Reprint 714

Retrieval of 3D Wind Field from LIDAR Velocity Data

X. Xu* & P.W. Chan

14th Coherent Laser Radar Conference,

Snowmass, Colorado, USA, 8 - 13 July 2007

* Chinese Academy of Meteorological Science

14th Coherent Laser Radar Conference

Retrieval of 3D Wind Field from LIDAR Velocity Data

Xiaoyong Xu (a) and P.W. Chan (b)

(a) Chinese Academy of Meteorological Sciences, Beijing, China

(b) Hong Kong Observatory, Hong Kong, China

pwchan@hko.gov.hk

INTRODUCTION The Hong Kong Observatory (HKO) operates a Doppler LIDAR at the Hong Kong International Airport (HKIA) for airflow monitoring and windshear alerting. Complex airflow occasionally occurs in the vicinity of HKIA due to terrain disruption. To better visualize the wind in the airport area, 2D wind retrieval based on the LIDAR’s radial velocity measurement is conducted1. This paper is an extension of the work by using a more sophisticated technique to retrieve the 3D wind field around HKIA.

RETRIEVAL METHOD The 4DVAR assimilation retrieval technique for Doppler radar data is adopted in this work. This method was initially demonstrated2 using simulated Doppler radar data and later applied to a dry gust front case using real Doppler radar observations3. A series of identical twin experiments was conducted4 using a modified version of Sun’s original algorithm with synthetic data generated by large eddy simulations to explore the potential of retrieving microscale flow structures from single-Doppler lidar data. Modifications included the introduction of a surface layer parameterization scheme based on Monin–Obukhov similarity theory. A variable eddy diffusion profile was also incorporated5 and the algorithm was applied to High Resolution Doppler LIDAR (HRDL) data collected under clear-sky, daytime convective conditions during the Cooperative Atmosphere/Surface Exchange Study (CASES-99) field campaign.

The forward model consists of a set of equations describing the motion of the flow. The forward model used here is similar to that used in the previous studies2,3,4,5. It contains four prognostic equations: the three momentum equations and the thermodynamic equation, and four prognostic variables: the three wind components and the

potential temperature. The perturbation temperature can be diagnosed from the prognostic variables. All model variables are scaled by their typical values and the numerical model is coded in terms of dimensionless variables. The reason for doing this is to balance the magnitude of the different variables such that each variable has a similar weight during the assimilation, and hence a better convergence rate.

The objective of 4DVAR is to find an initial state of the model that can, upon model integration, produce output matching the observations at all times as closely as possible. The misfit between the model output and the observations is measured by the cost function defined as

])([,

2∑ −=τσ

obrrv VVηJ (1）

where the summation is made over the spatial domain σ and the assimilation period τ . The quantity vη is the weighting coefficient for radial velocity. The quantity is the observed radial velocity. The

obrV

rV is its model counterpart and can be calculated using the model outputs of Cartesian velocity (u ,v ,w) by

wr

zzv

ryy

ur

xxV

i

i

i

i

i

ir

−+

−+

−= (2）

where the is the distance between a grid point (

irx , , ）and the lidar location（ , , ）. y z ix iy iz

Now the constrained variational problem is constructed through minimizing the cost function (1) with the model equations representing the constraints. The minimization procedure can be found in detail in the reference2.

The wind retrieved is performed over an assimilation period τ of 6 minutes, which consists of two “volume scans” of the LIDAR. Each “volume scan” has three Plan-position Indicator (PPI) scans, namely, with elevation angles of 0, 1 and 4.5 degrees.

14th Coherent Laser Radar Conference

EXAMPLES OF RETRIEVED WIND FIELD Two examples are discussed in this paper. The first case occurs at about 00:16 UTC, 8 March 2006, in which easterly wind prevailed over the airport area. The 00 UTC radiosonde ascent in Hong Kong (not shown) gives a neutral layer up to 300 m and a stable layer aloft. The generally stable boundary layer favours the occurrence of a mountain wake to the west of the airport, as confirmed with the reversed flow in that region (Figure 1(a)). The east-southeasterly jet and the wake are well captured in the retrieved wind field (Figure 1(b)).

The hill Lo Fu Tau (location in Figure 1(a)) has a height of 465 m which is inside the stable layer, favouring the appearance of mountain wave6 as confirmed by LIDAR velocity data (Figure 2(a)). The retrieved wind field also gives alternating upward and downward motion of the air at that location (Figure 2(b)). Cross section along the lee wave region (Figure 2(c)) shows that three wavelengths of the wave could be discerned, with the wave amplitude decreasing with increasing distance downwind of the hill.

