A melting layer model investigated using doppler spectra

Phys. Chem. Earth (B), Vol. 25, No. 10-12,

Pergamon

pp. 1069-1071,200O

0 2000 Elsevier Science Ltd 1464- 1909/00/$

All rights reserved - see front matter

PII: Sl464-1909(00)00154-4

A Melting Layer Model Investigated Using Doppler Spectra M. D’Amico, C. Capsoni and R. Nebuloni DEI, Politecnico Received

di Milano,

Piazza L. Da Vinci 32, Milan0

14 June 2000; accepted

20133, Italy

30 June 2000

Abstract. The effects of the melting layer on the propagation of electromagnetic waves are of concern for the radar and remote sensing communities; a new microphysical model of the melting layer developed at Politecnico di Milan0 has been recently integrated into a physically-based radar simulator, a software tool that is able to generate accurate synthetic radar signal in the time domain, by solving the radar equation over a synthetic meteorological environment. In this work we first illustrate the melting layer model; we then describe its integration into the physically-based radar simulator; we eventually report the results of first comparisons of synthetic Doppler spectra, generated through the improved radar simulator, with those collected (with vertical pointing) in late 1999 by an S-band Doppler radar located near Milano, Italy. 0 2000 Elsevier Science Ltd. All rights reserved. 1

trical, and meteorological parameters of the “virtual” radar system and environment; from this stream of virtual radar samples it is possible to evaluate the complete spectral and statistical properties of the radar echo; the melting layer model in its original formulation, on the contrary, is able to predict only time-averaged quantities (i.e. radar reflectivity Z, mean Doppler velocity Vd, etc.). In this work we report the first comparisons of synthetic Doppler spectra, generated through the improved radar simulator, with that measured by our S-band Doppler radar.

2

The radar

data set

The data presented here have been collected by the meteorological S-Band radar located near Milano, Italy. The radar operates at 2.8 GHz, with a peak power of 500 kW and a PRF of 500 or 1000 Hz. The duration of the transmitted pulses is 0.5 psec, corresponding to radar bin sizes 75 metres in length. The receiver has both a logarithmic and a linear IF chain; LOG, I and Q samples are simultaneously available for “conventional” and Doppler operation. The antenna is a parabolic reflector 3.6 metres in diameter, corresponding to a beamwidth of 2 degrees. Since a fast TR is employed, the first useful1 radar cell is only 350 metres away from the radar.

Introduction

The melting layer is the region of the atmosphere just below the 0°C isotherm level, where ice and snow hydrometeors turn into water drops. The effects of the melting layer on the propagation of electromagnetic waves are of concern for the radar and remote sensing communities; this current interest is testified by the development of several models, recently published in the open literature (Zhang W., 1994) (Russchenberg H.W.J., and L.P. Ligthart, 1996). A new microphysical model of the melting layer (D’Amica M., A. R. Holt, and C. Capsoni, 1998) has been recently integrated into a physically-based radar simulator (Capsoni C., and M. D’Amico, 1998) developed at Politecnico di Milano, a software tool that is able to generate accurate synthetic radar signal in the time domain, by solving the radar equation over a synthetic meteorological environment. The radar simulator generates radar samples on pulseby-pulse basis, taking into account geometrical, elec-

The data set used in this work has been collected on November 6th, 1999, at 19:33:50 IJTC, with the radar pointing vertically; 2048 adjacent samples of LOG, I and Q from 134 radar cells were gathered, corresponding to a maximum observation range of about 10 km and a total observation time of about 4 seconds (the PRF being 500 Hz). The acquired samples have been stored on disk for off-line processing. The LOG channel has been used to evaluate radar reflectivity Z; the mean Doppler velocity has been esti1069

M. D’Amico et al.: A Melting Layer Model

1070

21.9. 1.8. 1.7. E1.6_ Y s1.5. .o, 21.4. 1.3. 1.2. 1.1. 55

1. 0

5 Doppler velocity, m/s

10

Fig. 1. Vertical profiles of reflectivity and mean Doppler velocity; continuous line is measured data, dashed line is model

mated from the I and Q samples by applying a pulsepair algorithm. The I and Q samples have been also processed to obtain - through an FFT - the complete Doppler spectra, calculated over 64 frequency points; raw data have been Hanning windowed to reduce truncation effects. The measured vertical reflectivity profile is shown in Fig. 1 as a continuous line; the peak of the bright band is located at about 1650 metres of height; the measurements show a reflectivity enhancement (AZ) in the melting layer of about 9.5 dB, with respect to the reflectivity in the rain region underneath. The measured vertical profile of Vd is also shown in Fig. 1, as a continuous line; as theoretically expected, from the onset of the melting process (estimated to happen at about 2000 metres of height) there is a steady increase of the mean fall velocity.

