Exploitation of homogeneous isotropic turbulence models for optimization of turbulence remote sensing

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Delft University of Technology

A.C.P. Oude Nijhuis, C.M.H. Unal, O.A. Krasnov, H.W.J. Russchenberg and A. Yarovoy

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Outline

1 Introduction

The UFO project Research question

2 Overview of turbulence models Stochastic turbulence models Parametric turbulence model 3 Simulation of radar observables

Zephyros

4 Simulated radar measurements Scanning radar

Staring radar

Polarimetric radar spectra Canting angles

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Next section

1 Introduction

2 Overview of turbulence models

Stochastic turbulence models Parametric turbulence model

3 Simulation of radar observables

Zephyros

4 Simulated radar measurements

Scanning radar Staring radar

Inertia effect

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Ultra Fast wind SensOrs project

The UFO project

A solution to mitigate weather haz-ards and increase airport capacity. Prospect: WVs and weather hazards can be monitored under all weather conditions by using UFO scanning radars and lidars??!!

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Research question

How does turbulence look like from the radar?

1 How can turbulence models be used for simulation of radar

measurements?

2 How does turbulence look like in polarimetric radar

measurements?

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The problem with radar turbulence retrievals

Radar Doppler spectral width / Radar Doppler mean velocity variance

σ2 v = σ2d+ σ02+ σ2α+ ζI2σ2T Assumption of homogeneous isotropic turbulence moderate turbulence ζ2 Iσ2T∝ σ2d, σ20, σα2 light turbulence ζ2 Iσ2T σ2d, σ02, σ2α strong turbulence ζ2 Iσ2T σ2d, σ02, σα2 large footprint ζI = 1 small footprint ζI = ? DSD DSD

turbulence intensity turbulence intensity turbulence intensity

turbulence too small to measure

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Next section

1 Introduction

2 Overview of turbulence models Stochastic turbulence models Parametric turbulence model 3 Simulation of radar observables

Zephyros

Inertia effect

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Overview of turbulence models

Stochastic turbulence models

• Random initialization.

• With given parameters, the outcome is always different.

• Different applications and complexity. Parametric turbulence model

• With the given parameters, the outcome is always the same.

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Stochastic turbulence models

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Stochastic turbulence models

Example (Careta and Sagues (1993))

• Start from auxilary random scalar, which is transformed to a divergence free 2D field. • Used for study

of diffusion processes.

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Stochastic turbulence models

Example (Mann (1998)) • 3D wind field, spectral tensor is used. • Used in wind engineering.

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Stochastic turbulence models

Example (Pinsky and Khain (2006))

• 2D windfield, obeys the continuity equation • Used for simulation of diffusion processes

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Stochastic turbulence models

Example (Oude Nijhuis et al. (2014))

• 1D windfield, large dynamic range (mm-km scale) • Used for turbulence intensity retrieval studies.

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Parametric turbulence models

Defining parameter: turbulence broadeningσT, which depends on

turbulence intensity,, and the radar resolution volume parameters.

Solutions to integrate it in the radar measurements:

1 Smearing/smoothening/broadening of spectra. [typical approach,

not considered]

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Parametric turbulence models

Ensemble of isotropic vectors

For each particle, an ensemble of isotropic vectors is used:

~vp,∗=~vterminal+~vair +~vturbulence,∗, (1)

where for each 3D unit direction ˆk∗,

vturbulence,∗ =σT

√

3ˆk∗. (2)

The average cross section is obtained by averaging over all directions: σ = 1

n X

σ(~vp,∗). (3)

• The particle symmetry axis (/minor axis) is parallel to vp,∗.

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Parametric turbulence models

Ensemble of isotropic vectors

For each particle, an ensemble of isotropic vectors is used:

~vp,∗=~vterminal+~vair +~vturbulence,∗, (4)

0.1 mm 1.0 mm 5.0 mm

light turbulence, σ = 0.1 ms−1_.

heavy turbulence, σ = 2.0 ms−1_.

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Overview of turbulence models

Reference Application Features

CA93 Diffusion processes 2D

MA98 Wind turbine engineering 3D

PI06 Droplet tracks 2D

CTM14 EDR retrievals 1D, scale

symmetric PA15 (ensemble of

isotropic vectors)

Radar observables No field sim-ulation.

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Next section

1 Introduction

3 Simulation of radar observables Zephyros

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Zephyros

• Zephyros is a software package under development for wind/turbulence simulation and retrieval.

• Development version publicly available on GIThub.

• Written mostly in C, bit of Fortran. Interfaces for Python/Matlab.

• Has fast mode for retrievals (small ensemble of scatterers) and slow mode (large ensemble, better accuracy) for simulations.

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Next section

1 Introduction

Zephyros

4 Simulated radar measurements Scanning radar

Staring radar

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Scanning radar

Details of the simulation

• Radar scans in the xy-plane.

• No noise is added.

• frequency 3.298 GHz radar (S-Band)

• EDR = 0.1 m2s−3. (very strong turbulence!)

• LWC = 1 gm−3, rain with gamma distribution parameters, µ = 5, D0 = 2mm.

• resolution volume parameters, FWHM = 2.1 ◦, range resolution 30 m.

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Scanning radar

Doppler mean velocities

CA93 MA98 PI06

CTM14 0.1 mm1.0 mm 5.0 mm light turbulence, σ = 0.1 ms−1. heavy turbulence, σ = 2.0 ms−1. PA15

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Scanning radar

Doppler spectral width

CA93 MA98 PI06

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Staring radar

• Radar staresalong the x line.

