Carpe Diem 2nd Meeting-Barcelona 1

CARPE DIEM

University of Essex

Anthony Holt David Bebbington Martin Fleury

Stephan Siemen + ……+ ……..

Second Meeting: Barcelona 12-13 June 2002

Carpe Diem 2nd Meeting-Barcelona 2

Work packages

WP2 - Doppler Windfields

Post advertised for Research Officer - expect split between S. Siemen + applicant (with relevant experience)

Robert Watson occasional consultant in resurrection of software etc.

Polarization Review

- Anthony Holt (with some help from D.B.) has draft form of much of report. In next weeks hopes to be in university to access references etc. Ready end July?

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WP2 - Doppler Windfields

Dual Doppler Synthesis

3-D windfields may be retrieved using near simultaneously scanned Doppler from two radars in overlap away from baseline.

Dual Doppler Synthesis

3-D windfields may be retrieved using near simultaneously scanned Doppler from two radars in overlap away from baseline.

co-plane

r1 r2

u1 1

2 2

ˆ. ,

ˆ.

. 0

u r u

u r u

u

baselineDivergence conditionenables 3-D field tobe recovered by integrationgiven boundary conditions

Divergence conditionenables 3-D field tobe recovered by integrationgiven boundary conditions

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Dual Doppler in PADRE Project

SMRSan Pietro Capofiume

CSIMTeolo (PD)

80km

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Dual Doppler Synthesis

Dual Doppler windfield sliceat 1.5 km using NCAR CEDRIC

(R.J. Watson Thesis 1996)

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WP6 - Anomalous Propagation

Apparent elevation

M(z)

z

Strong surface’reflectivity’

dm

s dz

Progress

• purchase multiprocessor machine• update basic F90 code• write/update ABL physics code• top level design of application

In progress

• decide OMP compiler• recruit new RA

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Application design outline & principles

GUI(Tcl/Tk) F90

Application

NWP fields

(p,T,q)

(,,q)

PostScriptInterpreter

Fields,Anaprop image, etc

DEM,Coastlines,

Radar

+wind

(ghostscript)

Application designedfor portability.

Only F90/C interfaceto PS interpreter nonstandardized.

Parallel version underLinux. Basic versionWindows 95/8, Linux

O/p data I/p dataDriver/interfaces

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Parabolic equation methods: PEM

‘Split-step’ parabolic equation methods allow efficient numerical solution of radar wave field in atmosphere with stratified RRI M(T,q) = 106 (m-1)

Solutions advanced between adjacent coordinate planes. Wavefront sampling

must be denseto avoid aliasing:

O(100 m)

</2 per sample

2

20 2

0

12 1

2m k

x ik z

z

Equation becomes1st order ODE inFourier zp domain:

O(1 m)

2

0

( )

( ( 1 ) ) ( )2

x x

pexp i k m x x

k

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Hybrid method: Ray/PEM

It can be shown that the methodology for the PEM applies Huyghens’principle with stationary phase integration. The constructed field closely fulfills Green’s Theorem applied to the Helmholtz equation.

It is not necessary to select coordinate planes: any series of surfacesfor which stationary phase points can be determined will do.

The hybrid method generatessurfaces orthogonal to localray trajectories - surfaces thatare very nearly parallel to thewave front.

Phase aliasing is avoided, resulting in order of magnitudereduction in wavefront sampling

The hybrid method generatessurfaces orthogonal to localray trajectories - surfaces thatare very nearly parallel to thewave front.

Phase aliasing is avoided, resulting in order of magnitudereduction in wavefront sampling

Approximate wavefront

Ray trajectories predictapprox. positions of thewavefronts.

Key calculations arephase integrals whichover short paths can bevery accurately obtainedusing end-point valuesfor refractive index.

M(a) M(b)d

1. ( ) ( )

2M ds M a M b d

(because of stationarity)

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Interpolation Issues

Refractive index must be computed efficiently as a continuous or smooth function of position, interpolated in horizontal and vertical.

Plan view o(10km) spacingof NWP gridpoints

Vertical profile o(100m)

NWP Levels are not spatial - coordinates.

Ray plane

M(z)

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Proposed method

1. Hermite bicubic or cubic by quadratic interpolation

Flexible and efficient in storage and time.

2. Retain coordinates:

(a) rays can equally be computed in an arbitrary coordinate system

(b) the field propagation involves phase integrals between arbitrarily located points

(c) jumps in thermodynamic variables will tend to follow the h coords.

3. Height similarity scaling near coastal boundaries

Features in boundary layer scale with distance from coast- mitigates grid-undersampling of coastal features.

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Sampling

Refractive index jumps are not well sampled in model - we deal withthis by parametrizing a smooth function (tanh-like) in critical ranges.

Add more interpolationknots near ‘jump’

Discontinuity parametrization should be stable over large areas

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Summary

No major problems so far.

Most of infrastructure is in place.

Research Officer recruitment to take place ASAP.

Next efforts on transcribing NWP data in suitable form.

Most of anticipated effort in terrain/sea surface scattermodelling and understanding parameter sensitivity.