Can improved root zone storage capacity estimates simplify hydrological modelling?

Root zone storage (S_r,max) is a key parameter in hydrological and land-surface models that regulates water fluxes partitioning and the ability of vegetation to buffer against dry periods, and closely linked to the Budyko parameter ω describing long-term catchment precipitation partitioning (Ibrahim et al., 2025). S_r,max is defined as the maximum subsurface water volume accessible to plants to meet their transpiration demands. Because direct observations of rooting depth are scarce and limited to local scales, catchment-scale S_r,max is commonly calibrated or estimated using the memory-method. This method derives S_r,max from annual maximum water storage deficits calculated from water balance data, assuming a fixed extreme-value distribution (typically Gumbel), and a predefined return period of 20 years. Despite its broad application, uncertainties arising from these assumptions and their implications for hydrological modelling have rarely been quantified. Here, we systematically evaluate the uncertainty, robustness and practical applicability of memory-method S_r,max estimates across different hydroclimatic regions globally (≈ 5700 catchments). Annual maximum storage deficits (S_d) were derived following the original memory-method framework but instead of fitting Gumbel distribution to S_d , we used the Generalized Extreme Value (GEV) distribution to allow flexible tail behaviour. Analysis of the GEV shape parameter - which determines tail behaviour - within the Budyko framework reveals strong hydroclimatic control, with Pearson correlations of approximately -0.50 with both the aridity index and the evaporative index. Most water-limited catchments exhibit negative shape parameter indicative of bounded (reversed Weibull Type-III) extremes, whereas energy-limited catchments tend toward positive shape parameters associated with heavy tailed (Frechet type-II) behaviour.

Uncertainty in S_r,max estimates was quantified using bootstrap resampling and expressed as confidence bounds derived from 2-year and 80-year return periods. Uncertainty width was strongly climate dependent with the widest ranges (median ≈ 132mm) occurring in transitional climates (aridity index ≈ 0.5-2), while arid and humid regions exhibit comparatively narrow uncertainty envelops (median ≈ 72mm). To assess practical implications, S_r,max uncertainty bounds were propagated into hydrological model calibration (≈1950 catchments). Among the Pareto-optimal solutions, model performance metrics were very similar, indicating strong equifinality in S_r,max estimates. Median simulated S_r,max values show strong agreement with memory-method estimates, with a global Pearson corelation of 0.92 (RMSE ≈ 60mm) and corelations across Koppen-Geiger climate zones ranging from 0.91-0.98. When memory-method S_r,max was calculated using the GEV distribution, the strongest agreement with median simulated S_r,max occurred for return periods of 20-30 years (Pearson r ≈ 0.93) at the global scale, with particularly clear sensitivity in cold and temperate regions. Overall, our results demonstrate that the memory-method robustly captures spatial patterns of S_r,max and that the commonly used 20-year return period represents a physically meaningful and hydro-climatically consistent choice. Using memory-method-based S_r,max estimates, instead of calibrating it, can reduce model complexity and parameter uncertainty without compromising model performance, offering practical advantages for large-scale hydrological and land-surface modelling.

 

Reference:

Ibrahim, M., Van der Ent, R., Coenders, M., Markus Hrachowitz, M. & van Oorschot, F. 2025. Catchment precipitation partitioning in the Budyko framework is controlled by root zone storage capacity. Environmental Research Letters, (under review)