A Comparative Assessment of Gap-filling Techniques for Ocean Carbon Time Series

Abstract. Regularized time series of ocean carbon data are necessary for assessing seasonal dynamics, annual budgets, interannual variability and long-term trends. There are, however, no standardized methods for imputing gaps in ocean carbon time series, and only limited evaluation of the numerous methods available for constructing uninterrupted time series. A comparative assessment of eight imputation models was performed using data from seven long-term monitoring sites. Multivariate linear regression (MLR), mean imputation, linear interpolation, spline interpolation, Stineman interpolation, Kalman filtering, weighted moving average and multiple imputation by chained equation (MICE) models were compared using cross-validation to determine error and bias. A bootstrapping approach was employed to determine model sensitivity to varied degrees of data gaps and secondary time series with artificial gaps were used to evaluate impacts on seasonality and annual summations and to estimate uncertainty. All models were fit to DIC time series, with MLR and MICE models also applied to field measurements of temperature, salinity and remotely sensed chlorophyll, with model coefficients fit for monthly mean conditions. MLR estimated DIC with a mean error of 8.8 umol kg−1 among 5 oceanic sites and 20.0 ummol kg−1 among 2 coastal sites. The empirical methods of MLR, MICE and mean imputation retained observed seasonal cycles over greater amounts and durations of gaps resulting in lower error in annual budgets, outperforming the other statistical methods. MLR had lower bias and sampling sensitivity than MICE and mean imputation and provided the most robust option for imputing time series with gaps of various duration.