background-wind

General             -            Background on Wind Analysis

Non-Parametric Regressions

In ZeFir, wind regressions are performed by Non-parametric Wind Regression (NWR), and two Sustained Wind Incidence Methods (SWIM). Developed by Henry et al. (2009), this approach couples atmospheric concentrations with measured wind speed and direction, following the equation:

, where Ci, Wi and Yi are the concentration, wind direction and wind speed, respectively, at ti; sigma and h, the smoothing parameters; and K1 and K2, two kernel functions. This equation can be easily simplified as the weighing average of the concentration data at each (theta, v) couple, where the weighing coefficients are calculated through the Kernel functions. The idea is thus to give weight to concentration values that are associated to (Wi, Yi) relatively close to (theta, v). This concept of “relatively close” is endorsed by the smoothing parameters that widen or narrow the Kernel functions. In other words, the closer Wi is to theta, the higher the weighing coefficient will be, giving more weight to the associated concentration Ci. The figure below illustrates the weighing coefficients between (theta - Wi) = {-10;10} and sigma = {1;10}.