Parametric Reduced-Order Modeling of Urban Boundary-Layer Dynamics via Streaming DMD and Manifold Interpolation

  • Kuznetsov, Konstantin (GRASP Earth)
  • Dubovik, Oleg (GRASP Earth)
  • Litvinov, Pavel (GRASP Earth)
  • Alekseenko, Elena (Universit\'e du Littoral C\^ote d'Opale)

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Urban boundary-layer (UBL) dynamics over real cities are strongly controlled by heterogeneous roughness, thermal forcing and street-scale geometry. High-resolution CFD can resolve these effects but remains too expensive for real-time use and for parameter sweeps required by digital-twin and data-assimilation workflows. We present a parametric reduced-order model (pROM) for fast prediction of transient UBL fields over a complex urban domain, built from a database of CFD simulations over central Paris. The CFD setup uses an automatically generated terrain-following Cartesian mesh with building cut-cells and land-use dependent wall functions, and is driven by time-dependent Monin--Obukhov similarity boundary conditions. During the CFD runs, we compute a low-rank surrogate on the fly using Streaming Dynamic Mode Decomposition (sDMD), avoiding storage of full snapshot matrices and enabling scalable processing of large meshes. In the online stage, we predict new atmospheric regimes by interpolating reduced Koopman operators and modal subspaces across a four-dimensional parameter space (wind direction, wind speed, stability length and temperature). We compare two interpolation strategies: element-wise radial basis function interpolation of the reduced operator and manifold interpolation on Grassmann/Stiefel manifolds for subspace-consistent blending. Validation on unseen wind directions shows that operator interpolation yields velocity-field errors below 9\%, while manifold interpolation reduces errors below 4\% and remains stable for prediction horizons longer than the training window. The resulting pROM provides orders-of-magnitude speedup over CFD while retaining physically consistent UBL dynamics, offering a practical path toward urban-scale digital twins.