A Technique for Wind Measurement with high Spatial and Temporal Resolution

Investigators

Li-Chuan Chen, William Eichinger (University of Iowa)

Acknowledgment

We gratefully acknowledge the help from various individuals in the Los Alamos National Laboratory lidar team in the Earth and Environmental Science Division.

Sponsor

U.S. Army Research Office

Introduction

There has been a need for nonintrusive, high spatial and temporal wind measurement techniques for various applications. One such technique under development is a multiple beam laser-radar (lidar); a point laser-based. The technique provides instantaneous velocities as well as mean velocities. Thus some turbulence quantities ( e.g., turbulent intensities, Reynolds stresses, and higher moments or statistics) can be derived. In addition, particulate-related quantities can also be measured to obtain such quantities as cloud height and optical depth/reflectivity or boundary layer height and relative particulate loading with altitude. The system works by transmitting five laser beams into the atmosphere with a known spacing between them. As atmospheric structures translate across the beam, they generate sinousoidal fluctuations in the amplitude of the lidar return.  By performing a fast Fourier transform on the lidar data in time at a given range (altitude), one can determine the frequency at which the structure goes through the beams.

This frequency when multiplied by the distance between the beams at that altitude gives the wind velocity in the direction along the plane of the five beams. Two orthogonal sets of beams provide the complete horizontal wind vector. The Fourier transform gives the frequency and thus the wind speed along a given direction, but not the direction. This is obtained by using a quadrant detector in the back of the telescope. By comparing the two halves of the five beams, and performing a correlation analysis, the direction along the five beams can be determined. The vertical wind velocity is found from a correlation analysis.

The current system can provide wind measurements every 1.5 meters in altitude throughout the depth of the boundary layer (generally 1 to 3 km in altitude). Wind velocities can be determined on time scales as short as 2.5 seconds. Longer term averaging is also possible resulting in more precise wind measurements.

Hardware Design

The lidar is designed to be rugged enough to be left outside and operate with little user interaction. While it is built to be water-tight, the windows and mirrors must be kept clean and operation during rain is not expected to be productive. The lidar is housed in two shipping containers to make it easier to transport and move by hand. When set up, the two containers match and become a single water-tight box (top right). The ends are removable for ease of servicing the various components inside. One box houses the telescope, laser head and the associated optical train (bottom right). The other box houses the laser power supply and a computer with cards on the PC bus which control/monitor all of the activities taking place in the lidar. The laser used in the lidar is a Nd:YAG operating at 1.064 micron, 125 mJ per pulse, 50 pulses per second.

Applications and Planned Improvements

	At the left are data from a computer simulation of the output of the detector and the analysis routines. The top graph shows five separate sequences of 256 data points. The second is the average FFT of the five sequences. One can see that the fundamental frequency is quite distinct and usually has strong harmonics (f/2, f/3, f/4 and so on). The accuracy of the measurement is about 2%. This type of wind measurement system provides wind vectors on spatial and temporal time scales of twenty to thirty times better than those available from conventional sodar or radar wind sounders. It is, however, limited to that part of the atmosphere that has enough particulates to provide a strong return signal. This limits its use to the planetary boundary layer in most circumstances. In situations where cost is a factor, the instrument can be built for approximately three quarters of the cost of a simple sodar system and less than half that of a comparable radar system.
There are many applications for this type of instrument, most notably for use at airports to detect wind shear and wind velocities with altitude. Other applications include weather forecasting, air pollution monitoring, tracking of toxic releases, detection of wind shear, and scientific studies. Future upgrades to the instrument include the substitution of a laser capable of 5 kHz pulse rate. This will enable wind measurements to be made on time scales of approximately 0.1 second. The addition of 500 MHz digitizers will enable the range resolution to as little as 30 cm. This kind of capability will provide detailed turbulence information that is available from no other source to researchers and atmospheric modelers.

Verification of Closure Assumptions using a Multibeam Lidar for Wind Measurement

Use of high Spatial and Temporal Resolution Wind Soundings

Having an instrument capable of short time scale, high spatial resolution wind measurements such as the multibeam lidar, offers a number of opportunities to study the closure assumptions made in many of the mesoscale atmospheric models used today. These models are essentially solutions to the Reynolds Averaged Navier Stokes (RANS) Equations which are equations of conservation of mass and momentum. The Reynolds’ averaging technique produces equations that allow us to solve for the average values of the wind vectors rather than the instantaneous values.

Unfortunately, the Reynolds’ averaging technique produces terms that cannot be determined using the time averaged values. The last term in the last equation to the right is the covariance between two of the instantaneous velocities. These terms must be modeled because they are not properties of the mean flow.

In order to solve the equations, it is customary to add to the RANS equations, the equation for conservation of turbulent kinetic energy and for the dissipation rate of turbulent kinetic energy. These equations also produce terms which must be modeled.

Additional Equations Used to Solve a K-Epsilon Model

Testing of the Closure Assumptions

The closure assumptions made relate the calculated quantities (the average values of wind speed, kinetic energy and dissipation) to the unknown values which are covariances of the turbulent fluctuations in the mean quantities (which cannot be calculated). These assumptions generally model the transport of the covariance terms as gradient diffusion processes. In other words, a term like vi’vj’ as a constant times the gradient of Vi in the xj direction or CdVi/dxj. All of the equations in the lower left are models of this type. What few measurements have been made, show that the modeling of these transport terms as diffusive processes is only marginally correct. The terms may be dispersive, but that does not imply diffusive. These terms become increasingly important as efforts to reduce the grid sizes in these models continue. There are many practical applications for high resolution models (pollution control, atmospheric chemistry modeling, fire management, toxic spill situations, etc) that require the small scale features of the flow to be modeled well. As the scales of the current models are reduced, the fine scale features of the flow often do not resemble the actual situations found on the ground.

The multibeam lidar allows us to measure the wind vectors, their gradients, and in many cases the covariance terms as well. Supporting data will come from arrays of three dimensional sonic anemometers (to make direct measurements of the turbulent kinetic energy terms) and several hot wire anemometers (to make direct measurements of the dissipation rate). We will use this data to test the closure assumptions made in these models.

The intent is to improve our understanding of the relationships between the turbulent variations and the mean flow conditions so that we may develop improved closure assumptions that will enable greater fidelity in the current atmospheric models.