6
MULTIPARAMETER RADAR TECHNIQUES FOR RAINFALL RATE MEASUREMENTS G. Galati, E. Gorgucci , M. Naldi , G. Pavan , G. Scarchilli 1. INTRODUCTION The rainfall rate measurements by weather radar provide important information to many Human activities. In fact the use of the radar allows a high temporal and spatial resolution of the precipitation. A different sensor, like a raingauge, is not capable to provide a suitable resolution unless a very large number of devices are used. In addition measurements at large scale are only possible by a radar system. The main radarmeteorology applications are in: hydrology (to evaluate possible flood phenomena), agriculture (to support farmer decision), air traffic control (to better manage flights and to avoid possible crashes) and finally telecommunication (to analyse propagation aspects). In all previous activities it is important to know the rainfall rate r. Different techniques can be applied to extract the parameter r. The most recent techniques are analysed and the relevant features are described in this paper. 2. RAINFALL RATE ESTIMATION The rainfall rate r can be obtained as solution of the following integral equation: r=0.6-10-3x joDmN(D)D3 v(D) dD [nun h-11 where D is the raindrop equivolumetric diameter (mm), N(D) is the Drop Size Distribution (DSD) (me3 mm-') i.e. the number of raindrops per unit volume and v(D) is the fall speed of the hycirometeors (mm s-l) which can be expressed as v(D) = 3.778 [ 11. Analytical models and experimental measurements have shown that the natural variations in the DSD can be suitably described by a Gamma distribution [2]: N(D) = N,D~ exp ( - - 3'6i:p D] [m-3 mm-'1 Do represents the medlan volume dlameter: JOD0D3 N(D)dD=J: D3 N(D)dD 0 (3) The eqn. (1) is generally independent by the used sensor provided that N(D) is known. When a radar is employed it is necessary to relate the rainrate with the parameters measured by the sensor. These last ones, named radar osservables, can be divided in two types: those related to the backscatter phenomena (ZH, Z , , ZD,, 6) and osservables from the forward scatter phenomena (AH, A, QDP, KDP). 'The meaningful parameters are reported in the following. Refectiviry factor: G. Galati. M. Naldi and G. Pavan are uith Centro Vito Volterra and the Dep. of Electr. Engeneeting, Tor Vergata University, Rome E. Gorgucci and G. Scarchilli are with the National Council of Research (Institute for Atmosphc~c Physics), Rome 0 1995 The Institution of Electrical Engineers. Printed and published by the IEE. Savoy Place, London WC2R OBL, UK.

[IEE IEE Colloquium on Radar Meteorology - London, UK (24 Feb. 1995)] IEE Colloquium on Radar Meteorology - Multiparameter radar techniques for rainfall

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Page 1: [IEE IEE Colloquium on Radar Meteorology - London, UK (24 Feb. 1995)] IEE Colloquium on Radar Meteorology - Multiparameter radar techniques for rainfall

MULTIPARAMETER RADAR TECHNIQUES FOR RAINFALL RATE MEASUREMENTS

G. Galati, E. Gorgucci , M. Naldi , G. Pavan , G. Scarchilli

1. INTRODUCTION The rainfall rate measurements by weather radar provide important information to many Human activities.

In fact the use of the radar allows a high temporal and spatial resolution of the precipitation. A different sensor, like a raingauge, is not capable to provide a suitable resolution unless a very large number of devices are used. In addition measurements at large scale are only possible by a radar system.

The main radarmeteorology applications are in: hydrology (to evaluate possible flood phenomena), agriculture (to support farmer decision), air traffic control (to better manage flights and to avoid possible crashes) and finally telecommunication (to analyse propagation aspects).

In all previous activities it is important to know the rainfall rate r. Different techniques can be applied to extract the parameter r. The most recent techniques are analysed and the relevant features are described in this paper.

2. RAINFALL RATE ESTIMATION The rainfall rate r can be obtained as solution of the following integral equation:

r=0.6-10-3x joDmN(D) D3 v(D) dD [nun h-11

where D is the raindrop equivolumetric diameter (mm), N(D) is the Drop Size Distribution (DSD) (me3 mm-') i.e. the number of raindrops per unit volume and v(D) is the fall speed of the hycirometeors (mm s-l) which can be expressed as v(D) = 3.778 [ 11. Analytical models and experimental measurements have shown that the natural variations in the DSD can be suitably described by a Gamma distribution [2]:

N(D) = N , D ~ exp ( - - 3'6i:p D] [m-3 mm-'1

Do represents the medlan volume dlameter:

