Improved uncertainty estimates for the exponential filter method in a long-term error characterised root-zone soil moisture dataset.

Root zone soil moisture, as the water available for plant uptake, effects evapotranspiration and has an important role in predicting droughts and agricultural yields. While microwave remote sensing retrievals are limited to observing the topmost few centimetres of the soil, they can be used with a variety of methods to infer the water content in the root zone due to the existing link between the dynamics in both layers. Regardless of their methodologies, most root zone soil moisture datasets do not provide uncertainty estimates.
Among the techniques for approximating root zone soil moisture, the exponential filter method stands out as a relatively non-complex approach essentially smoothing and delaying surface observations which are generally characterized by greater temporal dynamics. The uncertainties of the exponential filter method are poorly analysed and typically unavailable. 
To address this gap, we extend the standard law for the propagation of uncertainties to characterize the random error variances of the exponential filter-based root zone soil moisture estimates. The proposed method considers the uncertainties of the input surface soil moisture retrievals and their availability in time as well as those of the exponential filter’s parameter and the method’s model structural error. The latter two components of the uncertainty budget are temporally-static values estimated from ground reference measurements at various depths. The resulting time-variant uncertainty estimates are realistic both in magnitude and temporal variations.