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

Jacob Searcy; Anish Dulal; Courtney Mathers; Scott Bridgham; Ashley Cordes; Lillian Aoki; Brendan Bohannan; Qing Zhu

cs.LGDec 1, 2025

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

Authors: Jacob Searcy, Anish Dulal, Courtney Mathers, Scott Bridgham, Ashley Cordes, Lillian Aoki, Brendan Bohannan, Qing Zhu, +1 more

Organizations: Department of Data Science, University of Oregon · Department of Computer Science, University of Oregon · Institute of Ecology and Evolution, University of Oregon · Environmental Studies Program, University of Oregon · Department of Biology, University of Oregon · Climate and Ecosystem Sciences Division, Lawrence Berkeley National Lab

Abstract

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.

Figures & tables

Figure 1: FAR Overview schematic. FAR is implemented as a two-arm deep neural network with a footprint prediction arm (A) and a flux prediction arm (B). These arms are then combined into a single aggregated prediction of the measured tower flux (C).

Figure 2: Comparison of $R^{2}$ scores by site for half-hour predictions. FAR, FAR $+$ Kljun, and XGBoost (XGB) are shown for all sites in the test_site data split. Panel (a) shows all sites with $R^{2}>0$ for all predictions. Panel (b) shows all sites for which at least one model has $R^{2}<0$ . Blue/red bars denote a positive/negative change in $R^{2}$ between XGBoost and FAR. The dashed line represents changes between FAR and FAR+Kljun. Bands denote the IGBP category of each site among wetlands (WET), Open Shrublands (OSH), Grasslands (GRA), Evergreen Needleleaf Forest (ENF), Deciduous Broadleaf Forest (DBF), and Croplands (CRO).

Model	HH	HH	HH	Monthly	Monthly	Monthly	Yearly	Yearly	Yearly
	$R^{2}$	RMSE	Bias	$R^{2}$	RMSE	Bias	$R^{2}$	RMSE	Bias
Footprint-Aware
FAR (default; $\lambda=10^{-3}$ )	0.631	3.37	0.02	0.765	1.97	0.02	0.817	1.17	-0.03
FAR+Kljun	0.634	3.37	0.16	0.751	2.03	0.18	0.822	1.16	0.11
FAR $\lambda=0$	0.624	3.41	-0.34	0.751	2.03	-0.35	0.783	1.28	-0.40
FAR $\lambda=-10^{-3}$	0.598	3.53	0.12	0.719	2.15	0.06	0.739	1.40	0.07

Table 1: Model performance across experiments. The

R^{2}

, root mean squared error (RMSE), and bias on all data from withheld sites ( test_site ) are shown. Models include XGBoost (XGB), FAR with Kljun footprints or different

\lambda

values, the FAR flux-prediction arm without a footprint model (FAR MLP), and linear models. Upscaling results describe FAR’s performance on sites for which PRISM data is available and FAR’s performance replacing tower data with PRISM data (FAR+PRISM). Results are shown for half-hour (HH) predictions, which are then averaged into monthly and yearly predictions. RMSE is reported in

\mu\mathrm{mol}\,\mathrm{CO_{2}}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}

. The best-performing result in each group is bolded.

Figure 3: The 68% and 95% contours for the monthly footprint climatology (the average of all half-hour footprints) from Kljun, FAR, and a fixed 150 m reference. Given that each model uses multiple features, NDVI is shown as an illustrative proxy. The background in each panel represents monthly average NDVI. The left column shows site US-Srr, the center column shows site US-HB1, and the right column shows site CA-DB2. Rows represent March, June, and September. The years selected are the most temporally proximal years of data.

Figure 4: SHAP values for the most important flux prediction features. SHAP values are grouped into 4 categories: 1. Environmental drivers (SW_IN, TA, RH), 2. Vegetation proxies (Red, NIR, Green, Blue), 3. Soil moisture (SWIR 1/2, TIRS 1/2, Coastal aerosol) and 4. Satellite corrections (SAA, SZA, VAA, VZA, TIME_MASK, Cirrus). Below each group is a selection of the highest-impact features. These are shown with red/blue points denoting higher/lower than average values. Red points on the right of the figure denote that a high value of that feature is associated with flux to the atmosphere, and blue points to the left denote that a low value of that feature is associated with ecosystem drawdown.

