Surface-level ozone (O₃) continues to be a significant health risk in the Greater Toronto Hamilton Area (GTHA) of Canada even though precursor emissions in the area have decreased significantly over the past two decades. In July 2015, Environment and Climate Change Canada (ECCC) led an intensive field study coincident with Toronto hosting the 2015 Pan American Games. During the field study, the daily 1-h maximum O₃ standard (80 ppbv) was exceeded twice at a measurement site in North Toronto, once on July 12 and again on July 28. In this study, ECCC’s 2.5-km configuration of the Global Environmental Multi-scale (GEM) meteorological model was combined with the Modelling Air-quality and CHemistry (MACH) on-line atmospheric chemistry model and the Town Energy Balance (TEB) urban surface parameterization to create a new urban air quality modelling system. In general, the model results showed that the nested 2.5-km grid-spaced urban air quality model performed better in statistical scores compared to the piloting 10-km grid-spaced GEM-MACH model without TEB. Model analyses were performed with GEM-MACH-TEB for the two exceedance periods. The local meteorology for both cases consisted of light winds with the highest O₃ predictions situated along lake-breeze fronts. For the July 28 case, O₃ production sensitivity analysis along the trajectory of the lake-breeze circulation showed that the region of most efficient O₃ production occurred in the updraft region of the lake-breeze front, as the precursors to O₃ formation underwent vertical mixing. In this updraft region, the ozone production switches from volatile organic compound (VOC)-sensitive to NOx-sensitive, and the local net O₃ production rate reaches a maximum. This transition in the chemical regime is a previously unidentified factor for why O₃ surface-level mixing ratios maximize along the lake-breeze front. For the July 12 case, differences between the model and observed Lake Ontario water temperature and the strength of lake-breeze opposing wind flow play a role in differences in the timing of the lake-breeze, which impacts the predicted location of the O₃ maximum north of Toronto.

The sensitivities of meteorological and chemical predictions to urban effects over four major North American cities are investigated using the high-resolution (2.5-km) Environment and Climate Change Canada’s air quality model with the Town Energy Balance (TEB) scheme. Comparisons between the model simulation results with and without the TEB effect show that urbanization has great impacts on surface heat fluxes, vertical diffusivity, air temperature, humidity, atmospheric boundary layer height, land-lake circulation, air pollutants concentrations and Air Quality Health Index. The impacts have strong diurnal variabilities, and are very different in summer and winter. While the diurnal variations of the impacts share some similarities over each city, the magnitudes can be very different. The underlying mechanisms of the impacts are investigated. The TEB impacts on the predictions of meteorological and air pollutants over Toronto are evaluated against ground-based observations. The results show that the TEB scheme leads to a great improvement in biases and root-mean-square deviations in temperature and humidity predictions in downtown, uptown and suburban areas in the early morning and nighttime. The scheme also leads to a big improvement of predictions of NO${}_x$, PM${}_{2.5}$ and ground-level ozone in the downtown, uptown and industrial areas in the early morning and nighttime.

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Motivated by the boundary contributions to the wave-activity invariants and stability theorems of a class of Salmon’s L₁-like Hamiltonian balance models, Arnold’s method is applied in this work to derive finite-amplitude wave-activity invariants and corresponding stability theorems for shallow water semigeostrophic (SWSG) dynamics. It is shown that the Jacobian term in the potential vorticity of the SWSG model affects the stability properties in two ways: it generates stability constraints in the interior, and it makes the stability condition of cyclonic shear of basic flow at boundaries inescapable even when Ripa’s “subsonic” condition is satisfied in the interior. The latter effect makes the stability properties of the SWSG model different from those of the L₁-like Hamiltonian balance models for which the condition of cyclonic shear of basic flow on the boundaries is not necessary when Ripa’s “subsonic” condition is satisfied. The physical reason for this difference is given and the implications of the stability theorems are discussed.

A 1-D diffusion model of temperature is employed to understand important features of temperature response to the changes of surface heat flux (SHF) and vertical diffusivity shown in 3-D model simulations. Analytical results show that the temperature response to the SHF change is the convolution of the SHF change and Green’s function (GF). Because the GF is inversely proportional to the square root of diffusion coefficient near the surface, weak/strong diffusivity in the early morning/noontime tends to generate a large/small temperature response by slowing/accelerating heat flow from surface to the atmosphere. The modulation effect of the GF and the convolution effect explain very different temperature responses to the SHF change during each period. Analytical results also show that the temperature response to the change of DF is equal to the convolution of the product of diffusion coefficient change, vertical gradients of reference temperature and the GF. Because the vertical gradient of the GF is negative below 80 m, enhanced/reduced diffusivity would enhance/weaken the urban temperature, if the vertical gradient of reference temperature is negative/positive. Numerical results with typical values of the changes of SHF and diffusivity suggest that the changes of SHF has the dominant contribution to the temperature response.