3

Simulations and comparisons

determined from the melted fraction. The melting later model has been integrated into a physical radar simulator (Capsoni C., and M. D’Amico, 1998), that generates a synthetic meteorological environment, simulates the transmission of an electromagnetic pulse, and solves the monostatic radar equation (Doviak R.J. and D.S. Zrnid, 1993), producing the stream of samples coming out of the “virtual” receiver. The synthetic external meteorological environment is generated as follows: the radar bin is located in space according to the antenna pointing, to the characteristics of the transmitted signal and to the receiver IF filter. In particular, its angular extension depends on the antenna directivity function, while the radial extension is evaluated taking into account, through the range weighting function, the duration of the transmitted pulse and the receiver finite bandwidth. Once the position and dimensions of the radar resolution bin have been established, the synthetic meteorological environment is generated, by distributing hydrometeors randomly and uniformly in the radar bin. The monostatic radar equation is then solved on this synthetic environment. Successively the position of the hydrometeors is updated: knowing the fall speed of the different hydrometeors it is possible to evaluate the change in their position after a time interval, equal to the pulse repetition period. The melted fraction is then calculated for the new height. Should a particle leave the radar bin during its fall, it will be replaced by a particle of the same mass, entering the radar bin from the upper boundary, in a random position. The model requires a very limited number of input parameters, i.e. the value of reflectivity in the rain region (41 dBZ in this case) and the “equivalent initial density” pa, that can be obtained from the reflectivity enhancement AZ (dB) using the simple relation proposed in (Goddard J.W.F., and M.M.G. D’Amico , 1993), and reported here for convenience: log,,(po)

The melting layer model (D’Amico M., A. R. Holt, and C. Capsoni, 1998) is built around the thermodynamic equations by Ekpenyong B.E., and R.C. Srivastava (1970); the melting particles are modeled as spheroids, and their ellipticity is assumed to be dependent on their degree of melting. Their canting angle is assumed to be uniformly distributed in a range of values whose spread is dependent on the melted fraction (i.e. on the quantity of liquid water with respect to the total mass of the particle). Please note that, since we are interested here in copolar measurements collected with vertical pointing, particles’ shape is of minor impact. The electromagnetic properties are evaluated assuming the particles to be composed of a uniform mixture of air and ice in a water matrix whose mixing ratios are

= 0.00033.

AZ2 - 0.076 . AZ - 0.046

(1)

In this case we obtain p0=0.18 g cmb3. The predicted reflectivity and mean Doppler velocity profiles are depicted as dashed lines in Fig. 1. The agreement between measured and predicted vertical profile of Z is quite good; there is a small discrepancy between measured and predicted vertical profile of Vd at the top and bottom of the melting layer; however, this difference is always smaller than 1 m s-l. More information can be inferred from the analysis of the spectral properties of the received echoes; Figures 2 and 3 show the measured Doppler spectra (solid lines) at 1650 and 1050 metres of height, normalized to their maximum value (0 dB), together with the predicted spectra (dashed lines).

M. D’Amico et al.: A Melting Layer

Height: 1650 metres 0

1

-301 0

5

15

20

Doppler v1Bqbcity,m/s Fig.

2. Doppler spectra of fall velocity, at 1650 metres of height;

continuous

line is measured data, dashed line is model

Fig.

0

Conclusions

A new model of the melting layer has been integrated into a physically-based radar simulator; the predicted radar quantities have been compared with those measured by a vertically-pointing S-band Doppler radar; in particular, the pulse-to-pulse time series have been analysed to yeld the full Doppler spectra. An encouraging agreement between predicted and measured quantities has been found, in spite of the very limited number of input parameters requested by the model. The results of these first comparisons represent a significant step forward for the full assessment of the applicability of the model.

-25 -

-30

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fall faster than larger, low-density, partially-melted particles. Another possible explanation is the presence of some turbulence, whose recognized effect is spectrum broadening. Unfortunately, we have no in-situ evidence to support our deductions, At 1050 metres (Fig. 3) we are at the very bottom of the melting layer, in the rain region. The measured spectrum is quite wide, spanning the velocity range 6 to 11 m s-l (at -10 dB). The predicted spectrum shown in Fig. 3 as a dashed line has been shifted right by 1 m s-i, to compensate for the observed offset in the mean Doppler velocity; once this offset has been compensated for, both width and shape of the predicted spectrum agree very well with that measured. This agreement supports the hypothesis that a downdraft, associated with the precipitation below the melting layer, could be responsible for the offset. Unforin-situ tunately, again, we can bring no experimental evidence of such a downdraft.

4

Height: 1050 metres

Model

5

10 Doppler Velocity, m/s

15

20

References

3. As Fig. 2, but for the rain region at 1050 metres of height

As a preliminary consideration, the measured data show a plateau of noise around -20 dB, that naturally doesn’t exist in the synthetic data. In order to make consistent comparisons, we have added white noise to the synthetic data; we have found that a S/N ratio of 10 dB corresponds to the best agreement with measurements. At 1650 metres of height the radar bin is centered around the reflectivity peak. The measured Doppler spectrum (Fig. 2) is quite narrow: the largest quota of energy is within the range 3 to 5.5 m s-l (at -10 dB), with an average fall velocity of 4 m s-i. The predicted spectrum agrees reasonably well with that measured, being just slightly narrower on the high velocities side. This discrepancy could be due to the presence of a higher number of high-density, almost-melted particles than that predicted by the model; those particles would

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