A REGULARIZED SPATIO-TEMPORAL MODELING FRAMEWORK FOR URBAN LAND-USE TRANSITION AND GROWTH-RATE PREDICTION ALONG THE EASTERN BYPASS CORRIDOR, NAIROBI, KENYA

Rapid road-infrastructure expansion in sub-Saharan African cities is reshaping peri-urban land at a pace that conventional planning instruments struggle to anticipate. The Eastern Bypass in Nairobi, Kenya, is a paradigmatic corridor where a single arterial investment has triggered sustained conversion of vegetation and bare land into built-up surfaces. This study develops and validates a regularized spatio-temporal modelling framework that couples a machine-learning suitability engine with a Cellular Automata–Markov (CA–Markov) allocation mechanism and an impedance-based regularization surface to jointly predict land-use transition and built-up growth rate along the corridor. Classified Landsat-derived land-cover maps for 2009, 2015 and 2021 were harmonized to a common 400 × 1200 raster grid and reduced to three thematic classes (vegetation, bare land, built-up). A bagged tree-ensemble classifier was trained on distance-to-built, distance-to-road and neighbourhood-density predictors to estimate development suitability, which was then constrained by a physically interpretable impedance surface penalizing road-remote, isolated and sprawl-prone cells. Multi-temporal Markov transition matrices were combined with matrix-logarithm projection to forecast the 2032 land-cover state, with growth quantity moderated by the mean corridor resistance. The regularized model reproduced the observed 2021 land cover with an overall accuracy of 99.8% and a Kappa coefficient of 0.986; because the calibrated model retains the established landscape and introduces only a disciplined growth increment, these agreement statistics are interpreted as evidence of spatial consistency and allocation discipline rather than out-of-sample generalization. The suitability classifier achieved an in-sample area under the receiver-operating-characteristic curve (AUC) of 1.00. Built-up area increased from 4,927 cells in 2009 to 5,662 cells in 2021, and is projected to reach approximately 6,001 cells by 2032. The annualized built-up growth rate declined from 43.78% per year (2009–2015) to 10.38% per year (2015–2021), and is projected to stabilize at roughly 0.54% per year under impedance regularization, signalling a transition from explosive frontier growth toward consolidation and infill. The results demonstrate that road corridors impose strong, spatially heterogeneous controls on urban expansion and that regularized spatio-temporal models can translate these controls into planning-relevant forecasts. We recommend that corridor-development control, infill-oriented zoning and green-space protection be embedded in Nairobi metropolitan planning to manage the consolidation phase the model anticipates.