Microphysical parameters retrieval of rainfall using a Ka band and VHF band radars in the central Andes of Peru

Jairo M. Valdivia1, Danny E. Scipión1 and Yamina Silva1

1 Instituto Geofísico del Perú (IGP), Perú.

Abstract

Instrumentation

Methodology

MIRA 35C

Ka band radar @34.85GHz

Monoestatic – pulsed – magnetron

Beam width, 0.6°

Peak power 2.5 kW

Single polarization

Time resolution, 6s

Range resolution, 31 m

Range, 0.2 – 13 km

PARSIVEL2 can measure the drops

size and velocity, using a laser

sheet. Data is recorded each

minute.

PARSIVEL2

Optical disdrometer

OTT

Figure 3.. From left to right, PARSIVEL2 photograph at Huancayo Observatory, PARSIVEL structure scheme, disdrometer basis scheme

Figure 1. Left, cloud radar profiler MIRA 35c. Right, picture of radar at Huancayo Observatory

• Bohren, C. F., & Huffman, D. R. (1983). Absorption and scattering of light by small particles. John Wiley & Sons.

• Gunn, R., & Kinser, G. D. (1949). The terminal velocity of fall for water droplets in stagnant air. Journal of Meteorology, 6(4), 243–248.

• Foote, G. B., & Du Toit, P. S. (1969). Terminal Velocity of Raindrops Aloft. Journal of Applied Meteorology, 8(2), 249-253.

Results y Conclusions

References

Figure 4. Study case of 26th September 2017. Axis: time vs range vs reflectivity a) MIRA 35C @35

GHz, b) CLAIRE @445 MHz.

Main motivation of this work is to achieve a correct quantification of hydrometeors of precipitations, and clouds. For this, we used a Ka band radar (MIRA 35C) and VHF band located at Laboratory of Atmopheric Microphysics And Radiation (LAMAR) of Huancayo Observatory, at 3300 m.a.s.l.; this information can be used to improve other methodologies, such as satellite estimates and numerical modeling. In this work, the microphysical parameters of rainfall are obtained calculating the raindrop size distribution from the Doppler spectrum, where the drop fall velocity is related to its size, and the droplet density for a given size is calculated using spectral reflectivity and Mie's theory; the other microphysical parameters are derived from the drop size distribution, and evaluated with in situ observed data.

CLAIRE – Turbulence and precipitation radar

• VHF band @ 445 MHz

• 3 Antennas 1 Tx. – 2 Rx.

• Peak power 5 kW

• Beam width 9.46°

• Time res. 20 s

• Range res. 37.5 m

• Range 10 km

Figure 2. CLAIRE. Left, reception antenna photograph. Right, 3D model of antennas.

We are using the Doppler radars at vertical incidence, the Doppler frequency shift arises from raindrops vertical velocity, 𝑣. 𝑣 is expressed by 𝑣 = 𝑣𝑡 + 𝑤 , where 𝑣𝑡 is the drop terminal velocity in still air and 𝑤 is the air motion; in this work we assuming that air is motionless. For both radars the spectral reflectivity 𝜂 𝑓 as function of Doppler frequency f is obtained by

𝜂 𝑓, 𝑟 = 𝑝 𝑓, 𝑟 . 𝐶. 𝑟2 where C is radar constant. The DSD is given by,

𝑁 𝐷, 𝑟 ∆𝐷 =𝜂 𝐷, 𝑟

𝜍(𝐷)∆𝐷

where 𝑁 𝐷, 𝑟 is the spectral density of drops at height r and 𝜂 𝐷, 𝑟 is the spectral backscattering cross section volume. The back scattering cross

section of a single particle, 𝜍(𝐷), is calculated using Mie scattering theory, (Bohren and Huffman, 1983). Drop diameter is calculated using the Gunn and Kinzer (1949) equation:

𝐷 𝑣, 𝑟 = 1

0.6ln

10.3

9.65 − 𝑣/𝛿(𝑟)

The height dependence of the terminal fall velocity due to change in air density, 𝛿(𝑟), is approximated as a second-order polynomial (Foote and Du Toit, 1969). From DSD different rain parameters are calculated:

𝑍 = ∫ 𝑁 𝐷 𝐷6𝑑𝐷 𝐿𝑊𝐶 = 𝜌𝑤(𝜋/6)∫ 𝑁 𝐷 𝐷3𝑑𝐷

𝑅 = (6𝑥105 𝜋)∫ 𝑁 𝐷 𝑣(𝐷)𝐷3𝑑𝐷 As CLAIRE is sensitive to air spectra, we need to separate rain echoes before.

We calculate the microphysical parameters for a event case of 26 September 2017. The event is shown in Fig. 4 by both radars. We computed DSD for the different instruments (Fig. 5) where the drop diameters seems very similar, but we found differences in the drops density. PARSIVEL2 has more concertation of drops (i.e. more drops density), this does not affect the reflectivity considerably (see Fig. 7). If we compute the cumulative rainfall from DSD, all instrument underestimate the observed rainfall (i.e. less than rain gauge) as we can see in the Fig. 7. Each instrument has different errors. The radars need a better calibration and attenuation correction. We don’t know the reason for the underestimation PARSIVEL2.

Figure 5. Drops size distribution (DSD) for Fig. 4 event. Axis: Time vs drop size vs drop density a)

PARSIVEL2, 1 m Above Ground, b) MIRA 35C, 250 m AG, c) CLAIRE, 750 m AG.

Figure 6. Cumulative rainfall, lines represents cumulative sum and bar 30 min cumulates for

rain gauge (green), PARSIVEL2 (black), MIRA 35C (blue) and CLAIRE (red).

Figure 7. Comparison of reflectivity retrieved for Fig. 4 event in nearest to ground same data.

PARSIVEL2 1 m Above Ground (black), MIRA 35C 250 m AG (blue) and CLAIRE 750 m AG (orange).

a

b

a

b

c

Fin

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Acknowledgement: