Role-Aware Conditional Inference for Spatiotemporal Ecosystem Carbon Flux Prediction

Yiming Sun; Runlong Yu; Rongchao Dong; Shuo Chen; Licheng Liu; Youmi Oh; Qianlai Zhuang; Yiqun Xie

cs.LGMar 3, 2026

Role-Aware Conditional Inference for Spatiotemporal Ecosystem Carbon Flux Prediction

Authors: Yiming Sun, Runlong Yu, Rongchao Dong, Shuo Chen, Licheng Liu, Youmi Oh, Qianlai Zhuang, Yiqun Xie,

Organizations: University of Pittsburgh, Pittsburgh, PA, USA · University of Alabama, Tuscaloosa, AL, USA · Purdue University, West Lafayette, IN, USA · University of Wisconsin-Madison, Madison, WI, USA ·

Abstract

Accurate prediction of terrestrial ecosystem carbon fluxes (e.g., CO $_2$ , GPP, and CH $_4$ ) is essential for understanding the global carbon cycle and managing its impacts. However, prediction remains challenging due to strong spatiotemporal heterogeneity: ecosystem flux responses are constrained by slowly varying regime conditions, while short-term fluctuations are driven by high-frequency dynamic forcings. Most existing learning-based approaches treat environmental covariates as a homogeneous input space, implicitly assuming a global response function, which leads to brittle generalization across heterogeneous ecosystems. In this work, we propose Role-Aware Conditional Inference (RACI), a process-informed learning framework that formulates ecosystem flux prediction as a conditional inference problem. RACI employs hierarchical temporal encoding to disentangle slow regime conditioners from fast dynamic drivers, and incorporates role-aware spatial retrieval that supplies functionally similar and geographically local context for each role. By explicitly modeling these distinct functional roles, RACI enables a model to adapt its predictions across diverse environmental regimes without training separate local models or relying on fixed spatial structures. We evaluate RACI across multiple ecosystem types (wetlands and agricultural systems), carbon fluxes (CO $_2$ , GPP, CH $_4$ ), and data sources, including both process-based simulations and observational measurements. Across all settings, RACI consistently outperforms competitive spatiotemporal baselines, demonstrating improved accuracy and spatial generalization under pronounced environmental heterogeneity.

Figures & tables

Figure 1. Illustration of (i) functional heterogeneity between fast drivers and slow conditioners, and (ii) their contrasting spatial similarity patterns.

