## 4 Discussion  
The previous figures present a strong relationship between the mean temperature difference, wind speed, and \(C_{n}^{2}\) values for both measured data and NAVSLaM estimates. Again, this trend is expected from Monin-Obukhov similarity theory upon which NAVSLaM is based upon and is confirmed from the actual turbulence results derived from the sonic measurements. Figure 6 shows the data points collected and estimated for the entire time period of the experiment and is provided to further explore this relationship. The top two plots of Figure 6 display the NAVSLaM log(\(C_{n}^{2}\)) estimates versus the mean air temperature difference between the upper and lower CSAT3 locations. The bottom two plots show the CSAT3 sonic anemometer log(\(C_{n}^{2}\)) values at each level versus the mean temperature difference. The color of the dots corresponds to the wind speed associated with each data point, as indicated by the color bar to the right of each plot. The two upper plots have log\(\left(C_{n}^{2}\right)\) estimates that range from \(-17\) to \(-11\) and are compared against the CSAT3 sonic measurements which range from \(-16\) to \(-12\). Again, we see that NAVSLaM tends to underestimate log\(\left(C_{n}^{2}\right)\) values relative to the sonics as the mean temperature difference approaches zero shown in the first two plots. Both the NAVSLaM estimates and CSAT3-derived values indicate that for unstable conditions, an increase in wind speed reduces \(C_{n}^{2}\), while the opposite is true for stable conditions. However, these trends are more prominent in the NAVSLaM results. The largest of the log\(\left(C_{n}^{2}\right)\) values are seen at the lower levels displayed in the top left and bottom left plots. We can attribute this to the sensor's proximity to the surface. It is also interesting to note the two separate curves seen in stable conditions of the NAVSLaM estimates. Previous research has attributed this occurrence to affects that relative humidity have on \(C_{n}^{2}\) values [1]. This was not investigated during this experiment, but allows the opportunity for future work to analyze this relationship more thoroughly.  
To gain a better understanding of how well NAVSLaM \(C_{n}^{2}\) estimates agree with the CSAT3 sonic anemometer measurements, we displayed the difference in these values against the mean temperature difference in Figure 7. The top plot correlates to the values of the upper sensors and the bottom plot to the lower sensors. A solid black line is added on both plots to indicate periods of time that NAVSLaM estimates had a perfect agreement with the sonic measurements. In the unstable region, or when the temperature difference is less than zero, we see that NAVSLaM estimates tend to slightly overestimate the \(C_{n}^{2}\) values compared to the upper sonic and yet have near-perfect agreement with the lower sensors. As seen in the previous figures, NAVSLaM begins to underestimate these values as conditions approach near-neutral regions. These estimates start to increase once more as we enter stable conditions, or a positive difference in mean temperature measurements. However, the best agreements are still seen when the temperature difference is less than zero.  
Although our results sometimes show significant differences between values of \(C_{n}^{2}\) derived from sonic measurements and values predicted by NAVSLaM, it should be noted that when those differences occur, the values of \(C_{n}^{2}\) tend to be very small. Such low levels of turbulence would have a smaller effect on laser beam propagation, so it is less essential to have accurate predictions of \(C_{n}^{2}\) during those times.  
Figure 6: Summary plots for the entire experimental period, showing \(log(C_{n}^{2})\) from NAVSLaM estimates and CSAT3 sonic anemometer measurements versus the temperature difference between the upper and lower sonic locations. A temperature difference of zero indicates near-neutral conditions.  
Figure 7: Difference between NAVSLaM-derived and CSAT3-derived \(C_{n}^{2}\) values.