Comments on “Surface Measurements of Solar Irradiance: A Study of the Spatial Correlation between Simultaneous Measurements at Separated Sites”

Long and Ackerman (1995) have addressed in their recent paper the spatial correlation between simultaneous irradiance measurements at distinct sites in a region for the purpose of defining the reasonable and scientifically acceptable distance between pyranometer sites. I believe that such studies should be encouraged not only in the assessment of areal irradiance data, but also for other atmospheric variables. It is also true that the representativeness of irregularly distributed measuring sites should be assessed. Therefore, the authors must be congratulated for such a timely attempt. Furthermore, similar studies are also useful for estimating the values of physical properties at unsampled sites within areas covered by existing observation networks through the interpolation procedure, or extrapolation if the desired point estimate is outside of the configuration of measurement sites. The problem consists of interpolating any unknown solar irradiance value at an ungauged site given the known set of multidimensional geographical position coordinates of measurement sites and the sampled values of solar radiation field. The methods are very similar and in fact are equivalent to the objective analysis procedures in meteorology summarized by Daley (1991). Among the procedures are local and global interpolation techniques with respect to the dataset management, and deterministic or stochastic interpolation techniques (including probabilities and statistics) with respect to the mathematical hypothesis. The authors have adopted in their study the statistical method for the application. Unfortunately, classical statistical estimation procedures are employed mechanically without physical, logical, or procedural feasibility at instances of the utmost importance. However, there are many points in the paper that require discussion, interpretation, and development of new methodologies for a proper assessment of the spatial data. In fact, the authors have treated the spatial data in the form of pairwise combinations, which does not reflect the regional structure of the irradiance data. I would like to raise