Model

TEM-MDM

FLUXNET

Global

N. America

S. America

Europe

Africa

Asia

Oceania

CH 4

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

RMSE

\downarrow

R^{2}

\uparrow

LSTM

3.06{\scriptstyle\pm 0.06}

0.94{\scriptstyle\pm.01}

3.12{\scriptstyle\pm 0.05}

0.93{\scriptstyle\pm.01}

2.03{\scriptstyle\pm 0.03}

0.75{\scriptstyle\pm.03}

1.84{\scriptstyle\pm 0.07}

0.96{\scriptstyle\pm.00}

1.41{\scriptstyle\pm 0.05}

0.90{\scriptstyle\pm.01}

3.49{\scriptstyle\pm 0.05}

0.97{\scriptstyle\pm.00}

8.09{\scriptstyle\pm 0.55}

0.76{\scriptstyle\pm.02}

54.48{\scriptstyle\pm 1.20}

0.44{\scriptstyle\pm.02}

EA-LSTM

5.91{\scriptstyle\pm 0.26}

0.76{\scriptstyle\pm.01}

5.51{\scriptstyle\pm 0.07}

0.80{\scriptstyle\pm.02}

3.15{\scriptstyle\pm 0.06}

0.39{\scriptstyle\pm.05}

3.04{\scriptstyle\pm 0.20}

0.90{\scriptstyle\pm.01}

2.53{\scriptstyle\pm 0.27}

0.68{\scriptstyle\pm.01}

7.94{\scriptstyle\pm 0.68}

0.82{\scriptstyle\pm.02}

15.14{\scriptstyle\pm 1.27}

0.17{\scriptstyle\pm.01}

57.09{\scriptstyle\pm 0.32}

0.39{\scriptstyle\pm.01}

P_sLSTM

8.80{\scriptstyle\pm 0.48}

0.39{\scriptstyle\pm.10}

7.16{\scriptstyle\pm 0.15}

0.61{\scriptstyle\pm.06}

6.00{\scriptstyle\pm 0.30}

-1.20{\scriptstyle\pm.34}

5.02{\scriptstyle\pm 0.50}

0.69{\scriptstyle\pm.03}

5.00{\scriptstyle\pm 0.22}

-0.57{\scriptstyle\pm.19}

13.11{\scriptstyle\pm 0.95}

0.45{\scriptstyle\pm.11}

18.58{\scriptstyle\pm 2.32}

-0.57{\scriptstyle\pm.05}

62.84{\scriptstyle\pm 0.78}

0.27{\scriptstyle\pm.02}

TCN

7.43{\scriptstyle\pm 0.14}

0.59{\scriptstyle\pm.03}

7.19{\scriptstyle\pm 1.02}

0.67{\scriptstyle\pm.03}

3.76{\scriptstyle\pm 0.23}

0.05{\scriptstyle\pm.08}

4.64{\scriptstyle\pm 1.19}

0.77{\scriptstyle\pm.04}

3.51{\scriptstyle\pm 0.23}

0.28{\scriptstyle\pm.04}

11.10{\scriptstyle\pm 1.04}

0.62{\scriptstyle\pm.02}

13.78{\scriptstyle\pm 3.46}

-0.14{\scriptstyle\pm.01}

82.04{\scriptstyle\pm 8.45}

-0.26{\scriptstyle\pm.26}

Table 1. Performance comparison of CH 4 prediction on TEM-MDM and FLUXNET datasets (mean

{\scriptstyle\pm\text{std}}

Model	Ecosys				FLUXNET
	GPP		CO 2		GPP		CO 2
	RMSE $\downarrow$	$R^{2}$ $\uparrow$	RMSE $\downarrow$	$R^{2}$ $\uparrow$	RMSE $\downarrow$	$R^{2}$ $\uparrow$	RMSE $\downarrow$	$R^{2}$ $\uparrow$
LSTM	$2.87{\scriptstyle\pm.19}$	$0.84{\scriptstyle\pm.02}$	$0.48{\scriptstyle\pm.04}$	$0.89{\scriptstyle\pm.02}$	$1.50{\scriptstyle\pm.05}$	$0.84{\scriptstyle\pm.01}$	$3.67{\scriptstyle\pm.10}$	$0.71{\scriptstyle\pm.02}$
EA-LSTM	$3.48{\scriptstyle\pm.21}$	$0.77{\scriptstyle\pm.03}$	$0.65{\scriptstyle\pm.02}$	$0.83{\scriptstyle\pm.01}$	$2.26{\scriptstyle\pm.28}$	$0.64{\scriptstyle\pm.09}$	$4.46{\scriptstyle\pm.24}$	$0.56{\scriptstyle\pm.05}$
P_sLSTM	$3.85{\scriptstyle\pm.84}$	$0.70{\scriptstyle\pm.13}$	$0.69{\scriptstyle\pm.13}$	$0.87{\scriptstyle\pm.18}$	$1.94{\scriptstyle\pm.07}$	$0.74{\scriptstyle\pm.02}$	$4.06{\scriptstyle\pm.16}$	$0.64{\scriptstyle\pm.03}$
TCN	$3.35{\scriptstyle\pm.27}$	$0.79{\scriptstyle\pm.03}$	$0.60{\scriptstyle\pm.01}$	$0.86{\scriptstyle\pm.00}$	$1.52{\scriptstyle\pm.07}$	$0.84{\scriptstyle\pm.02}$	$3.69{\scriptstyle\pm.20}$	$0.70{\scriptstyle\pm.03}$

Table 2. GPP and CO 2 performance on Ecosys and FLUXNET (mean

{\scriptstyle\pm\text{std}}

), with best performance highlighted in bold.

Panel of Figure 3 — Figure 3. Spatial distribution of point-wise $R^{2}$ on TEM-MDM in test year 2018, comparing LSTM (left) and RACI (right).

Figure 4. Annual mean CH 4 emissions over North America in 2018 from CarbonTracker, LSTM, and RACI prediction.

Metric	Full	-Temporal	-Monthly	-Yearly	-Both
RMSE	2.08	3.08	2.28	3.19	3.31
R 2	0.97	0.94	0.96	0.93	0.92

Table 3. Ablation study of RACI variants on TEM-MDM.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5. Comparison of daily CH 4 emission time series from observations and from LSTM and RACI predictions at five FLUXNET-CH 4 site-year sequences in the test set.

Figure 6. Monthly CH 4 flux maps over North America in 2018 from CarbonTracker, LSTM, and RACI prediction.

Panel of Figure 7 — Figure 7. Temporal attention patterns learned by RACI for CH 4 prediction.

Panel of Figure 8 — Figure 8. Yearly spatial retrieval similarity maps and retrieved locations for two adjacent FLUXNET-CH 4 sites in the Mississippi River Delta (US-LA1, left; US-LA2, right).

Table 4. Sensitivity analysis of RACI on TEM-MDM under different hyperparameter settings.

Figure 9. Example site–year from TEM-MDM showing ground-truth flux, RACI prediction, and MC Dropout uncertainty bands (mean $\pm$ 1 std and $\pm$ 2 std).

Spatiotemporal Forecasting

Spatiotemporal forecasting predicts how quantities change across locations and time, from traffic and weather to disease and environmental systems.

