Abstract
A calibration procedure that fits the observed modeled data is used to determine the parameters of a hydrological model. As a result, the model parameters are highly uncertain. Estimation and the impact of uncertainty on model parameters have long been a source of debate. The bootstrap statistics method assesses uncertainty in surface nuclear magnetic resonance (surface NMR) water content and transverse relaxation time. The fundamental issue associated with the surface NMR data is that the quality of the surface NMR data is reduced in the presence of ambient electromagnetic and environmental noise. The bootstrap statistics is particularly well suited for estimating the uncertainty of the data set. We demonstrate that a bootstrap resampling of the observed synthetic data can provide an uncertainty estimate that closely fits the known uncertainty using synthetic forward modeled data with various noise levels, i.e., 5nV, 15nV, 30nV, and 50nV. The thickness of bootstrapped profile represents the uncertainty in the water content and relaxation time profiles. The thickness of the bootstrapped water content profile increases with an increase in noise level in the synthetic NMR data sets. Also, the thickness of the profiles increases along with the subsurface depth. Finally, we present seasonal field surface NMR data sets collected during the pre-monsoons and post-monsoon seasons under realistic ambient noise conditions. The surface NMR model was run for a 500–500 bootstrap to assess the pre-monsoon and post-monsoon uncertainty. This method is computationally extensive but straightforward to apply, and it provides valuable uncertainty estimates for both relaxation time and water content results for smooth-mono surface NMR models.
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Singh, U: conceptualization, methodology, formal analysis, data curation, software, writing-original draft; Sharma, P. K.: Investigation, visualization, writing-review, and editing.
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Key Points
• The uncertainty of the subsurface water content and relaxation time is proportional to the thickness of bootstrapped profiles.
• Ambient noise condition influences the uncertainty of the surface NMR data.
• Uncertainty is proportional to the subsurface depth irrespective of the noise level.
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Singh, U., Sharma, P.K. Seasonal Uncertainty Estimation of Surface Nuclear Magnetic Resonance Water Content using Bootstrap Statistics. Water Resour Manage 36, 2493–2508 (2022). https://doi.org/10.1007/s11269-022-03155-8
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DOI: https://doi.org/10.1007/s11269-022-03155-8