There are several situations where we will only have data sets that consist of daily total solar radiation. This can be the case if that is all that is gathered or more significantly, if we are interested in, for instance, simulating the performance of a system dependent on solar radiation for a location where there is no data collection at all. For such a location, we can infer the daily total on a horizontal plane from satellite data. We have constructed an algorithm (see Section 10 for details on how to implement it) to obtain a smoothed average daily profile of hourly values corresponding to the daily total, from knowledge only of that total and of course being able to calculate sunrise and sunset. We rely also on knowledge gained from the time series modelling described in Chapter 11 of this book, defining exactly what intra-day cycles exist. We make the quite reasonable assumption that the solar radiation peaks at solar noon. All of this leads to a simple constrained optimisation problem to determine the necessary Fourier coefficients for the embedded cycles. Once we have this daily profile for the global, we can use Eq. (8.21) to estimate the diffuse fraction, and thus the diffuse at any time of the day. Figure 8.19 gives an illustration of this calculation, along with the direct normal radiation (calculated from the other two components).
Fig. 8.19 Estimating the diffuse radiation when we have had to infer hourly values from daily totals
Please note that there are Excel files containing the algorithms for modelling the diffuse fraction and for constructing the daily profile on the CD accompanying the volume. The algorithms are briefly described below.