An empirical MLR for estimating surface layer DIC and a comparative assessment to other gap-filling techniques for ocean carbon time series

Regularized time series of ocean carbon data are necessary for assessing seasonal dynamics, annual budgets, and interannual and climatic variability. There are, however, no standardized methods for filling data gaps and limited evaluation of the impacts on uncertainty in the reconstructed time series when using various imputation methods. Here we present an empirical multivariate linear regression (MLR) model to estimate the concentration of dissolved inorganic carbon (DIC) in the surface ocean, that can utilize remotely sensed and modeled data to fill data gaps. This MLR was evaluated against seven other imputation models using data from seven long-term monitoring sites in a comparative assessment of gap-filling performance and resulting impacts on variability in the reconstructed time series. Methods evaluated included three empirical models - MLR, mean imputation, and multiple imputation by chained equation (MICE) - and five statistical models - linear, spline, and Stineman interpolation; exponential weighted moving average; and Kalman filtering with a state space model. Cross validation was used to determine model error and bias, while a bootstrapping approach was employed to determine sensitivity to varying data gap lengths. A series of synthetic gap filters, including 3-month seasonal gaps (spring, summer, autumn winter), 6-month gaps (centered on summer and winter), and bimonthly (every 2 months) and seasonal (four samples per year) sampling regimes, were applied to each time series to evaluate the impacts of timing and duration of data gaps on seasonal structure, annual means, interannual variability, and long-term trends. All models were fit to time series of monthly mean DIC, with MLR and MICE models also applied to both measured and modeled temperature and salinity with remotely sensed chlorophyll. Our MLR estimated DIC with a mean error of 8.8 mu mol kg(-1) among five oceanic sites and 20.0 mu mol kg(-1) for two coastal sites. The MLR performance indicated reanalysis data, such as GLORYS, can be utilized in the absence of field measurements without increasing error in DIC estimates. Of the methods evaluated in this study, empirical models did better than statistical models in retaining observed seasonal structure but led to greater bias in annual means, interannual variability, and trends compared to statistical models. Our MLR proved to be a robust option for imputing data gaps over varied durations and may be trained with either in situ or modeled data depending on application. This study indicates that the number and distribution of data gaps are important factors in selecting a model that optimizes uncertainty while minimizing bias and subsequently enables robust strategies for observational sampling.