1. Carpe Diem 2nd Meeting-Barcelona1 CARPE DIEM University of Essex Anthony HoltDavid BebbingtonMartin Fleury Stephan Siemen + ……+ …….. Second Meeting: Barcelona 12-13 June 2002

2. Carpe Diem 2nd Meeting-Barcelona2 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?

3. Carpe Diem 2nd Meeting-Barcelona3 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 u baseline Divergence condition enables 3-D field to be recovered by integration given boundary conditions Divergence condition enables 3-D field to be recovered by integration given boundary conditions

4. Carpe Diem 2nd Meeting-Barcelona4 Dual Doppler in PADRE Project SMR San Pietro Capofiume CSIM Teolo (PD) 80km

5. Carpe Diem 2nd Meeting-Barcelona5 Dual Doppler Synthesis Dual Doppler windfield slice at 1.5 km using NCAR CEDRIC (R.J. Watson Thesis 1996)

6. Carpe Diem 2nd Meeting-Barcelona6 WP6 - Anomalous Propagation Apparent elevation M(z) z Strong surface ’reflectivity’  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

7. Carpe Diem 2nd Meeting-Barcelona7 Application design outline & principles GUI (Tcl/Tk) F90 Application NWP fields (p,T,q) ( , ,q) PostScript Interpreter Fields, Anaprop image, etc DEM, Coastlines, Radar +wind (ghostscript) Application designed for portability. Only F90/C interface to PS interpreter non standardized. Parallel version under Linux. Basic version Windows 95/8, Linux O/p data I/p data Driver/interfaces

8. Carpe Diem 2nd Meeting-Barcelona8 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) = 10 6 (m-1) Solutions advanced between adjacent coordinate planes. Wavefront sampling must be dense to avoid aliasing: O(100 m) < /2 per sample zz Equation becomes 1st order ODE in Fourier z  p domain: O(1 m)

9. Carpe Diem 2nd Meeting-Barcelona9 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 surfaces for which stationary phase points can be determined will do. The hybrid method generates surfaces orthogonal to local ray trajectories - surfaces that are very nearly parallel to the wave front. Phase aliasing is avoided, resulting in order of magnitude reduction in wavefront sampling The hybrid method generates surfaces orthogonal to local ray trajectories - surfaces that are very nearly parallel to the wave front. Phase aliasing is avoided, resulting in order of magnitude reduction in wavefront sampling Approximate wavefront Ray trajectories predict approx. positions of the wavefronts. Key calculations are phase integrals which over short paths can be very accurately obtained using end-point values for refractive index. M(a) M(b) d (because of stationarity)

10. Carpe Diem 2nd Meeting-Barcelona10 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) spacing of NWP gridpoints Vertical profile o(100m) NWP Levels are not spatial -  coordinates. Ray plane M(z)

11. Carpe Diem 2nd Meeting-Barcelona11 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.

12. Carpe Diem 2nd Meeting-Barcelona12 Sampling Refractive index jumps are not well sampled in model - we deal with this by parametrizing a smooth function (tanh-like) in critical ranges. Add more interpolation knots near ‘jump’ Discontinuity parametrization should be stable over large areas

13. Carpe Diem 2nd Meeting-Barcelona13 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 scatter modelling and understanding parameter sensitivity.