Modal decomposition for the analysis of solar radiation variability in urban areas

The morphological heterogeneity of three-dimensional structures largely contributes to causing significant variations in the solar radiative flux density received by a specific intra-urban region, resulting in a multi-dimensional signal expanding across a wide range of spatial and temporal scales. This paper presents a unique approach for analysing the spatiotemporal variability of the irradiance field in an urban context by means of modal decomposition. A parametric investigation is conducted on a set of mid-high latitude districts, defined as homogeneous arrangements of cuboids with grey opaque Lambertian materials. Changes in the buildings density (total site coverage $\kappa$) and average height (global aspect ratio $H^{\ast }$) are investigated. For each configuration, the annual shortwave radiative flux density on the envelope of the central building is obtained with a backwards Monte Carlo method under clear sky conditions. Simulated fields are preprocessed to account for urban-only effects and decomposed in their eigenbases of variation using Principal Component Analysis (PCA). Results demonstrate the potential of modal decomposition like PCA for apprehending the separate variability of urban irradiance in both space and time, paving the way for the classification of district regions prone to specific variations of the solar resource. Characteristic temporal frequency bands are represented by successive modes, pointing out annual and daily periods of high variability. Related spatial disruptions to the global irradiance field from urban geometries are portrayed, informing about dominant morphological specificities. Changes in the diffuse radiation component depicted by prevalent modes are further distinguished from the blocking of direct radiation by urban obstacles portrayed by subsequent less-impactful eigencomponents.