Abstract
Linear regression is widely used in applied sciences and, in particular, in satellite optical oceanography, to relate dependent to independent variables. It is often adopted to establish empirical algorithms based on a finite set of measurements, which are later applied to observations on a larger scale from platforms such as autonomous profiling floats equipped with optical instruments (e.g., Biogeochemical Argo floats; BGC-Argo floats) and satellite ocean colour sensors (e.g., SeaWiFS, VIIRS, OLCI). However, different methods can be applied to a given pair of variables to determine the coefficients of the linear equation fitting the data, which are therefore not unique. In this work, we quantify the impact of the choice of “regression method” (i.e., either type-I or type-II) to derive bio-optical relationships, both from theoretical perspectives and by using specific examples. We have applied usual regression methods to an in situ data set of particulate organic carbon (POC), total chlorophyll-a (TChla), optical particulate backscattering coefficient (bbp), and 19 years of monthly TChla and bbp ocean colour data. Results of the regression analysis have been used to calculate phytoplankton carbon biomass (Cphyto) and POC from: i) BGC-Argo float observations; ii) oceanographic cruises, and iii) satellite data. These applications enable highlighting the differences in Cphyto and POC estimates relative to the choice of the method. An analysis of the statistical properties of the dataset and a detailed description of the hypothesis of the work drive the selection of the linear regression method.
Highlights
In technical and scientific applications, the linear regression fit is one of the most common models used to establish a relationship between two variables
As suggested by Loisel et al, (2001) [6], sub-micrometer particles are efficient backscatterers, such that there is confirmation that the dominant contribution to particulate organic carbon in the ocean is due to sub-micrometer particles that are in sufficiently higher concentrations allowing for dominance of the bbp in oceanic water determining, causing a strong correlation with POC
Derived from BGC-Argo bbp vertical profiles (0–250 m) using OLS and standard major axis (SMA) and relationships (b). We have used both type-I (i.e., OLS) and type-II (i.e., SMA) methods with bio-optical data collected over three years of monthly oceanographic cruises at the BOUSSOLE site (Figure 1) to derive linear regression coefficients that were applied to BGC-Argo vertical profiles for the estimations of phytoplankton carbon biomass and particulate
Summary
In technical and scientific applications, the linear regression fit is one of the most common models used to establish a relationship between two variables. The scientific conclusions must be based on the appropriate methodology, i.e., a methodology adapted to the statistical properties of the data set to be analysed In this regard, our primary goal is to evaluate the impact of the linear regression model (and methods) in optical and satellite oceanography. Long termE) site [27,28,29], during three years of monthly oceanographic cruises (2011–2013) and more than one year (July 2013–November 2014) of Biogeochemical-Argo (aka BGC-Argo) vertical profiles We applied both type-I and type-II regression methods to determine the coefficients of the linear equations of the total chlorophyll-a (TChla)-bbp and bbp -POC relationships from discrete samples. A similar analysis was conducted relying on satellite observations, namely Cphyto was evaluated, by using 19-years of monthly TChla and bbp
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