Does the level 1 detail coefficients obtained using Haar wavelet decomposition indicate only the noise content in the signal? Can it be intepreted in any other ways?
The 1 level details coefficients contain the noise as the details represent the higher frequencies of the signal and the gaussian white noise is a high frequency fluctuation as well. However, 1 level of DWT analysis is not enough to get rid of most of the noise and going deeply in 4 or 5 levels is highly recommended. At each level, a threshold can be chosen on the details part of the level for noise filtering before signal reconstruction.
I would indeed refrain myself in referring or representing level 1 or any further signal decomposition as only noise content. However, the interpretation is subjective and varies on the objective of the study.
Given my field knowledge (Nonlinear dynamics and hydroclimatology), level 1 detail coefficients capture the localized information which are high-frequency or transient features of the signal along with noise, if there is any. Referring the entire detail decomposition to noise is certainly not correct.
For example, in case of rainfall, finer scale processes might be the result of convective or localized phenomena whereas processes at a coarser scale might be driven by large-scale teleconnections (Agarwal et al., 2017; 2019).
Agarwal et al., (climate dynamics, submitted) shows that spatial proximity connections, defined by Tobler's first law of Geography which states that everything is connected to everything but nearby points are more connected, are higher at finer scale compared to coarser scale which again indicates that at finer scales localized information dominates.
Many studies, interested in the coarser scale process might consider the finer scale features as noise but technically it is not correct.
For further details refer:
https://www.researchgate.net/publication/331086252_Unraveling_spatio-temporal_climatic_patterns_via_multi-scale_complex_networks
https://www.researchgate.net/publication/320389162_Multi-scale_event_synchronization_analysis_for_unravelling_climate_processes_A_wavelet-based_approach
Cheers, A
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