Organizations: UM, IROKO · University of Montpellier, Inria, CNRS, LIRMM, Montpellier, France · LMD, LSCE, ESTIMR · Laboratoire des Sciences du Climat et de l’Environnement, UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay & IPSL, CEA Saclay l’Orme des Merisiers, 91191 Gif-sur-Yvette, France · London Mathematical Laboratory, 8 Margravine Gardens, London W6 8RH, UK · LMD/IPSL, ENS, Université PSL, École Polytechnique, Institut Polytechnique de Paris, Sorbonne Université, CNRS, Paris France
Extreme weather events, such as windstorms and heatwaves, are driven by persistent atmospheric circulation patterns that evolve over several consecutive days. While traditional circulation-based studies often focus on instantaneous atmospheric states, capturing the temporal evolution, or trajectory, of these spatial fields is essential for characterizing rare and potentially impactful atmospheric behavior. However, performing an exhaustive similarity search on multi-decadal, continental-scale gridded datasets presents significant computational and memory challenges. In this paper, we propose TRAKNN (TRajectory Aware KNN), a fully unsupervised and data-agnostic framework for detecting geometrically rare short trajectories in spatio-temporal data with an exact kNN approach. TRAKNN leverages a recurrence-based algorithm that decouples computational complexity from trajectory length and efficient batch operations, maximizing computational intensity. These optimizations enable exhaustive analysis on standard workstations, either on CPU or on GPU. We evaluate our approach on 75 years of daily European sea-level pressure data. Our results illustrate that rare trajectories identified by TRAKNN correspond to physically coherent atmospheric anomalies and align with independent extreme-event databases.
Figures & tables
Figure 1: Execution time (in seconds) of TRAKNN compared to FAISS on both CPU and GPU as a function of (a) spatial dimension length, (b) number of time steps, (c) trajectory length, and (d) number of neighbors. The default parameters are n=27,000 , h=180,w=280 , d=1 , and k=1 .
Figure 2: RAM peak memory usage per algorithm
d
Ambient
ID
1
50,000
8±7
3
150,000
16±6
5
250,000
18±5
7
350,000
19±4
15
750,000
21±3
Table 1: Comparison of the ambient space dimension ( d×h×w ) and the mean local intrinsic dimension (ID) as a function of the trajectory duration on the mean sea level pressure
Figure 3: Composite analysis on the three main clusters of mean sea level (msl) pressure anomalies
Dataset
Storm type
d
Random
1
3
5
7
CLIMK-WINDS
–
6
9
11
12
0.7
XWS
Insurance storms
6
5
2
4
0.2
Large storms
3
4
5
7
0.2
EM-DAT
Storm (general)
8
5
7
4
0.9
Storm (tropical)
0
0
1
1
0.1
Table 2: Number of identified dates associated with a storm, as a function of the trajectory duration d (in days) with TRAKNN, by dataset and storm subtype, compared to an averaged random estimator.