# Quantification and Correction of Wave-Induced Turbulence Intensity Bias for a Floating LIDAR System
## 4 Results and Discussion
### Theoretical Impact of Buoy Movements on the FLS Horizontal Velocity Estimates
#### 4.3.2 Model-Based Correction of Turbulence Intensity Measurements  
The model presented in Section 3.1 is applied to the experimental data in order to estimate the atmospheric turbulence from the floating LIDAR and the IMU. The gyroscopic and translational data are linearly interpolated to fit the 10 Hz discretization defined in the model. The initial measurement beam is defined in the North direction of the LIDAR, by default.  
Figure 15 shows the linear regression of the uncorrected and corrected turbulence intensity estimates for the entire 10-min data set evaluated during the 13 weeks of experimental data. At elevation 94.4 m (Figure 15a,b), the regression lines on the non-normalized data follow the equations: \(y_{uncorrected}=0.997x+0.032,\ R^{2}=0.673\) and \(y_{corrected}=1.006x+0.005,\ R^{2}=0.731\). The model compensates most of the mean bias introduced by wave motion: the slope of the curve changes little, but the value at the origin shifts from 0.032 without correction to 0.005 with correction. The dispersion of the data points is also impacted, it shifts from 0.673 without correction to 0.731 with the correction. At elevation 134.4 m (Figure 15c,d), the regression lines on the non-normalized data follow the equations: \(y_{uncorrected}=0.991x+0.033,\ R^{2}=0.692\) and \(y_{corrected}=0.993x+0.008,\ R^{2}=0.74\). The trend is similar to altitude 94.4 m, but the average bias of the corrected measurement is slightly larger for elevation 134.4 m.  
We note that the number of data is affected by the use of the model. The correction acts as a filter in the case of a negative motion-induced variance calculated by Equation (21). This situation occurs for 10-min samples lacking consistency between IMU and LIDAR  
Figure 15: Linear regression of the 10-min turbulence intensity measurement from the uncorrected and corrected floating LIDAR with respect to the fixed LIDAR measurement at two altitudes: 94.4 m and 134.4 m. All ticks are normalized by the fixed LIDAR’s mean TI from all the 10-min samples. (**a,c**) Raw floating LIDAR measurement at the two evaluated altitudes. (**b,d**) Floating LIDAR measurement corrected by the model at the two evaluated altitudes.  
measurements and/or not meeting model assumptions. From the 13 weeks of data selected, about 33% of the data are filtered out by the model (1738/5223 at altitude 94.4 m).  
Figure 16 shows the effect of the model-based correction on the time series of the harshest week (from 06/24/18 to 07/01/18). Without correction, we observe a large variation in the error of the floating LIDAR turbulence intensity measurement in a day, which is related to the variation of the wave period. The estimation of atmospheric turbulence by the model allows us to correct most of 10-min measurements. However, some corrected data still strongly overestimate the turbulence intensity (Figure 16b). As these points are mostly isolated, a peak filter can be easily applied to discard them and improve the performance of the correction. In particular, we draw the reader's attention to the filter presented by [PERSON] et al. [25], which removes the removal of isolated peaks.