Structural limits and ill-posedness of soil water storage balance method for diagnosing root water uptake

Abstract. Depth-resolved root water uptake (RWU) can be inferred through soil water storage balance (SWSB) from soil water content observations, yet their fundamental identifiability and robustness remain unclear. Using controlled numerical experiments with prescribed contrasting RWU profiles, we systematically evaluate the performance of SWSB-based RWU inversion under varying spatiotemporal aggregation and upper boundary conditions. Our results show that while accurate estimates can be obtained under idealized, error-free datasets, even modest uncertainties in soil hydraulic parameters (±10 %) and soil water content measurements (±1 %) lead to error amplification in RWU estimates by around 60-fold. Furthermore, the sensitivity analysis shows that SWSB-based RWU inversion is highly sensitive to soil water content, as it directly influences storage change (ΔV) and regulates the relationships between soil water content (θ) and pressure head (h), as well as saturated (k_s) and unsaturated (k) hydraulic conductivities. These findings highlight SWSB-based RWU inversion is fundamentally ill-posed and becomes non-identifiable under realistic uncertainties. Overall, this study delineates the conditions under which SWSB-based RWU inversion can be reliably applied and emphasizes the need for additional independent constraints.