Assessing the Steady-State Assumption in Water Balance Calculation Across Global Catchments

Abstract

It has long been assumed that over a sufficiently long period of time, changes in catchment water storage (ΔS) are a relatively minor term compared to other fluxes and can be neglected in the catchment water balance equation. However, the validity of this fundamental assumption has rarely been tested, and the associated uncertainties in water balance calculations remain unknown. Here, we use long-term (1982–2011) observations of monthly streamflow (Q) and precipitation (P) for 1,057 global unimpaired catchments, combined with four independent evapotranspiration (E) estimates to infer ΔS and to provide a global assessment of the steady-state assumption in catchment water balance calculations. Results show that when the threshold for steady state is set to 5% of the mean monthly P, ~70% of the catchments attain steady state within 10 years while ~6% of the catchments fail to reach a steady state even after 30 years. The time needed for a catchment to reach steady state (τs) shows a close relationship with climatic aridity and vegetation coverage, with arid/semiarid and sparsely vegetated catchments generally having a longer τs. Additionally, increasing snowfall fraction also increases τs. The imbalance (ewb) caused by ignoring ΔS decreases as averaging period for water balance calculations increases as expected. For a typical 10-year averaging period, ewb accounts for ~7% of P in arid, but that decreases to ~3% of P in humid catchments. These results suggest that catchment properties should be considered when applying the steady-state assumption and call for caution when ignoring ΔS in arid/semiarid regions.