Abstract The cross-correlation algorithm [1] is a numerical method used to estimate the motion of features between two frames in image sequences. Prior to this research, it was applied to real aerosol lidar for wind measurements [2, 3]. However, an evaluation of the cross-correlation algorithm involving precise control of aerosol features and flow fields has not been performed. Therefore, we have evaluated performance of the cross-correlation algorithm using synthetic backscatter images and flow fields. The results show that the cross-correlation algorithm provides reliable displacement vectors if the flow is uniform, but the performance of the cross-correlation algorithm decreases as non-uniformity of the flow fields increases Methodology We create a synthetic backscatter image in computer using Interactive Data Language (IDL). This is done by two-dimensional array filled with random numbers and smoothing the array with a two-dimensional moving average. Then, we randomly place Gaussian features in the array and diffuse the features using turbulent fluctuation fields [4, 5]. We call this array “Block 1”. Next we create a two-dimensional, two-component, velocity field (u, v) by sum of an analytical function of flow field and a turbulent fluctuation field (u’, v’) based on the model of Jacob Mann [4, 5]. Then, we move each pixel in “Block 1” to a new location according to the velocity at that pixel location. An image of the displaced pixel distribution is formed by applying a bicubic interpolation. The new image with dispaced features is reffered to as “Block2”. The cross-correlation algorithm is applied to the images to estimate the displacement vector. Test is repeated by using different synthetic backscatter images (N=100). Then, the mean displacement vector and the standard deviation due to different synthetic backscatter images are calculated. Finally, we compare the displacement vector with the prescribed velocity field. (Block 1) (Block 2) Calculate Cross Spectra . Complex Conjugate of Fast Fourier Transform f * (τ) Fast Fourier Transform g ( r + τ ) (Velocity Field) To make a better approximation of the displacement vector, we move the “Block 2” according to the initial estimation of the displacement vector, and apply the cross-correlation algorithm again (multi-pass approach). In this case, we use a polynomial fit to estimate the subpixel fluctuation of the displacement vector. Finally we add the initial estimate of the displacement vector and the subpixel fluctuation of the displacement vector to get the resultant displacement vector. [1] Schols, J. L. and E. W. Eloranta, 1992: The calculation of area-averaged vertical profiles of the horizontal wind velocity from volume-imaging lidar data. J. Geophys. Res., 97, 18 395–18 407. [2] Eloranta. E. W., J.M.King and J. A. Weinman, 1975: The determination of wind speeds in the boundarylayer monostatic lidar. J. Appl. Meteor, 14, 1485-1489. [3] Mayor, S. D., J. P. Lowe, and C. F. Mauzey, 2012: Two-component horizontal aerosol motion vectors in the atmospheric surface layer from a cross-correlation algorithm applied to elastic backscatter lidar data, J. Atmos. Ocean. Technol., 29, 1585-1602. [4] Mann, J. 1994: The spatial structure of neutral atmospheric surface-layer turbulence, J. Fluid Mech., 273, 141-168. [5] Mann, J. 1998: Wind field simulation, Prob.Engng. Mech. 13, 269-282 "This work was supported by NSF AGS 1228464." References 2. Uniform Flow with Turbulent Fluctuations 4. Convergent Flow with Turbulent Fluctuations 3. Divergent Flow with Turbulent Fluctuations 5. Circular Flow with Turbulent Fluctuations 6. Shear Flow with Turbulent Fluctuations 1. Uniform Flow Results Conclusion The results show that the cross-correlation algorithm provides reliable displacement vectors if the flow is uniform. However, because the cross-correlation algorithm only results in one displacement vector for the entire block, information that could describe non-uniformity is not retrived. As a result, ambiguity increases, and the performance of the cross-correlation algorithm decreases as non-uniformity of the flow fields increases. Why Use Synthetic Backscatter Images? We cannot control the atmosphere to test. Velocity Field Mean (10.000, 0.000) Pixels/Frames SD (0.000, 0.000) Pixels/Frames Velocity Field Mean (11.083, 0.104) Pixels/Frames SD (1.971, 1.232) Pixels/Frames Velocity Field Mean (11.083, 0.103) Pixels/Frames SD (1.971, 5.728) Pixels/Frames Velocity Field Mean (11.083, 0.103) Pixels/Frames SD (1.971, 6.183) Pixels/Frames Velocity Field Mean (11.232, 0.104) Pixels/Frames SD (13.870, 1.232) Pixels/Frames Velocity Field Mean (1.083, 0.104) Pixels/Frames SD (5.462, 5.922) Pixels/Frames CCF Resultant Displacement (N=100) Mean (9.98426, 0.00005) Pixels SD (0.00355, 0.00044) Pixels CCF Resultant Displacement (N=100) Mean (10.7476, 0.07016) Pixels SD (0.77810, 0.28854) Pixels CCF Resultant Displacement (N=100) Mean (10.5628, 0.55299) Pixels SD (1.72201, 5.34860) Pixels CCF Resultant Displacement (N=100) Mean (10.7123, -0.39521) Pixels SD (1.54535, 3.53784) Pixels CCF Resultant Displacement (N=100) Mean (0.34509, -0.11779) Pixels SD (3.37916, 4.33848) Pixels CCF Resultant Displacement (N=100) Mean (4.94471, -0.11452) Pixels SD (14.1630, 0.97839) Pixels Peak of the Cross-Correlation Function (CCF) represents the displacement vector Take Inverse Fourier Transform to calculate the Cross-Correlation Function (CCF) (Cross-Correlation Function) Tests of the Cross-Correlation Algorithm Using Synthetic Backscatter Lidar Images and Wind Fields Masaki Hamada, Pierre Dérian and Shane D. Mayor, Department of Geological and Environmental Sciences, California State University, Chico, U.S.A. e-mail: mhamada1@mail.csuchico.edu, pderian@csuchico.edu, sdmayor@csuchico.edu Paper Number: A13G-0311