JOD0D3 N(D)dD=J: D3 N(D)dD 0

(3)

The eqn. (1) is generally independent by the used sensor provided that N(D) is known. When a radar is employed it is necessary to relate the rainrate with the parameters measured by the sensor. These last ones, named radar osservables, can be divided in two types: those related to the backscatter phenomena (ZH, Z,, ZD,, 6 ) and osservables from the forward scatter phenomena (AH, A,, QDP, KDP). 'The meaningful parameters are reported in the following. Refectiviry factor:

G. Galati. M. Naldi and G. Pavan are uith Centro Vito Volterra and the Dep. of Electr. Engeneeting, Tor Vergata University, Rome E. Gorgucci and G. Scarchilli are with the National Council of Research (Institute for Atmosphc~c Physics), Rome

0 1995 The Institution of Electrical Engineers. Printed and published by the IEE. Savoy Place, London WC2R OBL, UK.

Page 2: [IEE IEE Colloquium on Radar Meteorology - London, UK (24 Feb. 1995)] IEE Colloquium on Radar Meteorology - Multiparameter radar techniques for rainfall

where Z,, Z, and oH, ov represent the reflectivity factors and radar cross sections at horizontal (H) and vertical (V) polarisation, respectively; h is the wavelength and K = (m2-l)/(m2+2), nith m2 the compiex refiacion index of water. Diferential Reflectiviy ZDR:

Intrinsic Diferential Phase cDDP (due to one-way propagation)

0 D p = J o R c ~ D p ( ~ ) a Wgl (6)

where R, is radar range to the observation cell, while K, is the Specific Differential Phase given by:

(7) K D P =X 180 1 hJ[fH(D)-fv(D)].N(D)m) [deg h-']

with fH and f, are the forward scatter amplitudes at H and V polarisation respectively [3]. In most of the applications, the radar alternate sampling operation (H, V, H, V...) allows to obtain the reflectivity parameters using the following estimators:

where N is the number of pulses used to estimate the backscattered power at horizontal (P,) and vertical (P,) polarisation. The phaseshift cDDP is estimated by means of a modified pulse pair algorithm to take into account of the dual polarisation [4]:

where w1 = a r g C H , -V;l+l , \v2 =argxV;I , I . H21+2 with H,, and V2,+1 coherent (complex) time

samples coming fiom a radar cell. It is important to point out that the measured ODP includes a component due to the backscatter. Such a quantity (6) is neglectable at S band, but not at C and X band as will later be explained

In this context we suppose no differences between defined and estimated radar osservables. This is true only when N+ 00.

The main rainfall rate measurement problem is related to the resolution of the eqn (1). This is because there is a large number of drop site distributions N(D) that satisfy eqn (1) for a fixed ramate value. In fact the number of indipendent parameters of N@) is always greater than one (three for a Gamma dstribution, two for an Exponential one).

If only the reflectivity factor Z is measured, it is possible to fix n-1 parameters of DSD (e.g. based on the past and present climatology experiences) to derive analytical relationships between Z and r . For example, assuming No = 8000 mm-' me3, A = 4.1 rO.21 mm-', p = 0, with A = 3.67/D0 , it results:

Z = 296 r1.47 (10) with Z in mm6 m-3 and P in mm h-l. Different empirical formulas can be used to estmate ramfall rate (see Marshall and Palmer: Z = 200.i-19.

1 I

*I

If other lndependent radar measurements are available (Z,,, mDp), it is possible to work in two ways.

4/2 -

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a) In the first method, one DSD parameter is fixed (for example p = 0), the remaining parameters are derived by measurements, so the eqn (1) is solved to determinate r. This method, complex from a computational point of view, is not very used. b) In the second case, the relationships between r, and the radar osservables (Z,, ZDR, ODP) are obtained, by computer simulation, to estimate r minimizing error over a given range of rainfdl intensities. The computer simulation validity implies the following conditions: owing to physics considerations, an interval for the DSD parameters, has to be defined; in addition a DSD probability density function has to be specified, in that interval, for the DSD parameters.

In the computer simulation the DSD parameters are varied as suggested by lJlbrich [2]: No has been varied uniformly between 103.2-kp(2.8p) and 104.5-Pexp(3.57p) m 3 mm-l-p, Do has been vaned uniformly between 0.5 and 2.5 mm, and p is varied uniformly between -1.0 and 4.0. After computing Z,,,, ZDR, KDP and r, for each DSD, the values of Z,, and r greater than 55 dBz and 300 mm h-' respectively, have been discarded. By this procedure the cumulative distribution function of r gives the following values: r I 20 mm h-l for 58.3% of the trials; r I 50 "h-l for 66.3% ofthe trials; r I 100 mm h-1 for 88.2% and r 5 200 mm h-l for 97.0% of the trials. It would be convenint venfy this values with a set of data collected in a f i~ed location to better define the probability density function.

