Nihanth W. Cherukuru a Ronald Calhoun a Manuela Lehner b Sebastian Hoch b David Whiteman b a Arizona State University, Environmental Remote sensing group, Tempe, Arizona b University of Utah, Mountain Meteorology Group, Salt Lake City, Utah Instrument Configuration for Dual-Doppler Lidar Coplanar scans: METCRAX II

Outline 1 Objective Overview of the technique o Domain dimensions and scan speed o Weighting function o Equivalence of LS method with the average method (LS= Least squares) Error analysis Field experiment results Summary and future work

2 -Resolve the flow in a 2D cross plane and study the spatial and temporal evolution of downslope windstorm type flows. -Need to determine the best possible scanning strategy and lidar parameters to perform a coplanar dual Doppler Lidar analysis for METCRAX II Why Dual Doppler ? Objective X (î) Y(ĵ) V L.O.S θ(Elevation angle) VrVr -A single Lidar measures the radial velocity. -We can combine the radial velocities from different look directions to reconstruct the actual wind velocity. V = √(u 2 + v 2 ) V r = u cosθ + w sinθ L.O.S = Line of sight

3 Why Dual Doppler ? Objective V L.O.S from Lidar 1 V r1 -A single Lidar measures the radial velocity. -We can combine the radial velocities from different look directions to reconstruct the actual wind velocity. V = √(u 2 + v 2 ) V r = u cosθ + w sinθ L.O.S = Line of sight L.O.S from Lidar 2 V r2 -Resolve the flow in a 2D cross plane and study the spatial and temporal evolution of downslope windstorm type flows. -Need to determine the best possible scanning strategy and lidar parameters to perform a coplanar dual Doppler Lidar analysis for METCRAX II (Newsom et al Hill et al Stawiarski et al. 2013)

4 Overview of the Technique Lidar 1 Lidar 2 1.Set the lidars such that the angle between their LOS not close to 0 or 180 degrees. 2.Overlay a Cartesian grid over which the velocity components are retrieved

5 Lidar 1 Lidar 2 R Overview of the Technique 3. At each grid intersection point define a region. 4. Assign the range gates to the corresponding grid intersection point.

6 Lidar 1 Lidar 2 Overview of the Technique Repeat for all points …

7 -Grid spacing must be greater than range gate length i.e, R ≥ (Δp/√2) -Total scan time should be : Domain Dimensions and scan speed Lidar 1 Lidar 2 (PRF=Pulse Repeatition Frequency)

8 Weighting Function -The radial velocity measured at a range gate can be considered to be an average over a finite distance along the LOS. (Frehlich et al. 1998)

9 R'R' A B C D E F G H ∆p R R’= R + (∆p/2) Weighting Function - The weighting function relates to the portion of the range gate that falls within the circle of influence (R)

Equivalence of LS method with the average method 1. From the LS method 2. Upon expanding each term of the matrix: 10

3. Replacing the elevation angles with one single value corresponding to the grid centre: Where, 4. Rearranging the terms in matrix form 5. Above system of equations is valid when the 2x2 matrix on LHS has an inverse 11 Equivalence of LS method with the average method

12 Error Analysis (From Lidar Simulator) - Temporal error - Spatial error - Retrieval error Error due to the the cells with skewed LOS from Lidars. i.e., angle between the LOS close to 0 degrees or 180 degrees. time Errors are dependent on both averaging and range gate size (Lhermitte and Miller 1970 )

13 Red : Temporal errors Blue : Spatial errors (a): errors in u (b): errors in w -Temporal errors increase with pulse averaging. -Temporal errors increase with range gate length -Spatial errors are independent of averaging used -Spatial errors increase with range gate size (a)(b) Error Analysis (From Lidar Simulator)

14 Lidar-1 parameters PRF15kHz Averaging10,000 Range gate24 m Elevation angle at the beginning of the scan150 Elevation angle at the end of the scan10 Time taken for the one scan30 s Scan rate4.5 deg/s Sector140 Lidar-2 parameters Accumulation time0.75 s Range gate25 m Elevation angle at the beginning of the scan -10 Elevation angle at the end of the scan20 Time taken for the one scan30s Scan rate1.0 deg /s Sector30 Domain specifications Number of cells in X direction36 Number of cells in Y direction19 Cell dimensions26.8 m x 26.8m Lidars on site * WALL-E_03.jpg. Digital image. Wikia. N.p., 27 Mar Web. 8 Aug *

15 Field Experiment results

16 Summary and Future Work -Coplanar Dual Doppler Technique can be used to study complex flows. -Care must be taken in choosing the lidar parameters to get the best temporal and spatial resolution of the phenomenon. -Analysis can be simplified with certain assumptions and for small range gate lengths, the results are very close. -Investigate the significance of weighting function for alternate approaches and larger range gate lengths. Acknowledgements -Research work supported by National Science Foundation (NSF) grants AGS and We would like to thank Dr. William O.J Brown from NCAR.

Questions