One informative segment of model performance is the comparison of model elements or functions to previously-developed similar model components. Examples include so-called “simple” broadband or spectral transmittance models. These types of models were briefly mentioned in Sect. 4, and described in Eq. (20.4). Comparisons of individual transmittance functions from some similar models are detailed elsewhere (Gueymard 1993, 2003b). These model elements may be changed or improved during the model’s development or as different, possibly more detailed information on model parameters become available.
For instance, Bird and Hulstrom (1981a, b) compared the transmittance functions developed for their model with those of several other authors (Atwater and Ball 1978; Davies and Hay 1979; Hoyt 1978; Lacis and Hansen 1974; Watt 1978). This pioneering work is regularly updated (Gueymard 1993, 2003b). Of course, for models of this type, the number of parameterized transmission functions need not be identical, nor the input parameters match exactly (e. g., relative humidity and ambient temperature in place of dew point for estimating, or as surrogates for, pre – cipitable water).
A similar example is provided by Thornton and Running (1999) who developed an improved version of a model for solar radiation based solely on ambient temperature developed by Bristow and Campbell (1984). Thornton and Running expanded the model with improved parameterizations of the coefficients, and consideration of a single additional (optional) input variable of dew-point temperature. Their sensitivity study is also remarkable. One site at a time is systematically removed from the set of 40 sites. Model parameters are derived from the remaining 39 sites. The ‘new’ model is applied to the excluded site, and the MABE for that site is computed. The procedure is iterated over all sites, providing data for a multi-way analysis to minimize the pooled MABE for the data set. This also provides a means of testing the influence of specific sites (or sets of sites, say, clear vs cloudy or desert vs continental) on the model’s parameters.
These comparisons and modifications of model elements are helpful in developing model improvements and quantifying the causes of relative model biases and differences. The real test of model performance comes from evaluations performed by other authors, using different sets of input data, and especially measured solar radiation data, as discussed above in Sect. 3.
