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92 CHAPTER 3 Forecasting of Intermittent Solar Energy Resource

where y is the mean value of y. Other indices exist and can be used such as the cor-
relation coefficient R (Pearson coefficient) and the index of agreement (d) normal-
ized between 0 and 1.
When different forecasting methods are evaluated using different data sets, com-
parisons using score functions are not accurate. Skill scores that relate a specific
score function with a base model overcome this problem:

Metric forecasted Metric reference MSE forecast
SkillScore ¼ ¼ 1 (3.7)
Metric perfectforecast Metric reference MSE reference

where Metric forecasted is the score obtained by the method being evaluated,
Metric perfectforecast is the score obtained by an optimal forecast (i.e., by using obser-
vations as forecasts when computing the score rule), Metric reference is the score
obtained by a reference model, which is usually found either in climatology
(forecast is the average of available measures or of previously obtained average)
or persistence (last available measure is used as forecast).
“Trivial” forecast methods can be used as a reference [56]. The most common
one is the persistence model (“things stay the same”) where the forecast is always
equal to the last known data point. The persistence model is also known as the naı ¨ve
model or the RandomWalk (a mathematical formalization of a path that consists of a
succession of random steps).
The solar irradiance has a deterministic component because of the geometrical
path of the sun. This component, for example, may be added as a constraint to
the most basic form of persistence in considering the measured value of the previous
day or the previous hour at the same time as a forecast value. Other common refer-
ence forecasts include those based on climate constants and simple autoregressive
methods. Such comparison with referenced Numerical Weather Prediction (NWP)
model is shown in Fig. 3.7. Generally after 1 h, the forecast is better than the persis-
tence model. For forecast horizons ahead of 2 days, climate averages show lower er-
rors and should be preferred.

6. FORECASTING METHODS FOR DIFFERENT FORECAST
HORIZONS

This paragraph presents state-of-the-art approaches to solar irradiance forecasting at
different time scales. At first, some generalities concerning time-scale and temporal
resolution, about the link between PV production and weather forecast, are devel-
oped. Then, very short-term forecasting within a temporal range of 0e6 h and fore-
casts from 6 h to days ahead will be reviewed.