Loading...

Loading...

Loading...

Loading...

Observation equation: $$y_t = \alpha_t + \beta X_t + \epsilon_t$$ State equation: $$\alpha_t = \alpha_{t-1} + \eta_t$$ Where:

- \(y_t\) = observed data of the outcome
- \(\alpha_t\) = the underlying trend: part 1 of the state
- \(\beta\) = regression coefficients for the external covariates: part 2 of the state
- \(X_t\) = observed data of the external covariates
- \(\epsilon_t\) = error unexplained by the model, assumed to follow a constant variance \(\Sigma_\epsilon\)
- \(\eta_t\) = how much the trend can update each time-step on a random walk, assumed to follow a constant variance \(\Sigma_\eta\). NB: \(\beta\) can be included here so that the regression coefficients are time-varying, but this is not used in this model

- \(y_t\) = measured NO2
- \(\alpha_t\) = underlying detrended NO2
- \(X_t\) = meteorological measurements and temporal variables
- \(\beta\) = coefficients for meteorological and temporal factors
- \(\epsilon_t\) = error unexplained by the model
- \(\eta_t\) = how much the NO2 detrended series can update each day (on a random walk)

Furthermore, a log transform is applied to the outcome in order to help stabilize the variance (NO2 exhibits right skew), and to enforce positivity.

This website contains live dashboards to monitor the impact of Clean Air Zones (CAZ) on NO2 concentrations in multiple cities in the UK. It has been developed by researchers at the Wolfson Atmospheric Chemistry Laboratories at the University of York as part of a research project into techniques for identifying local changes in NO2 emissions arising from policy changes. The dashboard was setup prior to the introduction of CAZs in two UK cities: Newcastle (30th January 2023) and Sheffield (27th February 2023), providing a real-time online estimate of the CAZ's effectiveness. This provides a more realistic estimate of how much information can be gleamed in real-time, rather than a post-hoc study once a significant duration has passed with the benefit of hindsight. However, it also means there is additional uncertainty in the estimates, both due to the limited information contained in the data, but also due teething issues being identified in the methodology itself. As such, the following disclaimer is provided on each dashboard as a reminder that this is a work-in-progress and the estimates should not be used as-is without thoroughly understanding the limitations of the approach.

Disclaimer: the estimates shown here are not validated and are still undergoing active research, as such they should not be treated as definitive and should be viewed with caution.A modelling based approach is used to extract changes in the underlying NO2 concentrations, free of confounding factors such as the local meteorology and seasonal factors. The resulting detrended series is used to identify the changes since the intervention took place. See the Methodology tab for full details of the modelling.

`stuart.lacy`

at `york.ac.uk`

if you have any questions or would like to discuss this work.
The source code for both the state-space modelling and the Shiny web-app are publicly available on GitHub: https://github.com/wacl-york/ncaz