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Characterizing and understanding the environment affecting quantum systems is critical to elucidate its physical properties and engineer better quantum devices. We develop an approach to reduce the quantum environment causing single-qubit dephasing to a simple yet predictive noise model. Our approach, inspired by quantum noise spectroscopy, is to define a "self-consistent" classical noise spectrum, that is, compatible with all observed decoherence under various qubit dynamics. We demonstrate the power and limits of our approach by characterizing, with nanoscale spatial resolution, the noise experienced by two electronic spins in diamond that, despite their proximity, surprisingly reveal the presence of a complex quantum spin environment, both classically-reducible and not. Our results overcome the limitations of existing noise spectroscopy methods, and highlight the importance of finding predictive models to accurately characterize the underlying environment. Extending our work to multiqubit systems would enable spatially-resolved quantum sensing of complex environments and quantum device characterization, notably to identify correlated noise between qubits, which is crucial for practical realization of quantum error correction.