**
Optimization of a measurement procedure using an uncertainty model
**

Richard Kranenburg

Supervisor: Kees Vuik

Site of the project:

TNO Bouw en Ondergrond

Princetonplein 9

3584 CC Utrecht

start of the project:
September 2009

In January 2010 the
Interim Thesis has been appeared
and a
presentation has been given.

The Master project has been finished in May 2010
by the completion of the
Masters Thesis
and a final presentation has been given.
For working address etc. we refer to our
alumnipage.

**Summary of the master project:**

The description of the model uncertainty gives a quantification of the
expected difference between the model and the measurements. Averaged over the
year this description is in accordance with the measured differences.
Since the accuracy of the measurements is high the observed difference
can be attributed to uncertainties in the model.

As a practical application it is possible to give for every modelling result
an interval such that the concentrations are in this interval with a certain
probility, for instance a 1-sigma interval.
At certain time steps the model can be outside this interval. Sometimes
the size of the interval is large. In such a case the extra information
of this interval is limited.

The first aim of the master thesis work is to develop a method where at each
time step the uncertainty interval is as small as possible. Since the model
is cheap to compute and only a small number of parameters is involved
a Kalman filter is a good choice to achieve this.

The second aim it to apply the developed Kalman filter in order to answer
questions about the measurement procedure. The main question is: which
measurements reduces the uncertainty interval the most?

For all experiments we expect that the stochastic model
should be adapted or enhanced. For this reason it is important to start
as soon as possible with realistic applications.

Expected yearly averaged concentration NO2 (ug/m3) in the
Rijnmond area for 2006

Expected concentration NOx (green) and 2-sigma accuracy interval (blue)
for the concentration NOx for the first week in 2006 in measuring point
Overschie (measurements in red). Aim of the master thesis project
is to make the accuracy interval as small as possible
## Contact information:
Kees
Vuik

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