Uncertainty in root zone storage capacity estimates and its implications for hydrological modelling

Abstract. In hydrological and land-surface models, root zone storage (S_r,max) plays a fundamental role in the partitioning of terrestrial water fluxes and, consequently, in the ability of  vegetation to withstand dry periods. It represents the maximum volume of subsurface water that can be accessed by vegetation to sustain transpiration. As direct measurements of rooting depth are generally unavailable at the catchment scale, S_r,max is inferred either through hydrological model calibration or by applying the memory method. The memory method estimates S_r,max from a series of annual maximum water storage deficits based on an assumed extreme value distribution, commonly the Gumbel distribution, and a fixed 20-year return period. However, the uncertainties in S_r,max estimates associated with these assumptions have not been systematically quantified. Here, we systematically quantify and evaluate these uncertainties across ~5700 catchments worldwide by replacing Gumbel distribution with the more flexible Generalized Extreme Value (GEV) distribution and applying a bootstrap framework to derive uncertainty bounds on S_r,max. Analysis of the GEV shape parameter (ξ) shows a strong hydroclimatic control. Most catchments in water-limited environments are characterized by a negative ξ, indicative of bounded extremes: extension of root systems beyond these bounds does not have benefits for vegetation as most of the available water is already used by vegetation. In contrast, positive values of ξ are more commonly found in energy-limited catchments, indicating a heavy tailed distribution of annual maximum water storage deficits. This implies that vegetation benefits from adapting root systems and thus S_r,max to dry periods with longer return periods, as in these environments sufficient water is available in the subsurface to be accessed and used by these larger root systems. Overall, uncertainties in S_r,max estimates varied systematically across climatic conditions. The widest uncertainty ranges were observed in transitional climates (aridity index 0.5–2) with a median value of approximately ±66 mm, whereas humid and arid regions exhibited substantially smaller uncertainty ranges (median ~± 36 mm). Using these uncertainty ranges as calibration bounds for S_r,max in a hydrological model resulted in many parameter sets yielding comparable model performance for the majority of catchments. Yet memory method S_r,max estimates show a strong agreement with median calibrated S_r,max values, with a RMSE ~50 mm and a global Pearson correlation coefficient of ρ = 0.93, with ρ ranging from 0.91 to 0.98 across different climate zones. The strongest agreement between calibrated and memory method estimates of S_r,max is consistently found for return periods of 20–30 years, with higher sensitivity in cold and temperate regions. Overall, the findings of this study demonstrate that the memory method is robust in capturing S_r,max spatial patterns. They also suggest that the use of a 20-year return period is supported by underlying hydroclimatic behaviour and physically processes, rather than being an arbitrary assumption. Memory method based estimates of S_r,max provide an alternative to calibration, thereby reducing model complexity and parameter uncertainty while preserving model performance, particularly in large scale hydrological and land-surface modelling.