The Thin Plate Regression Spline (TPRS) was introduced as a means of
smoothing off the differences between the satellite and in-situ observations
during the two dimensional (2D) blending process in an attempt to calibrate
ocean chlorophyll. The result was a remarkable improvement on the predictive
capabilities of the penalized model making use of the satellite observation.
In addition, the blending process has been extended to three dimensions
(3D) since it is believed that most physical systems exist in the three
dimensions (3D). In this article, an attempt to obtain more reliable and accurate
predictions of ocean chlorophyll by extending the penalization
process to three dimensional (3D) blending is presented. Penalty matrices
were computed using the integrated least squares (ILS) and integrated
squared derivative (ISD). Results obtained using the integrated least squares
were not encouraging, but those obtained using the integrated squared derivative
showed a reasonable improvement in predicting ocean chlorophyll
especially where the validation datum was surrounded by available data
from the satellite data set, however, the process appeared computationally
expensive and the results matched the other methods on a general scale. In
both case, the procedure for implementing the penalization process in three
dimensional blending when penalty matrices were calculated using the two
techniques has been well established and can be used in any similar three
dimensional problem when it becomes necessary.
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Eppley, R.W., Stewart, E., Abbott, M.R. and Heyman, U. (1985) Estimating Ocean Primary Production from Satellite Chlorophyll. Introduction to Regional Differences and Statistics for the Southern California Bight. Journal of Plankton Research, 7, 57-70. https://doi.org/10.1093/plankt/7.1.57
Gregg, W.W. and Conkright, M.E. (2001) Global Seasonal Climatologies of Ocean Chlorophyll: Blending in Situ and Satellite Data for Coastal Zone Color Scanner Era. Journal of Geophysical Research, 106, 2499-2515.
Onabid, M.A. (2017) Calibrating Remotely Sensed Ocean Chlorophyll Data: An Application of the Blending Technique in Three Dimensions (3D). Open Journal of Marine Science, 7, 191-204. https://doi.org/10.4236/ojms.2017.71014