A Re-Evaluation of Long-Term Flux Measurement Techniques Part II: Coordinate Systems

To convert measurements of windspeed, eddy flux and scalar concentration into estimates of surface scalar exchange, we implicitly or explicitly assimilate the measurements into mathematical statements of the mass balance in a control volume on a representative patch of the surface. The form of this statement depends on the coordinate system in which it is written and the coordinate system should be chosen so that measurements can be used optimally. This requirement imposes a set of conditions on the coordinates. Here we perform a comparative analysis of some candidate coordinate systems, concentrating on the Cartesian and physical streamline systems. We show that over gentle topography there are definite advantages in working in streamline coordinates. Transforming measurements of vector and tensor quantities measured in the reference frame, s_i, of the anemometer into the reference frame, e_i, of the chosen coordinate system involves using the measured statistics of the wind field to define three Euler rotation angles. We compare the method in most common use, which employs the components of the mean wind vector and the Reynolds stress tensor to define these angles, with the more recent planar-fit method that uses instead an ensemble of mean wind vectors to define the rotations. We find that, in real flows, the standard method has a previously unrecognized closure problem that ensures that the third rotation angle defined using the stress tensor or scalar flux vector will always be in error and often give unphysical results. An alternative procedure is recommended. Finally, the relationships between measurements and model outputs are discussed.