ARTU: a second-order solar reference, worked example

Worked example / Exemple chiffré. All input values below are fictitious teaching values, not observations or results from the cited paper.

Result: the published lookup table gives K = -0.03 and α = 0.81 for the illustrative correlations below. The resulting forecast is 496.628 W/m².

Begin with the right variable

Here κ(t) = GHI(t)/CS(t) is a dimensionless clear-sky ratio. It is distinct from the additive clear-sky gap used in some course examples. Near night and twilight, a ratio needs the safeguards specified by the algorithm.

Read the coefficients, then calculate

  1. Choose training-only correlations ρ₁ = 0.80 at lag h and ρ₂ = 0.65 at lag 2h. These are fictitious inputs.
  2. Choose the source table R0.05.mat (R = 0.05). At this exact grid node, row 37 and column 34 in MATLAB’s one-based indexing, res_K = −0.03 and res_a = 0.81. No interpolation is needed here.
  3. Form S = α + K = 0.78 and P = αK = −0.0243.
  4. Take κ(t) = 0.60, κ(t−h) = 0.65 and historical mean κ̄ = 0.70.
  5. Compute κ̂ = Sκ(t) − Pκ(t−h) + (1+P−S)κ̄ = 0.468 + 0.015795 + 0.136990 = 0.620785.
  6. With future clear sky CS(t+h) = 800 W/m², multiply κ̂ by 800 to obtain 496.628 W/m². A cap β = 1.2 is inactive in this example.

Compare meaningful references

For this same clear-sky value, ratio persistence gives 0.60 × 800 = 480 W/m²; climatology gives 0.70 × 800 = 560 W/m². Without a future observation, none can be declared more accurate.

What this study contributes

The benchmark study introduces ARTU as a second-order reference alongside simpler baselines. ARTU’s table-based parameters must not be confused with fitting an arbitrary two-lag AR model by least squares.

Reproduce and check the limits

Download K_alpha.zip, load R0.05.mat and inspect res_K(37,34) and res_a(37,34). The source PDF, Algorithm 5, specifies the update and preprocessing. The current K_alpha.m function takes an argument named Q but tests R internally; check that variable mismatch before running the wrapper. This example reads the table directly and does not modify the repository. Do not silently extrapolate beyond the table or use future observations for correlations.

Source repository, tables and Algorithm 5

À retenir : ARTU utilise deux corrélations et une table de coefficients. Cet exemple suit la table publiée ; il ne s’agit pas d’un AR(2) ajusté librement.

Authors, source and citation

Cyril Voyant, Gilles Notton, Jean-Laurent Duchaud, Luis Antonio García Gutiérrez, Jamie M. Bright, Dazhi Yang. Benchmarks for solar radiation time series forecasting. Renewable Energy. doi:10.1016/j.renene.2022.04.065.

Cyril Voyant wrote this teaching page. The method belongs to the complete author team credited above.

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