence anisotropy. Two approaches were compared: using dimensional variables directly or employing non-dimensional groups as model input. To address cross-correlation among features, we developed a new selection method, Recursive Effect Elimination. Finally, interpretability methods were used to identify the most influential variables. Contrary to expectations, variables related to terrain influence were not found to significantly impact turbulence anisotropy. Instead, non-dimensional groups of common turbulence length, time and velocity scales proved more robust than dimensional variables in isolating anisotropy drivers, enhancing model performance over complex terrain and reducing location dependence. A ratio of integral and turbulence memory length scales was found to correlate well with turbulence anisotropy in both daytime and nighttime conditions, both over flat and complex terrain. During the day, a refined stability parameter incorporating both the surface and mixed layer scaling emerged as the dominant driver of anisotropy, while at night, parameters related to rapid distortion were strong predictors.

physics.flu-dyn↗

arXiv2024

Unsupervised multi-scale diagnostics

The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in modern scientific problems from, for instance, weather and climate prediction, neurology, epidemiology, and turbulence. Multi-scale data is characterized by a combination of processes acting along multiple dimensions simultaneously, spatiotemporal scales across orders of magnitude, non-stationarity, and/or invariances such as translation and rotation. Existing methods are not well-suited to multi-scale data, usually requiring supervised strategies such as human intervention, extensive tuning, or selection of ideal time periods. We present the multi-resolution Coherent Spatio-Temporal Scale Separation (mrCOSTS), a hierarchical and automated algorithm for the diagnosis of coherent patterns or modes in multi-scale data. mrCOSTS is a variant of Dynamic Mode Decomposition which decomposes data into bands of spatial patterns with shared time dynamics, thereby providing a robust method for analyzing multi-scale data. It requires no training but instead takes advantage of the hierarchical nature of multi-scale systems. We demonstrate mrCOSTS using complex multi-scale data sets that are canonically difficult to analyze: 1) climate patterns of sea surface temperature, 2) electrophysiological observations of neural signals of the motor cortex, and 3) horizontal wind in the mountain boundary layer. With mrCOSTS, we trivially retrieve complex dynamics that were previously difficult to resolve while additionally extracting hitherto unknown patterns of activity embedded in the dynamics, allowing for advancing the understanding of these fields of study. This method is an important advancement for addressing the multi-scale data which characterize many of the grand challenges in science and engineering.

math.DS↗

arXiv2024

PyDMD: A Python package for robust dynamic mode decomposition

The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a variety of optimizations and extensions that make the algorithm practical and viable for real-world data analysis. As a result, DMD has grown to become a leading method for dynamical system analysis across multiple scientific disciplines. PyDMD is a Python package that implements DMD and several of its major variants. In this work, we expand the PyDMD package to include a number of cutting-edge DMD methods and tools specifically designed to handle dynamics that are noisy, multiscale, parameterized, prohibitively high-dimensional, or even strongly nonlinear. We provide a complete overview of the features available in PyDMD as of version 1.0, along with a brief overview of the theory behind the DMD algorithm, information for developers, tips regarding practical DMD usage, and introductory coding examples. All code is available at https://github.com/PyDMD/PyDMD .

stat.CO↗

arXiv2024

The TEAMx-PC22 Alpine field campaign -- Objectives, instrumentation, and observed phenomena

The multi-scale transport and exchange processes in the atmosphere over mountains -- programme and experiment (TEAMx) wants to advance the understanding of transport and exchange processes over mountainous terrain as well as to collect unique multi-scale datasets that can be used, e.g., for process studies, model development and model evaluation. The TEAMx Observational Campaign (TOC) is planned to take place between 2024 and 2025. In summer 2022 a TEAMx pre-campaign (TEAMx-PC22) was conducted in the Inn Valley and one of its tributaries, the Weer Valley, to test the suitability and required logistics of measurement sites, to evaluate their value for the main campaign, and to test new observation techniques in complex terrain. Scientifically, this campaign focused on resolving the mountain boundary layer and valley wind systems on multiple scales. Through the combined effort of six institutions the pre-campaign can be deemed successful. A detailed description of the setup at each sub-target area is given. Due to the spatial distribution of instruments and their spatio-temporal resolution, atmospheric processes and phenomena like valley winds have been investigated at different locations and on different scales. Furthermore, scale interactions were detected and are discussed in detail in two example cases. Additionally, observational gaps were determined which should be closed for the TOC. Data of the pre-campaign are publicly available online and can be used for process studies, demonstrating the utility of new observation methods, model verification, and for data assimilation.

physics.ao-ph↗