The second case is again an east to southeasterly wind event in the spring time – at about 16:16 UTC, 17 April 2006 (Figure 3(a)). This time the neutral layer near the ground reached a higher altitude of about 450-600 m with a stable atmosphere aloft, as given by the radiosonde ascents (not shown). The retrieved vertical velocity (Figure 3(b)) shows that there is wave motion downstream of Tung Chung Gap (location in Figure 3(a)). This is consistent with the Range-height Indicator (RHI) scan data of the LIDAR (Figure 3(c)), in which jump-like feature was observed after the wind climbed over the gap7. This jump-like feature is successfully captured in the retrieved wind field based on PPI scan data alone (Figure 3(d)). The retrieved winds also show that there is a wave (of one wavelength) occurring over the airport. Banta et al.7 speculated that under such condition, jump-like feature could also take place on the other side of the hill, viz. downstream of Tai Fung Au (location in Figure 3(a)). This is confirmed in the retrieved wind field (Figure 3(e)). However, compared with the wind coming out of Tung Chung Gap, no wave motion could be analyzed downstream of the jump-like feature. In this event, the jump also appears to be elevated and does not dip close to the ground.

SUMMARY 4DVAR assimilation technique is applied to the PPI scan data of the LIDAR at HKIA to retrieve the three components of the wind. Two consecutive “volume scans” of the LIDAR are used for the retrieval, which is based on the momentum equations and the thermodynamic equation. The capability of the method is demonstrated in the analysis of two cases of terrain-disrupted airlfow at HKIA in spring-time. The retrieval provides additional information about vertical motion of the air. As shown in the examples, the vertical velocity associated with mountain waves and jump-like features as obtained in the retrieval appear to be reasonable and compare well with LIDAR data.

REFERENCES 1 Chan, P.W. and A.M. Shao, “Two-dimensional wind retrieval using a Doppler LIDAR,” 13th International Symposium for the Advancement of Boundary Layer Remote Sensing, Garmisch-Partenkirchen, Germany. (2006) 2 Sun, J., D. W. Flicker and D. K. Lilly, “Recovery of three-dimensional wind and temperature fields from simulated single Doppler radar data,” J. Atmos. Sci., 48, 876–890 (1991) 3 Sun, J. and A. Crook, “Wind and thermodynamic retrieval from single Doppler measurements of a gust front observed during Phoenix II,” Mon. Wea. Rev., 122, 1075–1091 (1994) 4 Lin, C.-L., T. Chai and J. Sun, “Retrieval of flow structures in a convective boundary layer using an adjoint model: Identical twin experiments,” J. Atmos. Sci., 58, 1767–1783 (2001) 5 Chai, T., C. L. Lin and R. K. Newsom, “Retrieval of microscale flow structures from high-resolution Doppler lidar data using an adjoint model,” J. Atmos. Sci., 61, 1500–1520 (2004) 6 Shun, C.M., et al., “LIDAR observations of wind shear induced by mountain lee waves,” 11th Conference on Mountain Meteorology and MAP Meeting 2004, Mount Washington Valley, USA (2004) 7 Banta, R.M., et al., “Detection and diagnosis of windshear and turbulence using Doppler LIDAR at Hong Kong International Airport,” ESRL/NOAA and HKO, 130 pp. (2006)

14th Coherent Laser Radar Conference

LIDAR

Figure 1 The 1-degree PPI image of the radial velocity of the LIDAR at 00:16 UTC, 8 March 2006 (left) and the retrieved 2D wind field at 100 m AMSL (wind barbs) at about the same time (right). The shaded contours on the right refer to the magnitude of the horizontal wind component.

(b)

A

B

(a)

Lo Fu Tau

(c)A B Figure 2 The 4.5-degree PPI image of the radial velocity of the LIDAR at 00:18 UTC, 8 March 2006 (a). The retrieved 2D wind field with shaded contours of vertical velocity (m/s) is shown in (b). (c) refers to the cross section AB, with the wind component projected on the cross-sectional plane (arrows, vertical velocity x 10), vertical velocity (original value) in line contours and horizontal wind magnitude in shaded contours.

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(b)

A

B

C

D(a)

Tung Chung Gap Tai Fung Au

(c)

(d) A B

(e) C D

Figure 3 The 4.5-degree PPI image of the radial velocity of the LIDAR at 16:16 UTC, 17 April 2006 (a). (b) shows the retrieved 2D wind field and vertical velocity (shaded contours) at 450 m AMSL and the locations of the cross sections. (c) is the LIDAR’s RHI scan image at Tung Chung Gap, and (d) is the corresponding retrieved winds. (e) is the retrieved winds at Tai Fung Au. The meanings of the contours and the wind arrows in the cross sections (d) and (e) are the same as those in Figure 2(c).