Using a nonlinear regression (C band) [5] a relationship between r, Z,, ZDR can be found:

r=3.61.10-3 Zo.95 H 2-1.28 DR [mm h-'1 while a linear relationship is determinated for KDp [j]:

r = 19.8 KDp [mm h'] (12) with Z, in mm6 m-3, ZDR in dB and KDp in deg Km-1.

In Fig. 1 the scatter plot of Z, versus r is shown (C band, T = 5 "C:). We point out that the only measurement of Z, allows an exact estimate of r only if r < 10 mm h-1. Fig. 2 shows the scatter plot of KDp versus r (S, C, X band, T = 5°C). A good linear trend can be found in all three bands, see [9] for details.

From the analysis of the results, in C band, we can affirm that the rainfall rak estimate errors are smaller if arelationshipZ=ur-bisusedandr5 10mmh-l;theeqn(ll)canbeusedwhen 1 0 I r I 9 0 m m h - ' , while for r > 90 mm h-l eqn (12) gives better results [j].

n f 20.01 10.0

z b 3

9

4 25.0

J !

20.0 4

15.0 I . . . 1

10.0

5.0

0.0

0 50 100 150 200 250 300 0 50 1 0 0 150 200 250 300 Rainrate (&h) Rainrate (mmih)

Fig. 1 Scatter plot Z, vs r. C band. T = 5°C. Fig. 2 Scatter plot KDp vs r. S, C. X band, T = 5°C.

3. ATTENUATION CORRECTION PROCEDURE Reflectivity measurements at C and X band are significantly affected by the attenuation due to the

precipitation existing between the radar and the observed cell. Differential reflectivity measurements at C and X band are similarly affected by the differential attenuation.

The specific absolute attenuation a, and the specific differential attenuation aD are related to DSD as follows: c

413 .

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aD=aH-av [dB Km-']

where fH and f, have been defined in eqn (7). aH and aD, using a nonlinear regression analysis and by means of the radar observables Z, and ZDRcan be estimated [6]:

aH = 7.78-10-6.zo~97.10-1.19.2~~ [dB K m q (15)

aD = 6.62.10-7.ZI.01.10~.~%1~ H [dB Km-'] (16)

In Table 1 some values of aH and aD (obtained from eqns (13) and (14)) versus r are reported, with

The first method is based on the use of an iterative cormtion scheme [6]: the corrected value of the reference to the C and X band. To take into account of the attenuation, two algorithms are proposed.

horizontal reflectivity (dBz) and of the differential reff ectivity at the n* range gate can be estimated as follows:

where M is the range gate distance in Km, aH and aD are determined from eqns (15) and (16), the index M means "measured". It is important to point out that calibration errors can affected the reflectivity factor. As a consequence these errors result in not correct aH and aD estimates.

When both reflectivity and differential phase measurements are available it is possible to use the following compensation algorithm [7]: 1.

2.

3.

4.

5 .

The first nearest radar cell is supposed not to be affected by attenuation and ZzR, ZgR, @Ep are estimated without correction.

a, and aD are evaluated from OFp and by using the following relationships:

CLH = 0.055.K~p (C-band) , a H = 0.176.KDp (X-band)

a D = 0.013.KDp (C-band) , a D = 0.030.KDp (X-band)

(19)

(20) The eqns (19) and (20) have been obtained as a linear best fit of the data reported in Fig. 3 and 4 respectively.

Z;, ZgR measurements are corrected, as in the first method: eqns ( I 7) and ( I 8).

In order to compensate the differential phase shift due to the backscatter (6) the ZgR corrected value is

used. The purpose is to adjust the cDEp : &DP = @& - 6 , where is estimated from Z D R .

'a

KDp is estimated on a given range interval AR (or by linear fitt) by: KD, =- and used in eqn (12) to

evaluate r for large rainrates, while for low rainrates the estimators (10) and (1 1) can be used. More

generally, a new parametrization of r versus the three corrected osservables Z, , Z D R , aDP can be devised.

