## 4 Results
### Time Development of a Sample Time Series  
Therefore, especially for the measurement on 19 October 2010, a possible transient behavior of the shape factor was investigated in more detail. The time development of measured data is presented in Table 2.  
The measurements started at 8:44 a.m. when \(s_{p}^{2}\) was high and the turbulence intensity from cup anemometers was low. In the following 7 min, the time series were found to have \(s_{p}^{2}\approx 0\), with the mean velocity and potential temperature of the air remaining constant. Only the turbulence intensity increased from about 4 to about 8%.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Date \& Time**} & \multirow{2}{*}{**Location**} & \(\mathbf{v_{W}}\) & \(\mathbf{Ti}\) & \(\mathbf{Ri}\) & **Boundary** \\  & & & **(m/s)** & **(\%)** & **(-)** & **Layer State** \\ \hline
21 October 2010, 7:56 a.m. & Offshore & 6.6 & 8.2 & \(-0.54\) & Unstable & \\
28 April 2008, 9:35 a.m. & Onshore & 6.1 & 11.9 & \(-0.15\) & Unstable & \\
19 October 2010, 8:57 a.m. & Offshore & 10.8 & 2.2 & \(-0.13\) & Unstable & \\
19 October 2010, 8:44 a.m. & Offshore & 10.2 & 3.1 & \(-0.12\) & Unstable & \\
19 August 2010, 8:13 a.m. & Offshore & 12.7 & 2.8 & \(-0.06\) & Unstable & \\ \hline
25 March 2008, 2:55 p.m. & Onshore & 11.3 & 10.8 & \(-0.03\) & Unstable & \\
29 March 2008, 11:44 a.m. & Onshore & 15.3 & 10.6 & \(-0.01\) & Neutral & \\
30 March 2008, 6:04 p.m. & Onshore & 15.7 & 5.6 & 0.00 & Neutral & \\
28 April 2008, 2:20 p.m. & Onshore & 5.8 & 2.1 & 0.01 & Neutral & \\
1 May 2008, 2:55 a.m. & Onshore & 6.0 & 6.0 & 0.10 & Stable & \\
12 April 2008, 7:24 p.m. & Onshore & 5.2 & 11.0 & 0.28 & Stable & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of selected Atmospheric Boundary Layer (ABL) stability cases: wind speeds (\(v_{W}\)) and turbulence intensities (\(T\)) from cup anemometers, \(Ri\) numbers and estimated ABL states.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Time**} & \multirow{2}{*}{\(\mathbf{\theta}_{air}\)} & \multirow{2}{*}{\(\mathbf{\theta}_{grad}\)} & \(\mathbf{v_{W}}\) & \(\mathbf{Ti}\) & \(\mathbf{Ri}\) & **Boundary** \\  & & & **(K)** & **(m/s)** & **(\%)** & **(-)** & **Layer State** \\ \hline
8:44 a.m. & 283.6 & 286.8 & 10.2 & 3.1 & \(-0.12\) & Unstable & * \\
8:45 a.m. & 283.5 & 286.8 & 10.2 & 3.9 & \(-0.13\) & Unstable & \\
8:47 a.m. & 283.4 & 286.8 & 10.0 & 7.5 & \(-0.14\) & Unstable & \\
8:49 a.m. & 283.4 & 286.8 & 10.1 & 7.3 & \(-0.13\) & Unstable & \\
8:50 a.m. & 283.5 & 286.8 & 9.3 & 6.7 & \(-0.16\) & Unstable & \\
8:52 a.m. & 283.5 & 286.8 & 11.2 & 6.0 & \(-0.11\) & Unstable & \\
8:54 a.m. & 283.5 & 286.8 & 10.8 & 7.7 & \(-0.11\) & Unstable & * \\
8:55 a.m. & 283.2 & 286.8 & 11.2 & 4.2 & \(-0.12\) & Unstable & * \\
8:57 a.m. & 283.1 & 286.8 & 10.8 & 2.2 & \(-0.13\) & Unstable & * \\ \hline \hline \end{tabular}
\end{table}
Table 2: Development of Time Series on October 19. Potential temperatures (\(\theta\)), wind speeds (\(v_{W}\)) and turbulence intensities (\(T\)) from cup anemometers, \(Ri\) numbers, and estimated ABL states.  
At 8:54 a.m., the shape factor began to rise (see also curve (2) of Figure 4). Promptly, the turbulence intensity dropped more than 5.5 percentage points, and also, the potential temperature of the air decreased by 0.4 K with the rising shape factor.  
Our interpretation is summarized as follows: the boundary layer, corresponding to time interval from 8:45 a.m. to 8:49 a.m. was stratified, and turbulent pressure fluctuations were distributed in a Gaussian way. At 8:50 a.m., a cluster of warm air rose up from the warmer sea surface to higher (and colder) regions (\(\theta_{air}\approx\) constant, \(v_{W}\) fluctuating). This may have led to a stronger vertical shear, thereby disturbing the (Gaussian) turbulent structures.