Solar forecasting explained · 22 October 2026 · Published article, open code

How variable is the sun, and how forecastable? sCV and F explained

Before choosing a forecasting model, it helps to know how difficult the site is. Two numbers answer that: sCV, the variability that clouds add to the course of the sun, and F, how much of that variability can be anticipated at a given horizon.

Why the usual coefficient of variation misleads

The coefficient of variation CV = σ/μ mostly measures the day: the sun rises and sets, so a perfectly clear sky already has a large CV (about 1.2 in the figure below). Two sites with the same clouds but different day lengths get different CVs. A forecaster needs the part the sun's course does not explain: the clouds.

sCV: variability around clear sky

sCV measures the spread of the measured irradiance I around the clear-sky irradiance I_clr, not around the mean:

sCV = √2 / |d − 1| × RMSE(I, I_clr) / √(σ_clr² + μ_clr²)

• RMSE(I, I_clr) is the error of the clear-sky model used as a forecast;
• √(σ_clr² + μ_clr²) is the root mean square of the clear-sky curve;
• d = 0.2 is the diffuse floor: the fraction of clear sky that remains under a thick cloud.

sCV = 0 for a clear sky and 1 for the most variable sky the article considers, one that switches at random between clear sky and the diffuse floor. Night hours change nothing.

F: forecastability at a horizon

With ε = I − I_clr and ρ_max the largest autocorrelation of ε over the lags from the horizon n to half a day:

F = 1 + sCV × (ρ_max − 1)

F lies between 1 − sCV (clouds with no memory) and 1 (clouds that last). A cloudy site can be forecastable if its clouds persist; a site with fast, random clouds is not. sCV describes the site; F describes the forecasting task at a horizon.

Worked example by hand

1. RMSE of clear sky: √(131 600 / 4) ≈ 181.4 W/m².
2. Root mean square of clear sky: √(1 600 000 / 4) ≈ 632.5 W/m².
3. sCV = √2 / 0.8 × 181.4 / 632.5 ≈ 0.51.
4. If the residuals keep ρ_max = 0.6 at the horizon of interest: F = 1 + 0.51 × (0.6 − 1) ≈ 0.80.

Fictitious teaching values.

F predicts forecast error

This is the article's conclusion on synthetic series and on 68 stations of the Spanish SIAR network: F is the better predictor of how hard forecasting will be, sCV the better description of variability. Use at least a year of data and a time step of a few minutes or more.

Code

The repository gives scv.m and forecastability.m (base MATLAB), a demonstration that writes the figures above, and the article's own scripts, unchanged.

s = scv(I, I_clr);                       % d = 0.2
F = forecastability(I, I_clr, 24, 1);    % hourly data, one hour ahead

MATLAB code and demonstrationRelated: NICE metrics