Panel of Figure 5 — Figure 5: Footprint Characteristics. (a) The footprint-weighted mean of the coordinates versus wind direction. For context, the sine and cosine of the wind direction scaled by 30 m are overlaid to show the expected upwind pattern. (b) The square root of the area containing 95% of the footprint obtained from different models for three tower height groups.

Figure 6: Within-footprint variation of satellite bands, where values near 0 indicate homogeneous contributing regions and values near 1 indicate variation comparable to the full dataset.

Figure 7: 10-Year (2013–2022) average flux predicted by FAR for a region of Oregon’s Western Cascades. The left panel shows FAR’s 30 m resolution and the right panel shows FAR’s results averaged to 990 m. Blue represents net $CO_{2}$ drawdown and red represents net $CO_{2}$ sources.

Figure 8: Histogram of the average 10-year predicted fluxes shown in Figure 7 at both high (30 m) and low (990 m) resolutions. Both histograms are density-normalized such that the total area under each histogram equals one.

Product	Mean NEP	Temporal comparison			Spatial comparison
		$R^{2}$	Bias	Slope	$R^{2}$	Bias	Slope
FAR	334.5	-	-	-	-	-	-
FLUXCOM-X	529.6	0.681	195.3	1.092	0.464	202.1	1.019
SMAP	3.2	0.642	-331.6	0.624	0.671	-323.4	0.327
GloFlux	767.3	0.765	430.3	1.676	0.254	455.7	0.770
GEO3-NEP	420.3	0.744	84.7	0.903	0.481	92.5	-0.771

Table 2: Mean NEP from FAR and other products for the region shown in Figure 7 from January 1, 2016, through December 31, 2021. Mean NEP is averaged over time and across the region. Temporal comparisons are based on linear fits of monthly, regionally averaged NEP between FAR and each specified product. The spatial comparison is based on a linear fit between NEP averaged over time for each product grid cell and FAR predictions averaged over time and over the pixels corresponding to that grid cell. For both comparisons,

R^{2}

, bias, and slope quantify agreement with FAR. NEP and bias are reported in

\mathrm{g}\,\mathrm{C}\,\mathrm{m}^{-2}\,\mathrm{yr}^{-1}

. The FAR 990 m aggregate

\rightarrow

predict row quantifies the bias due to Jensen’s inequality by averaging FAR’s

X^{landsat}

inputs to 990 m resolution before prediction.

Site ID	IGBP	Date Range	Train site-days	Test site-days (site/future)	Val site-days (site/future/val)
AR-CCg [ 193 ]	GRA	2018-2021	253	0/0	0/160/61
AR-TF1 [ 111 ]	WET	2016-2018	75	0/0	0/102/6
AR-TF2 [ 110 ]	WET	2017-2017	0	0/0	28/0/0
BR-CST [ 6 ]	DNF	2014-2015	6	0/81	0/0/0
BR-Npw [ 253 ]	WSA	2014-2017	217	0/0	0/100/32
CA-ARB [ 237 ]	WET	2013-2015	179	0/194	0/0/38

Table 3: Sites used in AMERI-FAR25. The complete list of AmeriFlux sites used in each dataset split in AMERI-FAR25. Sites are exclusively divided between train , val_site and test_site , with sites in the train dataset also appearing in the val , val_future , and test_future datasets.

Figure S1: Tower measurements are compared against FAR predictions. The dashed black line denotes a perfect agreement reference. Half-hour results (HH) are plotted as a histogram due to the large number of estimates with counts concentrated near the reference line and shown on a log color scale. Monthly and yearly values are plotted as scatterplots. These values correspond to the FAR row in Table 1 .

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Open paper AskPDF arXiv

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.

Abstract

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