Calibrating Remotely Sensed Ocean Chlorophyll Data: An Application of the Blending Technique in Three Dimensions (3D)

In this article, the extension to three dimensions (3D) of the blending technique that has been widely used in two dimensions (2D) to calibrate ocean chlorophyll is presented. The results thus obtained revealed a very high degree of efficiency when predicting observed values of ocean chlorophyll. The mean squared difference between the predicted and observed values of ocean chlorophyll when 3D technique was used fell far below the tolerance level which was set to the difference between satellite and observed in-situ values. The resulting blended field did not only provide better predictions of the in situ observations in areas where bottle samples cannot be obtained but also provided a smooth variation of the distribution of ocean chlorophyll throughout the year. An added advantage is its computational efficiency since data that would have been treated at least four times would be treated only once. With the advent of these results, it is believed that the modelling of the ocean life cycle will become more realistic.

Estimating Ocean Chlorophyll Using the Penalized Three Dimensional (3D) Blending Technique

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.

Modeling Ocean Chlorophyll Distributions by Penalizing the Blending Technique

Disparities between the in situ and satellite values at the positions where in situ values are obtained have been the main handicap to the smooth modeling of the distribution of ocean chlorophyll. The blending technique and the thin plate regression spline have so far been the main methods used in an attempt to calibrate ocean chlorophyll at positions where the in situ field could not provide value. In this paper, a combination of the two techniques has been used in order to provide improved and reliable estimates from the satellite field. The thin plate regression spline is applied to the blending technique by imposing a penalty on the differences between the satellite and in situ fields at positions where they both have observations. The objective of maximizing the use of the satellite field for prediction was outstanding in a validation study where the penalized blending method showed a remarkable improvement in its estimation potentials. It is hoped that most analysis on primary productivity and management in the ocean environment will be greatly affected by this result, since chlorophyll is one of the most important components in the formation of the ocean life cycle.