A Multiparametric Nonlinear Regression Approach for the Estimation of Global Surface Ocean pCO2 Using Satellite Oceanographic Data

Estimation of the partial pressure of carbon dioxide (pCO<sub>2</sub>) and its space–time variability in global surface ocean waters is essential for understanding the carbon cycle and predicting the future atmospheric CO<sub>2</sub> concentration. Until recently, only basin-scale distribution of pCO<sub>2</sub> has been reported by using satellite-derived climatological data due to the lack of models for global-scale applications. In the present work, a multiparametric nonlinear regression (MPNR) for the estimation of global-scale distribution of pCO<sub>2</sub> on the ocean surface is developed using continuous <italic>in-situ</italic> measurements of pCO<sub>2</sub>, chlorophyll-<italic>a</italic> (Chl<italic>a</italic>) concentration, sea surface temperature (SST), and sea surface salinity (SSS) obtained on a number of cruise programs in various regional oceanic waters. Analysis of these measurement data showed strong relationships of pCO<sub>2</sub> with Chl<italic>a</italic>, SST, and SSS, because these three parameters are governed by the complex interactions of oceanographic (physical, biological, and chemical) and meteorological processes and thus influence pCO<sub>2</sub> levels over different spatial and temporal scales. In order to account for regional differences in the influences of these processes on pCO<sub>2</sub>, model parameterizations are derived as a function of Chl<italic>a</italic>, SST, and SSS data with different boundary conditions. Because the strength of each influencing parameters on pCO<sub>2</sub> differed at different Chl<italic>a</italic>, SST, and SSS ranges, measurement data were grouped with reference to the Chl<italic>a</italic>, SST, and SSS ranges and significant correlations of the pCO<sub>2</sub> with dominant processes were established: for example, an inverse correlation of the pCO<sub>2</sub> with Chl<italic>a</italic>, SST, and SSS in polar and subpolar regions, a positive correlation of the pCO<sub>2</sub> with SST and SSS and an inverse correlation of the pCO<sub>2</sub> with Chl<italic>a</italic> in tropical and subtropical regions, and an inverse correlation of the pCO<sub>2</sub> with SST and a positive correlation of the pCO<sub>2</sub> with Chl<italic>a</italic> and SSS in equatorial regions. This indicates that the relationship of pCO<sub>2</sub> versus biological and physical parameters is more complex and an individual parameter alone would not serve as an accurate estimator of basin- and global-scale pCO<sub>2</sub> trends. Thus, changes in Chl<italic>a</italic>, SST, and SSS were systematically analyzed as they account for biological and physical effects on pCO<sub>2</sub> and best constrained based upon their strong relationships with pCO<sub>2</sub> using the MPNR regression approach. The accuracy of the MPNR was assessed using independent <italic>in-situ</italic> data and satellite pCO<sub>2</sub> data derived from global Level-3 Chl<italic>a</italic>, SST, and SSS data. Validation results showed that satellite-derived pCO<sub>2</sub> data agreed with direct <italic>in-situ</italic> pCO<sub>2</sub> measurements with an RMSE 6.68–7.5 μatm and a relative error less than 5%, which is significantly small as compared to the errors associated with earlier satellite pCO<sub>2</sub> computations. The distribution and magnitude of spatial and temporal (monthly and seasonal) amplitude of satellite-derived pCO<sub>2</sub> in climatic zones and ocean basins were further examined and agreed well with the shipboard pCO<sub>2</sub> observations and climatological surface ocean pCO<sub>2</sub> data.