PhD Thesis, 2007 - University College Cork

Chapter 3
Materials and Methods
assumption that the evolution of position and velocity of a fluid element is
described by a Markov process (Hsieh et al., 2000), thus a random process
whose future probabilities are determined by its most recent values. The
weakness of the Lagrangian-stochastic approach is the need for relatively
detailed knowledge of turbulent flow characteristics (Sogachev & Lloyd, 2004).
These footprint models are generally much less used than Eulerian models
because of their high computational requirements. Examples of these models
were developed by Hsieh et al. (1997), Flesch (1996) and Leclerc and Thurtell
(1990).
- Large eddy simulation (LES) approach. These models can simulate the
turbulence statistics and the scalar concentration field under any given
conditions (Sogachev & Lloyd, 2004). The LES models are free of a predescribed
turbulence field and can also cope with horizontal inhomogeneity,
but are computationally expensive and limited to relatively simple flow
conditions by a number of grid points in the flow simulation. This approach is a
trade-off between the level of complexity of the model and computational
expense using a closure model of suitable order (Vesala et al., 2004).
For our footprint analysis we used an eulerian analytical model developed by Hsieh
et al. (2000) (Chapter 5 and 6, Appendix 1 and 2). This model is based on a
combination of Lagrangian stochastic dispersion model results and dimensional
analysis. The main advantage of this model is its ability to analytically relate
atmospheric stability, measurement height and surface roughness length to flux and
footprint. The model by Hsieh et al. (2000) estimates the location of the peak and
of the length of the positive skew distribution curve that defines the footprint. A
cut-off at 67 % of the footprint length was used to filter fluxes originating from
outside the pristine part of the bog (see 3.4.4, Chapter 6, Appendix 1). Furthermore
the definition of the 67 % of the footprint length was used as a cut-off point for the
upscale of chamber measurements to the EC footprint with the aim of comparing
CO 2 fluxes measured with the EC and chamber techniques (Appendix 3).
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