2006/4/13 中尺度氣象學 ii real-time retrieval of wind from aliased velocities measured by...

2006/4/13 II中尺度氣象學

Real-Time Retrieval of Wind from Aliased Velocities Measured by Doppler radars

Hochin Chang

Tarary, P. and, G. Scialom, 2001: Real-time retrieval of the wind from aliased velocities measured by Doppler radars. J.Tech, 18, 875-881

2006/4/13 II中尺度氣象學

Outline

• Introduction– Aliasing– Nyquist velocity

• Method– VAD– Modified VAD

• Result• An operational application of the algorithm• Concluding Remarks

2006/4/13 II中尺度氣象學

Introduction

• Doppler radar measurements provide the radial wind within an unambiguous interval due to the limited value of the sampling frequency ( pulse repetition frequency )

2006/4/13 II中尺度氣象學

Introduction

• unambiguous range and unambiguous velocity

2

4

8

sa

as

a a

cTr

v Tcr v

2006/4/13 II中尺度氣象學

Introduction

• There are two directions to overcome this difficulty, that is , to dealias velocity measurements.– It is possible to increase nyquist velocity by alte

rnatively using to different PRF.– To build algorithms in order to put a posteriori

Vr in the right interval by continuity on the measurements.

2006/4/13 II中尺度氣象學

2006/4/13 II中尺度氣象學

Method

• VAD (Velocity Azimuth Display)

00 0

00 0

u uu u x yx y

v vv v x yx y

2006/4/13 II中尺度氣象學

Browning and Wexler, 1968

0 1 1

2 2

cos sincos 2 sin 2

rV a a ba b

2006/4/13 II中尺度氣象學

cos sincos cos

x ry r

T

x y zVr u v w vr r r

2006/4/13 II中尺度氣象學

00 0

00 0

u uu u x yx y

v vv v x yx y

cos sincos cos

x ry r

Tx y zVr u v w vr r r

0 1 1

2 2

cos sincos 2 sin 2

rV a a ba b

2006/4/13 II中尺度氣象學

0 1 1

2 2

cos sincos 2 sin 2

rV a a ba b

2

00 0

1 0

1 0

2

20 0

2

200

cossin2

cossin

cos2

cos2

Tr u va w v

x y

a vb u

r u vax y

r u vby x

2006/4/13 II中尺度氣象學摘自 Deng (1985)

時間

高度

2006/4/13 II中尺度氣象學

Modify VAD

• In the classical VAD analysis, a major requirement is that radial velocities have to be corrected for alising.

• This is the reason why to propose a modified version of the VAD analysis that can be applied to raw, that is , possibly aliased data.

2006/4/13 II中尺度氣象學

2006/4/13 II中尺度氣象學

Modify VAD

1 1

1 0

1 0

cos sin

coscos

rV a b

a ub v

2

00 0

1 0

1 0

cossin2

cossin

Tr u va w v

x y

a vb u

0 1 1 2 2cos sin cos 2 sin 2rV a a b a b

2006/4/13 II中尺度氣象學

Modify VAD

0 0

2

0 021

,

1 cos cos sin minqN

rq q q

q q

J u v

V u v

1 1

1 0

1 0

cos sin

coscos

rV a b

a ub v

2006/4/13 II中尺度氣象學

Modify VAD

• Select all data Mq of the sweep with the same gate number as M and with azimuth between θq+Δθ,and θ-Δθ,where Δθ is the half width of the angular search window.

2006/4/13 II中尺度氣象學

Modify VAD

• Reject all data Mq with radial velocity outside the Vr-ΔVr and Vr+ΔVr where ΔVr is the nyquist velocity.

2006/4/13 II中尺度氣象學

Modify VAD

• If the number of remaining data is sufficient, fit the resulting dataset to a straight line ( Vr =αθ+β)

• The slope is rV

2006/4/13 II中尺度氣象學

Modify VAD

• Estimate the quality of the fit σ by calculating the dispersion of the data around the straight line

0 0

2

0 021

,

1 cos cos sin minqN

rq q q

q q

J u v

V u v

2006/4/13 II中尺度氣象學

Results

• 0300 UTC 20 Sep 1999 • Mesoscale Alpine Program IOP#2• French C-band Doppler radar Ronsard • San Pietro Mosezzo in the southern forela

nd of the Alps.

2006/4/13 II中尺度氣象學

2006/4/13 II中尺度氣象學

Vertical profiles of the horizontal wind direction (a) and intensity (b).Diamonds mean classical VAD analysis to previously dealiased radial velocities and stars mean application of the method to raw radar data.

2006/4/13 II中尺度氣象學

An operational application of the algorithm

• Implementation– A similar VAD algorithm is operational at the th

ree radar sites of MeteoSwiss since August 1998

– It relies on exactly the same idea, but the calculation of derivative is somewhat simpler.

• Quality control

2006/4/13 II中尺度氣象學

Concluding remarks

• A method based upon a modified VAD analysis that provides an estimate of the wind profile directly from the raw( possibly aliased) radial velocities.

• The basic idea of the method is to estimate empirically the local azimuthal derivative of the radial velocity at each measurement and to perform a VAD analysis with that parameter instead of the radial velocity.

2006/4/13 II中尺度氣象學

Concluding remarks

• An illustration of the performance of the method has been carried out on a real case of the MAP Experiment ( 0300 UTC 20 Sep 1999) using data from the French C-band Ronsard radar.

• Difference in terms of wind speed and direction between the modified and classical VAD analysis are smaller than 10%.

2006/4/13 II中尺度氣象學

Concluding remarks

• A similar method has been implemented on Swiss C-band radar network in August 1998.

The End