# Millimeter Wave Attenuation Due to Wind and Heavy Rain in a Tropical Region
## 4 Results and Analysis
### Wind-Induced Attenuation Using Direct Inclination Angle Measurement  
Firstly, the effect of wind direction is demonstrated. The plots of the inclination angle (\(\theta\)) versus wind direction are shown in Figure 11, where Figure 11a is the angle magnitude and Figure 11b is the histogram of the angle magnitude exceeding the threshold of 0.5496\({}^{\circ}\) (Avg + SD). The plots of attenuation versus wind direction are shown in Figure 12, where Figure 12a contains all values of attenuation, and Figure 12b is the histogram of the attenuation exceeding the threshold of 3.3739 dB (Avg + SD). The top-view images of the pole and antenna orientation are also depicted, where the antenna is facing at 0\({}^{\circ}\)  
Figure 10: Average attenuation in 1-min intervals as a function of rain rate of two groups of data compared with ITU-R model and the combination of ITU-R and APT-AWG-REP-81 models. Figure 9: Maximum attenuation in 1-min intervals as a function of the rain rate of three groups of data: high wind speed, medium wind speed, and low wind speed. It was observed that the inclination angle or the attenuation was larger in specific wind directions. Hence, only the wind speed data are not sufficient to estimate the attenuation, in contrast to the previous study [27], where the wind speed can solely be used to estimate the attenuation using Equations (12)-(16). This may be due to the off-centered weight of the combine pole and antenna unit as well as the effects of the weather system and the surroundings of the different field trial location. It is recommended to directly measure the inclination angle, for example using accelerometers, as described in Section 3.3.2, in order to assess wind-induced reduction across various geographical locations. In this experiment, we analyze the correlation between the maximum inclination angle and the minimum received power within 10-s intervals, for consistency with the previous report [6; 27]. In the first data group in Figure 13, only the data with no rain (maximum rain rate = zero) in each interval have been included to eliminate the effect of rain attenuation. We see that both Equation (12) (APT-AWG-REP-81 model) and the datasheet can be used to estimate the lower limit of the wind-induced attenuation using a direct inclination angle measurement. From the measured data, initial axis misalignment of approximately 0.394\({}^{\circ}\) causes approximately 1.404 dB of attenuation, slightly lower than the expected attenuation of 2.16 dB from the model. Most data, however, do not show dependency with the pole inclination angle. This may be due to the inclination directions, which were not included in the model in Section 3. Figure 11: (**a**) Angle magnitude plot versus wind direction, with the threshold shown; (**b**) histogram of angle magnitudes that exceed threshold according to the wind direction (the number of samples \(\times\)1000). The antenna is facing 0\({}^{\circ}\). Figure 12: (**a**) Attenuation values plot versus wind direction, with threshold shown; (**b**) histogram of attenuation values that exceed threshold according to the wind direction (the number of samples \(\times\)1000). The antenna is facing 0\({}^{\circ}\). antenna pole in this setup produced a much lower attenuation, by two orders of magnitude (see the Supplementary Materials, Figures S1-S3). In Figure 14, the data include those with positive maximum rain rates. Compared to Figure 13, there have been many data points with much lower than expected received powers, predicted using the APT-AWG-REP-81 model, especially at small inclination angles due to the additional rain attenuation. We have shown that by starting with the model for wind-induced attenuation under zero-rain conditions (the green curve), the effect of rain attenuation calculated using the ITU-R model using a \(R_{0,01}\) rain rate (obtained in Figure 7) can be added. The combined model (the dark-red curve) can be used to estimate the lower limit of total attenuation.