Calibrating remotely sensed chlorophyll-a data by using penalized regression splines

The distribution and biomass of phytoplankton in the upper layers of the ocean are important indicators of productivity and carbon cycling. Large scale perturbations in phytoplankton are linked to global climate change, so accurate monitoring is increasingly important. The chlorophyll-a pigment concentration in the water is routinely measured as an index of algal biomass. Direct water sampling from ships and moorings provides accurate data, but woefully poor spatial and temporal coverage of the oceans. In contrast, multispectral sea surface reflectance data from orbiting satellite-borne sensors, which in principle can be used to derive pigment concentration, give the prospect of globally detailed spatial and temporal coverage. Unfortunately, there are some locally variable confounding factors, which the algorithms for converting reflectance data to ocean chlorophyll-a concentration do not take into account. Hence, statistical methods are needed to obtain accurate predictions of chlorophyll-a concentration by using data from both these sources. We use penalized regression splines to model water sample data as a three-dimensional function of satellite measurements, seabed depth and time of year. The models are effectively complex calibrations of the satellite data against the bottle data. We compare the results by using thin plate regression splines and tensor product splines using generalized cross-validation to choose the relative amounts of smoothing for each of the covariates. Since the thin plate spline penalty functional is isotropic, this requires the introduction of two scaling parameters, which are also chosen by generalized cross-validation, to scale the covariates relatively to one another. The tensor product spline smooths each covariate appropriately by use of separate smoothing parameters for each covariate. The models are tested by application to data from the north-east Atlantic, first randomly subsampling the data to achieve even coverage over the entire region. Both approaches perform equally well, achieving R2≈65%, both for the data that are used to fit the model and for a validation data set. Of particular concern in this application is that monthly predictions from the models should be biologically plausible over the whole region, describing the broad regional features that are apparent in the satellite data and extrapolating sensibly where satellite data are not available. To achieve this, the satellite data must be one of the covariates in the model; spatiotemporal covariates alone are not sufficient to extrapolate sensibly into areas where no data are available