Quantifying uncertainty in annual runoff due to missing data

Long-term streamflow datasets inevitably include gaps, which must be filled to allow estimates of runoff and ultimately catchment water budgets. Uncertainty introduced by filling gaps in discharge records is rarely, if ever, reported. We characterized the uncertainty due to streamflow gaps in a reference watershed at the Hubbard Brook Experimental Forest (HBEF) from 1996 to 2009 by simulating artificial gaps of varying duration and flow rate, with the objective of quantifying their contribution to uncertainty in annual streamflow. Gaps were filled using an ensemble of regressions relating discharge from nearby streams, and the predicted flow was compared to the actual flow. Differences between the predicted and actual runoff increased with both gap length and flow rate, averaging 2.8% of the runoff during the gap. At the HBEF, the sum of gaps averaged 22 days per year, with the lowest and highest annual uncertainties due to gaps ranging from 1.5 mm (95% confidence interval surrounding mean runoff) to 21.1 mm. As a percentage of annual runoff, uncertainty due to gap filling ranged from 0.2-2.1%, depending on the year. Uncertainty in annual runoff due to gaps was small at the HBEF, where infilling models are based on multiple similar catchments in close proximity to the catchment of interest. The method demonstrated here can be used to quantify uncertainty due to gaps in any long-term streamflow data set, regardless of the gap-filling model applied.