Chronosphere: Space-Time Tessellation of Local Climate Experts

Daniel Cher; Eric Xing; Kexing Li; Brian Wei; Isaac Corley; Nathan Jacobs

cs.CVSep 18, 2026

Chronosphere: Space-Time Tessellation of Local Climate Experts

Authors: Daniel Cher, Eric Xing, Kexing Li, Brian Wei, Isaac Corley, Nathan Jacobs

Organizations: Washington University in St. Louis · Taylor Geospatial Institute

Abstract

We introduce Chronosphere, a spatio-temporal neural field that learns representations of climate. A central challenge in geographic representation learning is modeling environmental processes whose spatial and temporal complexity varies widely. Yet existing location encoders typically fix a single level of detail everywhere. Global bases such as spherical harmonics spread capacity uniformly across space and time. Localized bases resolve only predefined regions. Learned tessellations adapt, but are inefficient at representing higher frequencies. Chronosphere unifies these approaches, pairing an adaptive tessellation of learnable sites on the spacetime torus $S^2\times S^1$ with a shared bank of local basis functions. Both where capacity is placed and how much detail each region carries adapt to the data, across space and time. Trained to reconstruct climatology, Chronosphere matches or leads state-of-the-art location encoders across spatial and temporal tasks, with the largest gains under spatial and temporal transfer.

Figures & tables

Figure 2: Chronosphere. A query, a location $x\in S^{2}$ and within-year time $t$ , is softly assigned to learnable sites on the spacetime torus $S^{2}\times S^{1}$ . At each site a shared bank of sine experts $f_{j}$ is mixed by per-site coefficients $\alpha_{k,j}(t)$ and added to the aggregated site embedding to form the location vector $z(x,t)$ , which the decoder reconstructs into climate fields.

	Spatial (iid / $10^{\circ}$ geo-extrap.)					Within-year (iid / window-extrap.)
	Acc. $\uparrow$		$R^{2}\,\uparrow$		RMSE $\downarrow$	$R^{2}\,\uparrow$			AUC $\uparrow$	AP $\uparrow$
Model	Bio	Eco	Elev	Traits	Canopy	NDVI	Snow	Streamflow	Fire	USA-NPN
SINR	0.67/0.55	0.48/0.12	0.57/ $-$ 0.05	0.59/0.12	6.1/7.3	0.68/0.59	0.48/ $-$ 0.30	0.08/ $-$ 0.38	0.81/0.79	0.11/0.09
CSP-iNat	0.59/0.46	0.54/0.08	0.34/0.13	0.42/0.20	7.0/8.0	0.56/0.47	0.44/ $-$ 0.33	0.08/ $-$ 0.37	0.77/0.76	0.10/0.09
GeoCLIP	0.60/0.41	0.60/0.09	0.39/ $-$ 0.06	0.37/0.15	8.2/9.6	0.41/0.40	0.39/ $-$ 0.31	0.05/ $-$ 0.36	0.75/0.75	0.11/0.10
SatCLIP	0.69/0.54	0.69/0.20	0.66/0.32	0.50/0.31	5.9/6.3	0.69/0.60	0.45/ $-$ 0.29	0.10/ $-$ 0.38	0.82/0.80	0.11/0.09

Table 1: Downstream performance (frozen encoders). Each cell is iid / extrapolation; bold = best, italic = second best, ranked separately within each half. Scores are means over three seeds. Chronosphere’s per-task standard deviation stays under

0.01

on every iid split. Under extrapolation it stays below

{\sim}0.03

on most tasks, rising to

0.04

–

0.06

on the few most sensitive to the split (plant traits, snow, elevation, streamflow).

Panel of Figure 3 — Figure 3: Temporal extrapolation across seasonal phase. Probe skill as the seasonal-phase gap $\delta$ between the training periods and the held-out window grows, from in-distribution (left) to a full season held out (right). Greenness and snow are scored by $R^{2}$ and burned area by burned/no-burned ROC-AUC, with the dotted line marking chance. Time-aware encoders only.

Figure 4: In-distribution versus out-of-distribution performance. Each model runs from a hollow marker at its in-distribution skill to a filled marker under extrapolation, with marker area the parameter count. A short segment toward the top-right means the encoder generalizes across both axes, and a long segment toward the bottom-left means it collapses out of distribution. Each axis is the min–max-normalized mean across that half’s tasks (best model

{\approx}1

, worst

{\approx}0

Time in assignment (vs. spacetime)
setting	NDVI	Snow	Streamflow	Fire	NPN
Chronosphere (daily)	0.87/0.86	0.89/0.85	0.58/0.40	0.88/0.86	0.25/0.12
cyclic	0.85/0.81	0.84/0.73	0.57/0.37	0.88/0.86	0.25/0.12
flow	0.83/0.81	0.83/0.76	0.53/0.27	0.87/0.85	0.23/0.12
Local field (vs. free mixture)
none (tessellation only)	0.82/0.79	0.86/0.79	0.55/0.31	0.85/0.81	0.23/0.10

Table 3: Chronosphere ablations (within-year, iid / window-extrap.). Chronosphere (daily) is from Table 1 . Spatial ablations are in the appendix (Architectural Ablations).

Panel of Figure 5 — Figure 5: The location vector carries seasonal structure that differs in phase and character across the globe. Left: seasonal amplitude of the monthly vector, $\lVert z(t)-\bar{z}\rVert$ , the distance the representation travels from its annual mean, with boxes marking the two regions shown at right. Right: the vector (PCA $\,\rightarrow$ RGB, one shared basis) in January, April, and July for NE Siberia and S-Central Africa. The two regions peak in opposite seasons and move along different color axes, one temperature-driven and one precipitation-driven, so a single shared embedding captures both when each cycle turns and what drives it.

Panel of Figure 6 — Figure 6: Index-perturbation maps. Each panel raises one climate index by $+1\sigma$ (the rest held at their mean) and shows the resulting change in the daily model’s mid-January reconstruction over land. Red is warmer or wetter, blue cooler or drier.

Geospatial Representation Learning

Geospatial representation learning builds reusable embeddings of places, imagery, maps, mobility, and Earth data for spatial prediction and reasoning.

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Geolocation encoders, which map geographic coordinates to learned representations, are emerging as an effective means of capturing visual and non-visual characteristics from a latitude-longitude pair alone. However, existing approaches project coordinates onto fixed bases (e.g., spherical harmonics), allocating representational capacity uniformly and devoting equal resources to the open ocean and to a developing city. We introduce Tessellating the Earth (TTE), a location encoder built from learnable Spherical Voronoi partitions that concentrates representational capacity where it is needed in a fully differentiable, end-to-end manner. Each Voronoi site carries its own embedding and migrates during training toward discriminative areas. To bridge the gap between local spatial structure and global semantic understanding, we introduce global semantic tokens: a set of shared learnable concept tokens that distill semantic knowledge from the satellite imagery into a compact vocabulary the location encoder can reference at inference, enabling geographically distant sites covering similar environments to share semantics. TTE sets a new state of the art for location encoders across a suite of geospatial classification and regression tasks, and achieves the strongest results when used as a geographic prior for fine-grained species classification on iNaturalist-2018. Code, and weights are available at https://github.com/mvrl/TTE.

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