A Lagrangian Stochastic Urban Footprint Model: Model Development and Evaluation

Built terrains, with their complexity in morphology, high heterogeneity, and anthropogenic impact, present substantial challenges in earth system modelling. In particular, the estimate of the source areas of atmospheric measurements in cities, i.e. the footprints, requires realistic representation of the landscape characteristics and physics of flow in urban areas, and has hitherto been heavily relied on large eddy simulations. In this study, we developed a physical parameterization scheme for estimating urban footprints based on the backward Lagrangian stochastic algorithm. A single layer street canyon geometry was used to represent the built environment, which can be readily incorporated into commonly used urban climate models such as the Weather Research and Forecasting model. The vertical profile of mean streamwise wind velocity is parameterized for the urban canopy and boundary layers. Comparisons against experimental observations show that the footprints estimated using the proposed model over homogeneous surfaces are in good agreement with those from the analytical model, under various stability conditions. The proposed model was then applied for case study with different scenarios of urban characteristics. Results show that roofs are the main contributor to the footprint when the sensing instrument is located above the canopy layer. Inside the canyon, windward walls contribute more to footprints as compared to leeward walls under unstable and neutral conditions, while the opposite holds under stable conditions. Increased canyon aspect ratio tends to separate flows inside the street canyon, form isolated vortices, and enhance the footprint contribution of roofs and walls. Owing to the isolated vortices, the canyon becomes the main source area of the measurement when the sensor is inside the canyon. The proposed model provides a useful numerical framework with combined computational efficiency and realistic urban representation for estimating concentration and flux footprints of atmospheric measurements in the built environment. With the potential of coupling with climate models, it can be predictive and provide insight into future changes of urban microclimate.