Delft University of Technology 1 CESAR Science Day, 19 June 2013 Albert Oude Nijhuis Dynamics of turbulence in precipitation: Unravelling the eddies

Delft University of Technology 2 CESAR Science Day, 19 June 2013 UFO project Retrieval of wind field with IDRA Retrieval of the Eddy Dissipation Rate The Inertia Effect Outlook Contents

Delft University of Technology 3 CESAR Science Day, 19 June 2013

Delft University of Technology 4 CESAR Science Day, 19 June 2013 UFO Project

Delft University of Technology 5 CESAR Science Day, 19 June 2013 UFO Project

Delft University of Technology 6 CESAR Science Day, 19 June 2013 UFO Project

Delft University of Technology 7 CESAR Science Day, 19 June 2013 UFO Project The combination of LIDAR and RADAR can be used to detect wake vortices in all weather conditions. Quantitative information on turbulence, e.g. the eddy dissipation rate, can be retrieved from the Doppler moments, velocity and spectral width, from LIDAR and RADAR instrument.

Delft University of Technology 8 CESAR Science Day, 19 June 2013 Retrieval of wind field with IDRA In contours: Doppler velocities Horizontal wind vectors are obtained via a least sqaures fit.

Delft University of Technology 9 CESAR Science Day, 19 June 2013 Retrieval of wind field with IDRA Model from Doviak and Zrnic (1992)

Delft University of Technology 10 CESAR Science Day, 19 June 2013 Retrieval of wind field with IDRA

Delft University of Technology 11 CESAR Science Day, 19 June 2013 Retrieval of the eddy dissipation rate The eddy dissipation rate (EDR) is based on the assumption of homogenous isotropic frozen turbulence. In the inertial sub-range the dissipation goes with a -5/3 power. Figure from O'Connor (2010).

Delft University of Technology 12 CESAR Science Day, 19 June 2013 Retrieval of the eddy dissipation rate Several retrieval methods are possible: 1. Use the Doppler spectral width. Subtract the fall speed distribution and compute the turbulence spectral width. Then calculate the EDR. 2. Use a sequence of Doppler velocities and compute the variance. Use an analytic relation to compute the EDR. 3. Use a sequence of Doppler velocities, and compute the vertical velocity energy density spectrum (FFT). Fit the slope from the loglog plot, which can be used to compute the EDR. The eddy dissipation rate (EDR) is based on the assumption of homogenous isotropic frozen turbulence. In the inertial sub-range the dissipation goes with a -5/3 power.

Delft University of Technology 13 CESAR Science Day, 19 June 2013 Retrieval of the eddy dissipation rate EDR from Doppler spectral width TARA (S-band RADAR) measures the vertical Doppler verlocity at Cabauw. EDR from Doppler velocitiy sequence O'Connors method (from the variance) LSF method 1 LSF method 2 Different retrieval methods lead to different answers!

Delft University of Technology 14 CESAR Science Day, 19 June 2013 Retrieval of the eddy dissipation rate EDR from Doppler spectral width EDR from the spectral width is quite a challenge, as it is depending on the drop size distribution!

Delft University of Technology 15 CESAR Science Day, 19 June 2013 Retrieval of the eddy dissipation rate EDR from Doppler velocitiy sequence O'Connors method (from the variance) The basics

Delft University of Technology 16 CESAR Science Day, 19 June 2013 Retrieval of the eddy dissipation rate Figure from O'Connor (2010). Power spectrum for a LIDAR instrument. Power spectrum from TARA (S-band RADAR). +/- 60 min. of data. For the RADAR the -5/3 power law seems not to be satisfied for the shorter spatial scales.

Delft University of Technology 17 CESAR Science Day, 19 June 2013 The inertia effect Large droplets have inertia. They need some time to participate in the turbulent motion. A very simple model can be used (Gorelik, 1964): - For each drop size there is a minimum length scale Lmin. - For turbulent motions larger than Lmin the drop is a perfect tracer. - For turbulent motions smaller than Lmin the drop will not participate in the motion. - For Lmin we use the approximation:

Delft University of Technology 18 CESAR Science Day, 19 June 2013 The inertia effect Large droplets have inertia. They need some time to participate in the turbulent motion. Power spectrum from TARA (S-band RADAR). +/- 60 min. of data. Theoretical power spectrum, with and without the inertia effect. Inertia effect??

Delft University of Technology 19 CESAR Science Day, 19 June 2013 Benchmark: plot vs. height Spectral width From variance, method from (O'Connor, 2010) Spectrum lsf method 1 Spectrum lsf method 2

Delft University of Technology 20 CESAR Science Day, 19 June 2013 Comparing retrieval methods LSF 2 (y-axis) vs. O'Connor LSF 1 (y-axis) vs. O'Connor

Delft University of Technology 21 CESAR Science Day, 19 June 2013 Outlook Benchmark / validate EDR retrieval methods Investigation of the inertia effect. Potentially it may be possible to retrieve the drop-size distribution. The addition of a Doppler LIDAR on CESAR would be helpfull. Then the LIDAR+RADAR combination performance for all weather conditions can be assessed.