Verification strategies for airborne in situ eddy dissipation rate (EDR) estimates

1. Verification strategies for airborne in situ eddy dissipation rate (EDR) estimates Larry B. Cornman National Center for Atmospheric Research

2. FAA EDR Standards Project • The purpose of this project is to develop performance standards for on-board energy dissipation rate (EDR) algorithms. • Team comprised of: Exelis, AeroTech Reseach, Rockwell-Collins, Panasonic Avionics, UCAR/NCAR, United, WSI.

3. EDR Performance Standards Process

4. Algorithm Inputs

5. Input Wind Datasets Category Wind Dataset Description Wind Dataset Specification Cases to Analyze Turbulence is random phenomena Simulated data has expected random characteristics for homogeneous turbulence (Gaussian process) • 25 von Karman datasets • EDR values between 0.1–0.7 • Length scales of 200-750 m Homogeneous – considering only the variability of this random process Turbulence structure does not always conform to algorithm assumptions “Modulated” simulation will be inhomogeneous • 3 Modulation Scenarios • Background: EDR = 0.06, L = 500m • “sharp,” “moderate,” and “slow” Non-homogenous –simulated convective, mountain wave, etc. Turbulence can be highly layered and change rapidly with altitude “Modulated” simulation can vary as a function of altitude • 8 von Karman datasets • EDR values between .01-0.3 • Length scale of 500m Highly layered turbulence Sensors and avionics produce noise Set of simulated data focuses on very low EDR levels • 15 von Karman datasets • EDR values btw 0.01-0.06 • Length scales of 200m and 500 m Low signal to noise ratio at low turbulence intensity Sensors and avionics produce errors N/A N/A N/A (included in all cases) Avionics limited computation capabilities N/A • N/A • N/A • (included in all cases)

6. Simulated Wind Field Generation Purpose: To have a controlled and repeatable dataset for statistical analysis. Simulation software based on peer-reviewed article: Frehlich, Cornman and Sharman, “Simulation of Three-Dimensional Turbulent Velocity Fields.” J. Applied Meteorology, 2001. Algorithm produces accurate (u, v, w) fields over 3-d grid.

7. Probability Density Function • All points • First 1024 points

8. Correlation Function • Average over all points • First 1024 points Black = data Red = theory

9. Power Spectra • Averaged over all points • First 1024 points Black = data Red = theory Green = “analytic”

10. Turbulence in the Real World • Turbulence is a very complicated phenomena, but to do practical calculations, we often use simplifying assumptions: • Homogeneity (statistics are the same over spatial position) • Stationarity (statistics are the same over time) • Isotropy (statistics are the same over spatial orientation)

11. Modulation for Simulating Inhomogeneous Fields • Linear scaling: • Simple isotropic scaling: • General (solenoidal) definition of energy dissipation rate: • For isotropic scaling case:

12. Modulation Model for Inhomogeneous Fields

13. Simulated Modulated Turbulence

14. Examples of Simulated Modulated Turbulence

15. EDR “Truth” Calculation • For this work, EDR “Truth” is defined as: “The best practical calculation of EDR, which is as independent from operational algorithms as feasible” • EDR has a precise definition from fluid dynamics (Navier-Stokes eq.), but it is not practical to compute. • So, we use an algorithm– unconstrained by operational implementation - that acts as a “lab standard”

16. Instantaneous Spectrum for Inhomogeneous Fields • Instantaneous correlation function: • Instantaneous spectrum (convolution): • Spatial-averaged spectrum:

17. Average Periodogram forInhomogeneous Data • Narrow Modulation • Wider Modulation

18. Instantaneous Spectrum vs.Average Periodogram