See all 423 papers

Mar 10, 2026

Task Aware Modulation Using Representation Learning for Upsaling of Terrestrial Carbon Fluxes

Accurately upscaling terrestrial carbon fluxes is central to estimating the global carbon budget, yet remains challenging due to the sparse and regionally biased distribution of ground measurements. Existing data-driven upscaling products often fail to generalize beyond observed domains, leading to systematic regional biases and high predictive uncertainty. We introduce Task-Aware Modulation with Representation Learning (TAM-RL), a framework that couples spatio-temporal representation learning with knowledge-guided encoder-decoder architecture and loss function derived from the carbon balance equation. Across 150+ flux tower sites representing diverse biomes and climate regimes, TAM-RL improves predictive performance relative to existing state-of-the-art datasets, reducing RMSE by 8-9.6% and increasing explained variance (R2) from 19.4% to 43.8%, depending on the target flux. These results demonstrate that integrating physically grounded constraints with adaptive representation learning can substantially enhance the robustness and transferability of global carbon flux estimates.

Aleksei Rozanov, Arvind Renganathan, Vipin Kumar

University of Minnesota, Twin Cities

Climate Science Physics-Informed ML

Ask PDF

Dec 1, 2025

A Footprint-Aware, High-Resolution Approach for Carbon Flux Prediction Across Diverse Ecosystems

Eddy-covariance (EC) flux towers provide in situ measurements of

CO_2

flux and serve as the ground-truth data for predictive `upscaling' models derived from satellite products. However, many satellites now resolve spatial scales smaller than an EC tower's footprint. We show theoretically that upscaling models trained on high-resolution data in heterogeneous landscapes must account for an EC tower's footprint to avoid bias in pixel-level predictors. To address this problem, we introduce Footprint-Aware Regression (FAR), a deep-learning framework that simultaneously predicts spatial footprints and pixel-level estimates of

CO_2

flux, and show it yields unbiased pixel-level predictions given sufficient training data. We demonstrate FAR on our AMERI-FAR25 dataset, which combines 205 site-years of tower data with corresponding Landsat scenes, and show that FAR outperforms non-footprint-aware models. FAR increased half-hourly

R^2

from approximately 0.575 to 0.634 and reduced RMSE by about 7% relative to the best fixed-footprint baseline on a dataset of withheld sites. Gains are larger for monthly and yearly averages relative to a coarser 990 m baseline. Site-level analyses show that these gains extend across multiple ecosystem types. These performance gains are observed whether footprints are learned jointly or estimated independently using an established footprint model, despite substantial variation in footprint size between methods. In a regional comparison over the Western Cascades, FAR produces flux estimates with a distribution comparable to that of existing high-resolution process-based models.

Jacob Searcy, Anish Dulal, Courtney Mathers +6

Department of Data Science, University of Oregon · Department of Computer Science, University of Oregon · Institute of Ecology and Evolution, University of Oregon +3

Remote Sensing

Ask PDF

May 19, 2026

FLUXtrapolation: A benchmark on extrapolating ecosystem fluxes

We introduce FLUXtrapolation, a benchmark for extrapolating ecosystem fluxes under progressively harder distribution shifts. Ecosystem fluxes are central to understanding the carbon, water, and energy cycles, yet they can only be measured directly at sparsely located measurement towers. Producing global flux estimates therefore requires training models on observed sites using globally available covariates and predicting in unobserved regions, that is, upscaling. Flux upscaling is a challenging domain generalization problem that is affected by a shift in covariate distribution across climates, ecosystem types, and environmental conditions, as well as by conditional shift: important drivers remain unobserved at global scale. We provide a quantitative analysis of both these shifts in

P_X

and

P_{Y\mid X}

. FLUXtrapolation is designed based on domain expertise on flux upscaling: it defines temporal, spatial, and temperature-based extrapolation scenarios and evaluates performance across held-out domains, temporal aggregations, and tail errors. In a pilot study, we find that baselines perform similarly under median hourly RMSE, but separate under the proposed tail-focused and multi-scale evaluation. FLUXtrapolation therefore poses a realistic and thus relevant challenge for machine learning methods under distribution shift; at the same time, progress on this benchmark would directly support the scientific goal of improving flux upscaling.

Anya Fries, Jacob A Nelson, Martin Jung +2

Seminar for Statistics, ETH Zürich Zürich, Switzerland · Max Planck Institute for Biogeochemistry Jena, Germany

Distribution Shift Robustness OOD Generalization Forecasting Benchmarks Spatiotemporal Forecasting

Ask PDF

Abstract

Spatiotemporal Forecasting

Explore similar work

Task Aware Modulation Using Representation Learning for Upsaling of Terrestrial Carbon Fluxes

A Footprint-Aware, High-Resolution Approach for Carbon Flux Prediction Across Diverse Ecosystems

FLUXtrapolation: A benchmark on extrapolating ecosystem fluxes