Satellite-based measurements of aerosol optical depth (AOD) over land are obtained from an inversion procedure applied to dense dark vegetation pixels of remotely sensed images. The limited number of pixels over which the inversion procedure can be applied leaves many areas with little or no AOD data. Moreover, satellite coverage by sensors such as MODIS yields only daily images of a given region with four sequential overpasses required to straddle mid-latitude North America. Ground based AOD data from AERONET sun photometers are available on a more continuous basis but only at approximately fifty locations throughout North America. The object of this work is to produce a complete and coherent mapping of AOD over North America with a spatial resolution of 0.1 degree and a frequency of three hours by interpolating MODIS satellite-based data together with available AERONET ground based measurements. Before being interpolated, the MODIS AOD data extracted from different passes are synchronized to the mapping time using analyzed wind fields from the Global Multiscale Model (Meteorological Service of Canada). This approach amounts to a trajectory type of simplified atmospheric dynamics correction method. The spatial interpolation is performed using a weighted least squares method applied to bicubic B-spline functions defined on a rectangular grid. The least squares method enables one to weight the data accordingly to the measurement errors while the B-splines properties of local support and C2 continuity offer a good approximation of AOD behaviour viewed as a function of time and space.
Two methods to estimate aerosol optical depth (AOD) at a relatively low computational cost, using the data of the sun photometers from the Aerosol Robotic Network (AERONET) are presented and compared. One interpolates the data and the other approximates the data. The technique is based on a geometric approach. Assuming that AOD can be represented as a highly continuous surface function of time and position, a height field approximating AOD using the data from the sun photometers is obtained. Both methods use an optimization-subdivision iterative algorithm to create a function that interpolates or approximates the AOD values measured by the sun photometers. The methods begin by constructing a Delaunay triangulation of the location of the sun photometer sites over the region were the AOD value is to be approximated. The algorithm then alternatively optimizes and subdivides the triangular mesh. At each iteration, the optimization step first creates a data dependent triangulation which is then subdivided. The results obtained by the two methods are compared with those obtained from piecewise linear interpolation.