Estimation of 3D Wind Field and Vorticity with Higher Spatial Resolution Using Multicompact X-Band Weather Radars

Introduction

Strong wind in a local area causes serious damage on transport systems such as highways, railways and airports. In order to prevent such disasters, real-time observation of wind field is very important. Especially the Dual polarimetric Doppler weather radar with high spatial resolution and temporal resolution gives us the most effective solution. The estimation of 3D wind field and vorticity using multi weather radars prevents the threat of wind shear, and safe commuting and traveling are realized.

Case study

[1] Triple-Doppler analysis

This study shows one interesting case study of 7 April 2016 when wide area rain was observed in Osaka-Bay area, Japan. Three radars, each of them a compact dual Polarimetric X-band Doppler weather radar, have been deployed in the Osaka-Bay area in Japan. Each distance among these radars is approximately 10 km. At 9:00 LST, low pressure came from west and hit Osaka-Bay area.

[2] Estimation of Vorticity

This study shows the influence of observation noise in the variational method when using two and three Doppler radars. Further, this study indicates three-dimensional wind field and vertical vorticity using the variational method in a simulation. Also, the performance of the variational method detects vertical vorticity.

Analysis results

[1] Triple-Doppler analysis

The observed data by three radars were processed by Triple-Doppler analysis. By deploying the three radars within 10 km range, horizontal wind field and vertical velocity of raindrops can be directly estimated by the Triple-Doppler analysis. As a result, horizontal wind velocity and vertical one of raindrop were obtained for each altitude. In this case, scanning strategy was volume scan. The radar observed 12 elevation angles from 0 to 90 degrees in 1 minute.

On the other hand, the reference data was acquired by VAD analysis at each radar. The VAD analysis made it possible to estimate the horizontal wind and the vertical drop velocity at each altitude. The analysis was compared with Triple-Doppler one. Each analysis was carried out at altitudes from 1000 m to 6000 m by 1000 m step.

Calculated wind field by Triple-Doppler analysis and one by VAD analysis were compared during 1 hour from 9:00 to 10:00 LST. As a result, tendencies of wind direction and wind speed were in good agreement as can be seen in Figure 1, Figure 2 and Figure 3. The averaged RMSE (Root Mean Squared Error) at each altitude was 1.2 deg in wind direction, 1.2 m/s in wind speed, 0.6 m/s in vertical drop velocity. Moreover those figures show that there was a significant altitude around 3000 m to 4000 m where the wind field quickly changed. This result suggests that vertical wind shear was observed by Triple-Doppler analysis.

[2] Estimation of Vorticity

This study used idealized data on the wind velocity field (u=10 m/s, v=10 m/s, w =0 m/s) satisfying the continuous equation with vorticity (0.1[/s]) at the center of each layer. The horizontal grid spacing is 200 m and vertical grid spacing is 100 m. This study shows the relationship between the number of the radars and percentage of noise in observation value. The number of observation points is 75000 (50000) when using three (two) radars. The variational method in this paper is based on Shimizu and Maesaka (2006).

The RMSE with three radars is smaller than that with two radars when the noise is less than 100 % of the observation wind velocity. On the other hand, when the noise exceeds 100 %, the RMSE with two radars is lower than that with three radars (Figure 4, Left). Since the actual observation noise is assumed to be around 1 m/s (Ishihara 2001), it is found that estimating accuracy improves by using three radars when the wind velocity is larger than about 2 m/s (Figure 4, Right).

Further, this study shows the estimation of three-dimensional wind field and vorticity using the variational method. The calculation result using three radars was reproduced well at RMSE = 0.1 m/s. It shows that artificial vorticity 0.1[/s] was reproduced without weakening (Figure 5). Vortex satisfying the continuous equation should not be recognized as an error in the variational method. Therefore, it is possible to estimate the vorticity using the variational method.

Conclusions

In a case study of 7 April 2016, when wide area rain was observed by three polarimetric weather radars, the result of Triple-Doppler analysis and VAD analysis are compared. The analysis using a compact dual polarimetric X-band Doppler weather radar indicates the possibility for understanding the horizontal wind field and vertical drop velocity.

The vorticity estimated by using three radars is more accurate than using two radars unless the noise exceeds 100 % of the observation. Hence, when the actual observation noise is assumed around 1 m/s, the vorticity estimated by using two radars would be effective in the weak wind filed (less than 2 m/s).

This study demonstrates to estimate the vorticity by using three-dimensional variational method. When the wind field satisfies a continuity equation, the vorticity is estimated without damping.

Therefore the estimation of 3D wind field and vorticity contributes to safe operations in urban transportation systems, and supports safe takeoffs and landings at airports during strong wind weather and severe storm.

KEYWORDS: Polarimetric Radar, Wind field estimation, Variational method.