A Multiparametric Nonlinear Regression Approach for the Estimation of Global Surface Ocean pCO<sub>2</sub> Using Satellite Oceanographic Data
Kande Vamsi Krishna, Palanisamy Shanmugam, P. V. Nagamani
Abstract
Estimation of the partial pressure of carbon dioxide (pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> concentration. Until recently, only basin-scale distribution of pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> on the ocean surface is developed using continuous in-situ measurements of pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , chlorophyll-a (Chla) 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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with Chla, 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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , model parameterizations are derived as a function of Chla, SST, and SSS data with different boundary conditions. Because the strength of each influencing parameters on pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> differed at different Chla, SST, and SSS ranges, measurement data were grouped with reference to the Chla, SST, and SSS ranges and significant correlations of the pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with dominant processes were established: for example, an inverse correlation of the pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with Chla, SST, and SSS in polar and subpolar regions, a positive correlation of the pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with SST and SSS and an inverse correlation of the pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with Chla in tropical and subtropical regions, and an inverse correlation of the pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with SST and a positive correlation of the pCO2 with Chla and SSS in equatorial regions. This indicates that the relationship of pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> trends. Thus, changes in Chla, SST, and SSS were systematically analyzed as they account for biological and physical effects on pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and best constrained based upon their strong relationships with pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> using the MPNR regression approach. The accuracy of the MPNR was assessed using independent in-situ data and satellite pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> data derived from global Level-3 Chla, SST, and SSS data. Validation results showed that satellite-derived pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> data agreed with direct in-situ pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> computations. The distribution and magnitude of spatial and temporal (monthly and seasonal) amplitude of satellite-derived pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> in climatic zones and ocean basins were further examined and agreed well with the shipboard pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> observations and climatological surface ocean pCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> data.