![]() ![]() This definition provides a more conservative definition of ITS than the previous one, and is still “data-derived”, i.e. Furthermore, it provides the most consistent assessment of the ITS across different runs, because the shape of the cross-correlation function tends to be pretty consistent and similar to the one shown in the figure, for small values of τ.Ĭross-correlation first crossing 0: The integral is stopped as soon as the cross-correlation function (which always starts at 1 for τ=0) crosses the x-axis. However, it provides the fastest execution and, more importantly, assures that a value of the ITS is virtually always found based on this definition. ![]() This gives the “shortest”, least conservative definition of the ITS. EddyPro provides three possible ways of defining this upper limit:Ĭross-correlation first crossing 1/e: The integral is stopped as soon as the cross-correlation function (which always starts at 1 for τ=0) attains the value of 0.369. ![]() In practical implementations, however, this integral must be stopped at a finite upper limit, which should be defined in such a way that the ITS represents the maximum correlation time of the two time series. The red line in the figure above represents the integral for any given value of the upper limit, which is theoretically set to infinity. The following integral represents the ITS: Normalized cross correlation and integral time scale over time. For τ=0 the cross-correlation function provides the covariance of w and c as τ attains values > 0 the cross-correlation function typically decreases towards values close to zero, representing an increasing non-correlation as τ increases (black line in Figure 6‑13). Where w is the vertical wind component, c is any scalar of interest (e.g., temperature, gas concentration, etc.), t is time and τ is the lag-time between the two time series. The cross-correlation function is given by: Both methods require the preliminary estimation of the Integral Turbulence time-Scale (ITS), which – for our purposes – can be defined as the integral of the cross-correlation function. EddyPro can calculate flux random uncertainty due to sampling errors according to two different methods: Mann and Lenschow (1994) and Finkelstein and Sims (2001). ![]()
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