Mitigating Representativeness Errors in Sparse Soil Moisture Observations Through Upscaling Constrained by Intra-Pixel Spatial Variability

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Abstract
The validation of soil moisture (SM) products has long been constrained by the point-to-pixel scale mismatch, limiting their utility for hydrological applications. In sparse in situ networks, single-site measurements lack sufficient representativeness at the pixel scale, and their direct use for validation inevitably introduces non-negligible representativeness errors. Existing upscaling approaches either rely on densely distributed observations, limiting their generalizability, or directly extrapolate machine-learning-based spatial estimates, which risks propagating model biases into validation metrics. To address this, we propose a single-site upscaling approach constrained by intra-pixel spatial variability. The core idea is to use spatial variability information to guide the estimation of upscaling conversion coefficients. Specifically, we integrate multi-source remote sensing auxiliary variables with automated machine learning (AutoML) to construct a high-resolution SM trend surface that characterizes intra-pixel spatial variations and quantifies site representativeness. We further design a progressive estimation strategy, from OLS to AOLS and SW-AOLS, to optimize the point-to-pixel conversion stepwise. Results show that upscaling performance is closely tied to site representativeness. SW-AOLS reduced median representativeness errors by approximately 57% and 64% for moderate- and low-representativeness sites, respectively. Validation across 24 SM products, including L/C/X-band, active-passive fusion, and reanalysis products, demonstrates that the upscaled single-site references closely approximate pixel-scale ground "truth" from dense networks. For moderate- and low-representativeness sites, the upscaling approach reduced validation errors by 72% and 89%, and uncertainty by 42% and 60%, respectively. Without requiring additional ground observations, this study enhances validation reliability under sparse conditions and supports more reliable SM information for hydrological applications.

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