AR

L A

The parameter 6 used at the step 4. is related to ZDR as shown in Fig. 5 . The relationshp can be

(21)

approximated by the polynomial best fit:

6 = &) + alZDR + a2ZhR + aG&R r

414

Page 5: [IEE IEE Colloquium on Radar Meteorology - London, UK (24 Feb. 1995)] IEE Colloquium on Radar Meteorology - Multiparameter radar techniques for rainfall

where at C band a, = 0.35; a, = -0.56; % = 0.05; a3 = 0.19. We recall that all, the above parametrizations of radar osservables have been obtained in the following intervals: 0 < 2, I 55 tBz and 0 < r I 300 mm h-1; however, we feel that a carefil selection of the interval are needed.

1.00 , . > , , , , , , , , , ( , I , , . , 1 ..

0.20 0.251--- ' I ' " " " ' ' I - 0.15 U,

P +!J 0.10 n 8

0.05

0.00

0' . * .

I .. ,.

0.0 5.0 10.0 15.0 20.0 0.00 5.00 10.00 15.00 20.00

Fig. 3 Scatter plot aH vs KDP ,C band, T = 5°C. Fig. 4 Scatter pilot aD vs KDp , C band, T = 5°C. (dwc"n KDP (degKm)

6.0 4 - 4.0

s OD

cc 3.0

2.0

1 .o

0.0

i 1

-f . - 8

t I

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ZDR (dB)

Fig. 5 Scatter plot 6 vs ZD, , C and X band, T := 5°C.

Table 1

415

Page 6: [IEE IEE Colloquium on Radar Meteorology - London, UK (24 Feb. 1995)] IEE Colloquium on Radar Meteorology - Multiparameter radar techniques for rainfall

4. CONCLUSION a.To estimate the rainfall rate from the radar osservables by means of parametxizitions it is necessary to r e d i e as much possible the a priori variability interval of the DSD parameters. This can be done by extensive and difficult measurements and/or through microphysical analysis and simulation to connect the DSD to dlfferent situations and altitudes instead of using a random, a priori variations of the DSD parameters [8].

b.The effects of the statistical fluctuation of radar osservables, due to the finite number of samples, should be evaluated, as well as the errors due to the radar itself. This can be not easy, especially when 2:tenuation is compensated.

c.The number of independent measurements has to be increased: therefore, it is necessary tr: make more complicated the radar and/or to integrate it with other sensor. In this frame, new parametrizarions (e.g. Z,, Z,, and ODp) and parametxizations at different bands (e.g. X) and frequencies should be studled.

d.Fmally it is important to d e h e the main characteristics of future radars taking into account both the constraints described in this paper and cost./&dveness considerations.

REFERENCES ATLAS D. , ULBRICH C.W. (1977) Path-and-area integreted rainfall measurements by microvawe attenuation in the 1-3 cm band J. Applied Meteorology, Vol. 16, pp. 1322-1331.

ULBRXCHCW. (1983) Natural variations in the analvtical form of raindrop size distribution J. Climate App. Meteor., Vol. 22, pp. 1764-1775.

OGUCHI T. (1973) Scattering properties of oblate raindrops and cross polarization of radio vawes due to rain part (II): calcilation at microvawe and millimeter vawe region J. of the Radio Research Laboratories, Vol. 20 n. 102 pp. 79-1 18

SACHIDANANDAM., D.S. ZRYIC (1986) Differential propagation phase shgt and rain fall rate estimation Radio Sci.. Vol. 21, pp. 235-247

SCARCHILLI G. , GORGUCCI E. (1992) (IX ITALLGN) Stima multiparametrica della precipitazione RADME 1992, Rome 9-10 June 1992. Universitaha

GORGUCCI E. , SCARCHILLI G. . C H ~ D R A S E W V. (1995) Radar and raingauge measurements of rainfall over the Amo basin A M s Conference on Hydrology, 15-20 J a n w 1995. Dallas Tx.

SCARCHILLI G. , GORGUCCI E. , CHASIRASEW V. .I SELIGATA (1993) Rainfall estimation using polarimetric techniques at C-bandfiequencies J. Applied Meteor.. Vol. 32 n. 6, pp. 1150-1 160, June 1993

ACCARDI L. , GALATI G. , KOROLIUK D. , PACM F. , REGOLI M. (1994) ( I N ITALIAN) Un modello statistic0 di formazione delle gocce di pioggia RADME 94. Rome 14-15 June 1994. Aracne Editrice

GALATI G. , P.4vk~ G. (1994) (IX ITALIAN) Parametrizzazioni del tasso di pioggia con gli ossen~abili radar nelle bande S, C e X Centro Wto Voltem, Report n. 181, Y d y 1994 Rome

416