• EDR = 0.1 m2s−3. (very strong turbulence!)

• resolution volume parameters, FWHM = 2.1 ◦, range resolution 30 m.

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Staring radar

Doppler spectra for hh

CA93 MA98 PI06

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Polarimetric radar spectra

• Radar stares at 45 ◦ in the xz-plane.

• EDR is varied in the simulations.

• Range is 1 km, resolution volume parameters: FWHM = 2.1 ◦, range resolution 30 m.

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Polarimetric radar spectra

Polarimetric variables for Mann (1998)

[m2_s−3_] ₁₀−5 ₁₀−2 ₁₀−1

σv ,hh [ms−1] 0.750 0.802 9.67

dBZdr 0.601 0.631 0.668

dBLdr -67.3 -46.0 -37.7

• Zdr, Ldr and spectral width contain turbulence intensity information.

< ZDR >= dB(< ηhh> / < ηvv >) (5)

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Polarimetric radar spectra

Polarimetric variables for the parametric model [m2_s−3_] ₁₀−5 ₁₀−2 ₁₀−1

σv ,hh [ms−1] 0.750 0.847 1.14

dBZdr 0.597 0.589 0.555

dBLdr -63.5 -43.2 -36.4

• Parametric model reproduces the same dependencies as the stochastic model!

< ZDR >= dB(< ηhh> / < ηvv >) (7)

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Polarimetric radar spectra

hh Doppler spectrum

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Polarimetric radar spectra

specific Zdr

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Polarimetric radar spectra

specific Ldr

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Canting angles

canting angle spread

MA98 PA15 Experiment

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Inertia effect

Solution

The inertial velocity term~v0

p is assumed to be small in comparison to

the total particle velocity:

~vp=~vterminal +~vair +~vp0 (9)

The solution is found by solving the equations of motion for a backward small trajectorie:

dvp,z

dt = Fg − Fb− Fd ,z =ηI ,zv

2

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Inertia effect

Solution

µ = 5, = 10−2 _{µ = 5, D}

0= 5 mm

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Next section

1 Introduction

Zephyros

Inertia effect

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Conclusions

• Zdr and Ldr contain information on the turbulence intensity, which can be used in turbulence retrievals in precipitation. It depends however on the DSD.

• The inertia effect can alter the Doppler spectral width.

• A parametric model is found that can reproduce the features of radar measurements for stochastic turbulence.

• The parametric model implicitly reproduces the canting angle distribution.

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References

K.V. Beard, V.N. Bringi, and M. Thurai. A new understanding of raindrop shape. Atmospheric research, 2010. A. Careta and F. Sagues. Stochastic generation of homogeneous isotropic turbulence with well-defined spectra. physical

review E, 1993.

R. J. Doviak and D. S.. Zrnic. Doppler radar and weather observations second edition. 2006. J. Mann. Wind field simulation. Prob. Eng. Mech., 1998.

A.C.P. Oude Nijhuis, C.M.H. Unal, O.A. Krasnov, H.W.J. Russchenberg, and A. Yarovoy. Simulation of atmospheric turbulence: Fractal turbulence. Poster presentation at the 21st Symposium on Boundary Layers and Turbulence, 2014.

M. Pinsky and A. Khain. A model of a homogeneous isotropic turbulent flow and its application for the simulation of cloud drop tracks. Geophysical & Astrophysical Fluid Dynamics, 2006.

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The end

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Backup slides: Radar filter

Radar filter

1 User input: drop size distribution, atmospheric temperature

profile, parameters that characterize the radar.

2 Dividing resolution volume in subvolumes. The resolution

volume is divided into equally weighted subvolumes.

3 Coordinate transformations BEAM → AZEL → ENU.

4 Interpolation of user input For each subvolume, the user input

that is required is interpolated.

5 Radar cross sections are calculated for each subvolume and for

each particle.

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Backup slides: Radar filter

Radar filter

The weather radar equation can be written as (details_{→ Doviak and} Zrnic (2006)): < P∗(r0)>= Cr r2 0 η∗, (11)

where< P∗ > is the expected received power, Cr a radar constant, r0

the range at the resolution center andη∗ the reflectivity. The

reflectivity,η∗ is defined as:

η∗=

Z

Ω

σ∗(De)N(De)dDe, (12)

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Backup slides: Radar filter

Radar filter radar reflec-tion < η∗>= X i η∗,i n reflectivity factor < Z∗>= 10· log10( λ4 _{< η} ∗ > π5_|K w|2 ) Doppler ve-locity < v∗,D >= X i η∗,i n vD,i . < η∗ > Doppler spectral width < σ2 v ,∗,D >= X i η∗,i n (vD,i− < v∗,D >) 2._{< η} ∗ > differential reflectivity < ZDR >= 10· log10(< ηhh > / < ηvv >) depolarisation ratio < LDR >= 10· log10(< ηhv > / < ηvv >)

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Backup slides: Radar filter

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Backup slides: Radar filter

Radar filter specific differential phase < KDP >= 103λ Z ∞ 0 Re(S_hhf − Sf vv)N(De)dDe

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Backup slides: Radar filter

Radar filter, spectra Doppler spectrum < η∗,1,2>= X i ,v1<vD,i<v2 η∗,i n /(v2− v1) specific dif-ferential re-flectivity < ZDR,1,2>= 10· log10(< ηhh,1,2> / < ηvv ,1,2>) specific de-polarization ratio < LDR,1,2>= 10· log10(< ηhv ,1,2 > / < ηvv ,1,2>) specific cor-relation co-efficients < ρ1,2 >= “· · · ·00 for v1< vD,i < v2