Spatiotemporal variability of solar radiations within an urban context: a characterisation by means of Principal Component Analysis

In a society where a substantial part of the global energy yield is being directly expended at the city scale, urban areas appear as serious candidates for the production of solar energy. The high occurence of diverse obstacles like buildings, vegetated elements and other urban infrastructures creates an aggregation of countless singular geometries with diverse morphological characteristics and material optical properties. This inherently causes important disruptions to incident solar radiations, adding on their natural variability brought about by the site specificities and diurnal/seasonal cycles. The field of irradiance received by a specific urban region (e.g. façade, building, district) may thus rapidly become the result of complex miscellaneous interactions between many degrees of freedom. In the presence of such high-dimensional phenomena expanding across a wide range of spatial and temporal scales, specific methods can be used to appreciate their global dynamics. Especially, Principal Component Analysis (PCA) has been widely adopted and validated in this context. PCA indeed decomposes the covariance of fluctuations in the original multivariate signal, and come up with a new set of uncorrelated features being linear combinations of initial variables. Their corresponding modes of variation now define a new basis of orthonormal features for the original signal pointing in the direction of its main variations, i.e. capturing most energy in the dataset. An approach is proposed here for analysing the variations in space and time of the solar resource within an urban context by means of PCA. A parametric investigation is conducted on a set of theoretical 100 m × 100 m urban districts, defined as homogeneous arrangements of cuboid-like buildings, with various typological indicators (Total Site Coverage, Global Aspect Ratio) and surface materials (Lambertian, highly-specular) at a typical mid-high latitude. For each configuration, the shortwave radiative flux density on the facets of the central building is modelled via backwards Monte-Carlo ray tracing [1] over a full year and under clear sky conditions, with a 15 min timestep and 1 m spatial resolution. PCA is subsequently applied to the simulated radiative fields to extract dominant modes of variation. First results validate energy-based orthogonal decompositions like PCA as efficient tools for characterising the variability distribution of multivariate phenomena in this context [2]. The issued separate representation of space and time variables allows for their independent examination, helping the identification of district areas subjected to important spatial and temporal variations of the solar resource. Characteristic time scales are clearly represented across successive orders of decomposition. Information about the district morphology is also obtained, with the contribution of surrounding geometries being portrayed by specific spatial modes. Similar prevalent variables are further repetitively encountered across multiple evaluated surfaces, but at different modal ranks. [1] Caliot, C., Schoetter, R., Forest, V., Eymet, V. and Chung, T., (2022). Model of Spectral and Directional Radiative Transfer in Complex Urban Canopies with Participating Atmospheres, Boundary-Layer Meteorology. [2] Le Gall, G., Thebault, M., Caliot, C. and Ramousse, J., (2023). Principal Component Analysis for the characterisation of spatiotemporal variations of the solar resource in urban environments. In: Proceedings of the 17th International Heat Transfer Conference IHTC-17, Cape Town, South Africa, 14–18 August, Begell House Inc.

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