Technical note: Mind the gap – benchmarking of various imputation approaches for precipitation stable isotope time series

Abstract. Stable isotopes of hydrogen and oxygen in precipitation (δₚ) are important natural tracers in wide range of environmental applications (e.g., the exploration of the water cycle, ecology and food authenticity), yet observational records commonly contain gaps, although applications in hydrology and earth science frequently require complete cases. Eight imputation approaches were benchmarked using monthly δₚ time series from Austria, Slovenia, and Hungary. Uninterrupted periods were selected, and monthly data were masked site-wise with an increasing degree of missingness, removing 1 to 32 % of the data using bootstrapping. The imputation performance of the following methods was assessed on the masked monthly data using the mean absolute difference and root mean square error between the observed and imputed values for primary and secondary isotopic parameters: Last Observation Carried Forward, Linear Interpolation, Spline Interpolation, Stineman Interpolation, Kalman Smoothing, Moving Average Imputation, Sinusoidal fit, and a spatial proximity-based imputation (SPbI) approach introduced in the present paper. SPbI estimates missing δₚ values using the mean of altitude-corrected δₚ data from within a predefined search radius. Across masking levels, SPbI was the most accurate and least prone to amplitude damping in δₚ records. Sinusoidal imputation remained robust under increasing missingness but has shown a tendency of reducing extremes, indicating amplitude loss in both δₚ and d-excess. Spline performed worst overall with the rest performing similarly up to ~16 % masking beyond which their performance deteriorated. A sensitivity analysis using non-cumulative 50-km distance bands up to 400 km showed that SPbI errors increase with distance; beyond ~250 km, mean errors approach those of the sinusoidal method, making the sinusoidal—or even the simpler linear interpolation—a viable alternative when proximal observations are sparse. The benchmarking results recommend the use of SPbI where station data are available within 250 km distance, and the sinusoidal or linear approach otherwise.