When weather changes a courtyard comparison

A small advantage is not a stable ranking.

For 100 m² floors and 5 m walls, the north–south 4:1 courtyard has slightly greater aggregate winter transmission than the square: +0.25 percentage points with SARAH3 and +1.24 with ERA5. Its advantage occurs in 14 of 18 SARAH3 winters and all 18 ERA5 winters.

Courtyard	PVGIS-SARAH3	PVGIS-ERA5
Square · 0°	29.76%	27.35%
4:1 · north–south	30.01%	28.59%
4:1 · east–west	14.83%	11.44%

Winter means contiguous December–February seasons labelled 2006–2023. Values are ratios of exposure sums under the primary isotropic-sky model. They are calculated transmission fractions, not measurements of courtyard performance.

Winter elongated-minus-square differences change sign in SARAH3 and remain positive in ERA5. — At 5 m height, SARAH3 paired differences range from −0.90 to +0.91 percentage points; ERA5 ranges from +0.71 to +1.68. These are descriptive year ranges. Download figure (SVG)

Winter and summer transmission for a square and north–south and east–west elongated courtyards, by radiation product. — Turning the elongated plan changes the seasonal pattern. The complete release also includes aspect ratio 2, 45° bearings and 2.5 and 7.5 m walls. Download figure (SVG)

External forcing, explicit provenance.

The study uses the European Commission Joint Research Centre’s PVGIS 5.3 SARAH3 satellite-derived and ERA5 reanalysis-derived radiation products at 32.3°N, 36.2°E, a model point near Mafraq, Jordan. The coordinate identifies the calculation, not a field station or institutional address.

Each product supplies 166,536 hourly records for the shared 2005–2023 period. Source timestamps, direct and diffuse components, provider flags, requests and original response hashes are retained. ABLAQ conducted the analysis in October 2026; the historical forcing was produced by the cited data providers.

All hourly labels are present, including leap days. This establishes temporal coverage, not the physical accuracy of every value. The products remain separate throughout the analysis; their disagreement is not a statistical confidence interval.

Data quality is part of the result

We identified 424 unflagged SARAH3 zero-radiation records across 220 UTC dates while the calculated sun exceeded 10° elevation. The primary calculation retains these values. A diagnostic removes the same affected dates from both products; the selected aggregate winter differences still round to +0.25 and +1.24 percentage points. The original records are not imputed or silently corrected.

This quality screen was added after data inspection. Its definition and the affected dates are recorded in the protocol and verification files.

Methods and comparison design.

The prescribed study holds floor area at 100 m² and varies three aspect ratios (1, 2, 4), three wall heights (2.5, 5, 7.5 m) and three bearings (0°, 45°, 90° clockwise from north). All 27 combinations are published. Annual and summer summaries cover 19 years; winter includes 18 complete cross-year seasons.

Solar direction comes from pvlib’s implementation of the NREL Solar Position Algorithm using geometric elevation. For each direction, an analytical shadow-overlap model determines the sunlit floor fraction f. The established rectangular view factor F₀ supplies the isotropic diffuse component.

T = Σ(B f + D F₀) / Σ(B + D)

B and D are horizontal direct and diffuse irradiance. The same hourly weight appears in numerator and denominator. Because the beam input is already horizontal, it receives no additional cosine factor.

Respecting the time convention

SARAH3 values are instantaneous samples at minute 09 in the captured responses. ERA5 values are hourly averages centred at minute 30. For ERA5, we integrate shading within the hour with cosine weighting under constant within-hour direct normal irradiance, preserving the supplied horizontal beam total. A five-minute versus 2.5-minute repeat tests numerical convergence.

Uniform opaque walls, a horizontal floor and an unobstructed opening define the system. Terrain, neighbouring buildings and reflections are excluded. The source, equations and complete parameter tables make these assumptions inspectable.

Testing the assumptions behind the ranking.

A prescribed zenith-weighted diffuse sky changes the small aggregate SARAH3 winter advantage to −0.03 percentage points; the corresponding ERA5 comparison remains positive. This is sensitivity to the modelled angular distribution, not a claim that either sky profile describes the site.

Winter ranking under horizon-weighted, isotropic and zenith-weighted sky distributions. SARAH3 crosses zero at the zenith-weighted scenario. — All profiles preserve the same horizontal diffuse exposure. L(α) is proportional to 1 + q sin(α), with q = −0.8, 0 or 2; the model has no circumsolar or azimuthal sky structure. Download figure (SVG)

Across the 2023 diagnostics, five-minute versus 2.5-minute integration changes total transmission by at most 0.00072 percentage points. Point sampling versus interval averaging changes it by up to 0.556 points, while the alternative NOAA solar-position approximation changes it by up to 0.240 points. Numerical convergence, time representation and physical model uncertainty are different questions.

Reproduced results and separate calculations.

A fresh process reproduced all computational outputs byte for byte. A separately implemented audit, which does not import the primary study code, uses polygon clipping and scalar accumulation to check six complete 2023 source–geometry combinations. Its largest transmission difference is below 5 × 10⁻¹³.

The study additionally compares 1,000 analytical and polygon geometries, two diffuse-sky integral formulations, all 3,024 seasonal energy identities and 162 aggregate rows. The separate audit shares pvlib’s astronomical library. These are internal numerical checks, not external peer review or independent replication by another researcher.

What this evidence supports.

The research extends seasonal solar geometry and direct–diffuse mixture analysis with historical external forcing. It shows why a direct-sunlight advantage should not be generalized to combined exposure without testing its margin, variability and sky assumptions.

The contribution is the reproducible comparison and robustness analysis using established physics. One model point and two gridded forcing products do not establish performance across Jordan. No courtyard measurements calibrate or validate the results. Wall reflections, sky anisotropy beyond the prescribed profiles, subhourly cloud variation, occupancy and thermal processes can change practical interpretation.

The report does not predict measured cooling, energy savings or comfort and does not select a universally optimal courtyard. The complete tables retain cases beyond the illustrated contrast.

Read, inspect and reproduce.

The complete package contains the original compressed forcing responses, acquisition receipts, pinned dependencies, primary source, separate verifier, reference results and reproduction instructions. Scientific calculations run locally and make no network requests.

Tested with Python 3.14.7 and the published dependency versions. Original ABLAQ code, calculated data and figures use CC0 1.0; external forcing and third-party software retain their source terms. Read the reuse and attribution terms.

Sources and methodological references.

Scientific responsibility.

Institutional author and publisher: ABLAQ Studios. Osama Khaled Ahmed Abdel-Qader, Scientific Research Lead and Founder & CEO, directs the research programme and its scientific decisions, interpretation, publication and corrections. His research remit connects this investigation to that accountability.

AI-assisted computational tools supported implementation, checks and documentation, as described in Methods. Scientific correspondence and corrections: osama.khaled@ablaqstudios.com.

ABLAQ Studios (2026). When weather changes a courtyard comparison. ABLAQ-R05, version 1.0.0. Download citation (BibTeX).