Research project AS/DD/09 (Research action AS)
1. Context
Air quality depends on many factors linked to emissions, topography and, above all, weather conditions and the chemical reaction that take place in the lower atmosphere (troposphere). Forecasting this quality and episodes of pollution is a complex operation. SMOGSTOP can do such forecasting for tropospheric ozone in the summertime. This model, which has been operational at CELINE/IRCEL since 1995, requires daily inputs of information about the meteorological situations to come but also the most recent measurements of the pollutants involved in ozone production. These measurements come from Belgium’s three regional air quality surveillance networks.
Improvements can be made upstream (meteorological and pollution inputs) and downstream from the model itself through the spatial and temporal representation of the predicted events. While SMOGSTOP’s graphic outputs make phenomena easy to understand by showing the localised or global nature of the event being monitored, the input data are prerequisites without which the model cannot predict changes in the ozone concentration over a two-day period.
2. Aims
The idea is to construct a programming module to determine the concentrations at all points other than the reference points based solely on values measured by sensors or calculated by the model. This interpolation step (passage through the reference points as opposed to smoothing, which places the curve in the neighbourhood of the reference points) will yield the closest fit to an actual continuum that is described only by points. The quality of the pollution field’s reproduction depends not only on the reference points’ spatial distribution, but also on the mathematical tool used to reshape necessarily continuous reality.
3. Users
Since the results of this study will be software that can be run on all PCs, all scientists who are interested in the problem of interpolating data across Belgium will be able to use it gainfully. However, some of the control parameters in this first version have been set according to CELINE/IRCEL’s databank. A later version will allow more general applications of the software.
Methods
The interpolation methods that were examined and chosen for scalar values revolve around four major methods, as follows:
1) Distance weighting using such specific methods as inverse distance weighting, Cresman’s method, Thiébaux-Pedder’s method, and Sasaki-Barnes’ method.
2) Methods based on Delaunay triangulation. These methods construct a global surface from interconnected elementary surfaces that passes through all of the reference points whilst simultaneously ensuring the derivatives zero-order continuity for linear interpolation, first-order continuity for quadratic interpolation, and second-order continuity for cubic interpolation (called Akima’s method).
3) The thin plate spline function method. Unlike the previous method, this method does not require partitioning the area of interest into triangles. It searches directly for a function that goes through all of the reference points and is subject to a general constraint instead of having to satisfy local conditions of continuity.
4) Kriging. This method relies on the spatial correlation of the information that is attached to the reference points. A large part of the method entails defining this structure explicitly by means of the varigram concept. Once this spatial structurality has been modelled, Kriging per se consists in searching for the minimal variance of error at each estimation point.
All of these interpolation methods were developed in a computer application written in Visual C++. They can be accessed by reading two files, one defining the measuring points or points corresponding to the results generated by a model and the other containing the measured or calculated concentrations for a study period set beforehand.
