Uncertainty-Aware Test-Time Adaptation for Cross-Region Spatio-Temporal Fusion of Land Surface Temperature

Abstract: Deep learning models have shown great promise in diverse remote sensing applications. However, they often struggle to generalize across geographic regions unseen during training due to domain shifts. Domain shifts occur when data distributions differ between the training region and new target regions, due to variations in land cover, climate, and environmental conditions. Test-time adaptation (TTA) has emerged as a solution to such shifts, but existing methods are primarily designed for classification and are not directly applicable to regression tasks. In this work, we address the regression task of spatio-temporal fusion (STF) for land surface temperature estimation. We propose an uncertainty-aware TTA framework that updates only the fusion module of a pre-trained STF model, guided by epistemic uncertainty, land use and land cover consistency, and bias correction, without requiring source data or labeled target samples. Experiments on four target regions with diverse climates, namely Rome in Italy, Cairo in Egypt, Madrid in Spain, and Montpellier in France, show consistent improvements in RMSE and MAE for a pre-trained model in Orléans, France. The average gains are 24.2% and 27.9%, respectively, even with limited unlabeled target data and only 10 TTA epochs.

• The paper introduces an uncertainty-aware test-time adaptation framework that adjusts only the fusion module to handle domain shifts in land surface temperature regression.
• It leverages MC dropout to quantify epistemic uncertainty and integrates land use/cover indices as physical priors to enforce consistency in model predictions.
• Empirical results across four diverse regions show significant reductions in RMSE and MAE with minimal target data and few adaptation epochs.

Uncertainty-Aware Test-Time Adaptation for Cross-Region Spatio-Temporal Fusion of Land Surface Temperature

Problem Formulation and Motivation

Deep learning methods have driven progress in remote sensing, particularly for spatio-temporal fusion (STF) of land surface temperature (LST), a canonical regression problem with applications in environmental monitoring and public health. However, these models are susceptible to performance degradation under domain shifts—that is, when deployed in regions with distinct land cover, climate, and acquisition characteristics from the source domain. Classic transfer learning and unsupervised domain adaptation approaches require source data or labeled target samples, posing scalability and privacy limitations.

Test-time adaptation (TTA) circumvents this by employing only unlabeled target data for adaptation. Nevertheless, extant TTA algorithms are almost exclusively classification-oriented, relying on entropy minimization or mutual information objectives predicated upon categorical output distributions. This restricts their applicability to regression scenarios where predictive outputs are continuous and unimodal.

This work directly addresses these limitations by introducing the first uncertainty-aware TTA framework for cross-region STF of LST, establishing a regime for regression tasks where 1) the source domain is inaccessible at adaptation/inference stage, and 2) target domain contains only unlabeled satellite observations.

Methodological Contributions

The core methodology comprises an uncertainty-aware, unsupervised loss tailored for regression model adaptation at test time. The adaptation procedure targets only the fusion module of a pre-trained WGAST STF network, leaving the encoder and decoder components fixed. The TTA loss is a weighted sum:

$$\mathcal{L}_\text{TTA} = \lambda_1 \mathcal{L}_\text{uncertainty} + \lambda_2 \mathcal{L}_\text{LULC} + \lambda_3 \mathcal{L}_\text{bias}$$

where the loss contains three critical elements:

1. Uncertainty-Aware Component ($\mathcal{L}_\text{uncertainty}$): Epistemic uncertainty is estimated with MC dropout, penalizing high variance in STF predictions, thereby guiding the fusion module toward high-confidence hypotheses under regional domain shift.
2. LULC Consistency ($\mathcal{L}_\text{LULC}$): This term encodes prior knowledge of LST’s dependence on land use/cover indices (NDVI, NDWI, NDBI). The loss penalizes weak correlations between predicted LST and these indices at sub-pixel scales, serving as a weak physical constraint.
3. Bias Consistency ($\mathcal{L}_\text{bias}$): This component enforces mean consistency between the upsampled high-resolution LST and lower-resolution MODIS LST at the target date, facilitating fast domain adaptation and alleviating regional radiometric bias.

TTA is performed via stochastic gradient descent on just the fusion module, providing efficient adaptation in the absence of any ground truth labels or direct access to source domain data.

Empirical Validation

The proposed framework is validated on four geographically and climatologically diverse regions: Rome (Italy), Cairo (Egypt), Madrid (Spain), and Montpellier (France). The source model is pre-trained in Orléans (France). Each region presents distinct land cover and climate profiles to evaluate adaptation robustness under severe domain shift.

Quantitative analyses demonstrate strong, consistent improvements over the non-adapted pre-trained model:

Region	RMSE Before	RMSE After	MAE Before	MAE After	RMSE Gain	MAE Gain
Rome	3.081	2.088	2.735	1.675	32.2%	38.8%
Cairo	3.463	2.778	2.926	2.344	19.8%	19.9%
Madrid	2.774	2.017	2.578	1.758	27.3%	31.8%
Montpellier	2.142	1.804	1.800	1.458	15.8%	19.0%
Average	2.865	2.172	2.510	1.809	24.2%	27.9%

The model achieves these gains with only 10 TTA epochs per region and minimal target data (4 samples for Rome; 3 for Cairo; 2 for Madrid and Montpellier), evidence for the efficacy and data efficiency of the proposed approach.

A significant claim: The method produces consistent adaptation improvements on regression tasks in remote sensing, unlike previous TTA methods limited to classification, and operates without any target domain labels or source data at adaptation time.

Theoretical and Practical Implications

From a theoretical standpoint, this framework demonstrates that epistemic uncertainty, when estimated via dropout-based Bayesian approximations, provides an effective unsupervised learning signal for TTA in regression problems. The augmentation with physically informed priors (LULC correlation constraints) and radiometric bias control further ensures model stability and spatial/land-use consistency—critical in geophysical regression contexts where direct supervision is absent.

Practically, this enables large-scale, multi-region deployment of STF models for LST estimation without the need for recalibration or manual labeling in each new geographic site. Such a framework is directly applicable for operational satellite monitoring, climate change assessment, and environmental health applications where new areas are continually encountered, and the collection of ground-truth LST is prohibitive.

Future Directions

Potential future directions include:

• Extending the framework to multitask settings involving joint regression and classification (e.g., multi-geophysical parameter retrieval).
• Integrating alternative uncertainty quantification techniques (e.g., deep ensemble-based estimation) to assess their effect on TTA quality.
• Application to a broader spectrum of regression tasks in Earth observation, including air quality, soil moisture, and vegetation index prediction.
• Exploration of meta-learning strategies for even faster region-specific adaptation and automated tuning of $\lambda$ coefficients.

Conclusion

This work presents an uncertainty-aware TTA strategy, extending adaptation-by-inference to regression problems within the remote sensing domain for the first time. The benefits are substantiated by strong cross-region adaptation results under minimal data and computational constraints. The methodological advance is both theoretically sound and practically significant, with substantial implications for scalable, domain-robust geospatial regression in global Earth observation contexts.