1264 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20
Cloud Liquid Water and Ice Content Retrieval by Multiwavelength Radar
NICOLAS GAUSSIAT AND HENRI SAUVAGEOT Universite Paul Sabatier, Observatoire Midi-PyreÂneÂes, Laboratoire d'AeÂrologie, Toulouse, France
ANTHONY J. ILLINGWORTH Department of Meteorology, University of Reading, Reading, United Kingdom
(Manuscript received 25 March 2002, in ®nal form 15 March 2003)
ABSTRACT Cloud liquid water and ice content retrieval in precipitating clouds by the differential attenuation method using a dual-wavelength radar, as a function of the wavelength pair, is ®rst discussed. In the presence of non- Rayleigh scatterers, drizzle, or large ice crystals, an ambiguity appears between attenuation and non-Rayleigh scattering. The liquid water estimate is thus biased regardless of which pair is used. A new method using three
wavelengths (long l, medium m, and short s) is then proposed in order to overcome this ambiguity. Two
dual-wavelength pairs, (l, m) and (l, s), are considered. With the (l, m) pair, ignoring the attenuation, a
®rst estimate of the scattering term is computed. This scattering term is used with the (l, s) pair to obtain an
estimate of the attenuation term. With the attenuation term and the (l, m) pair, a new estimate of the scattering term is computed, and so on until obtaining a stable result. The behavior of this method is analyzed through a numerical simulation and the processing of ®eld data from 3-, 35-, and 94-GHz radars.
1. Introduction drizzle, or crystals, so that there is no relation between the radar re¯ectivity factor and the liquid water content The radiative balance of the atmosphere is very sen- or the optical thickness of the cloud (Sauvageot and sitive to the distribution of ice and liquid water in clouds Omar 1987; Fox and Illingworth 1997). (Stephens et al. 1990; Cess et al. 1996). The micro- The most promising way to quantitatively observe physical features of clouds are not well known because the liquid water content in clouds seems to be the dif- of the lack of observational data, and, in order to collect ferential-attenuation-based dual-wavelength radar meth- such data, space missions are planned. However, reliable od. This method was proposed to observe the liquid methods and algorithms to be used for ice and liquid water content in single-phase clouds (Atlas 1954; Mart- water retrieval are not fully available. ner et al. 1993; Hogan et al. 1999), the liquid water and Single-radar re¯ectivity measurements do not enable ice content in mixed-phase clouds (Gosset and Sauva- the determination of the liquid water content pro®le of geot 1992; Vivekanandan et al. 1999), or the liquid wa- clouds. Two cases have to be considered: liquid and ter content in rain (Eccles and Muller 1971). mixed-phase clouds. Most often, the entirely liquid The principle of the method is the following: the large clouds are made up of a high concentration of small scatterers (drizzle drops or ice crystals), which dominate droplets, corresponding to the main part of the liquid the radar re¯ectivity, have a negligible effect on the water content and controlling the radiative transfer with, attenuation, whereas the small droplets, responsible for in addition, a low concentration of large droplets, or the liquid water content, dominate the attenuation. From drizzle, which only make a small contribution to the measurements of the range re¯ectivity pro®les for two liquid water content of the cloud. In ice clouds, the wavelengths, one being strongly attenuated, the other presence of updrafts sometimes induces the develop- weakly so, the differential attenuation can be determined ment of a liquid phase, in the form of small droplets, and, from it, the cloud liquid water content deduced (cf. mixed with ice crystals having a comparatively larger section 2). The method works, provided that all of the size (Young 1993). In both cases, the radar re¯ectivity scatterers are small enough to satisfy the Rayleigh scat- is dominated by the largest (non-Rayleigh) scatterers, tering conditions, for which the radar re¯ectivity factor Z is independent from the wavelength . In the presence of non-Rayleigh scatterers, an ambiguity is observed Corresponding author address: Dr. Henri Sauvageot, Universite Paul Sabatier (Toulouse III), Centre de Recherches AtmospheÂriques, between the differential attenuation and a re¯ectivity Campistrous, 65300 Lannemezan, France. difference appearing because Z is no longer independent E-mail: [email protected] from .
᭧ 2003 American Meteorological Society
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC SEPTEMBER 2003 GAUSSIAT ET AL. 1265
The aim of this paper is to discuss the dif®culty of 10 log(Zm,) ϭ 10 log(Z) ϩ 20 log|K()/Kw(, 0)| implementing the dual-wavelength differential attenu- r ation method in the presence of non-Rayleigh scatterers Ϫ 2 A (u) du. (3) and to propose a new method using an additional wave- ͵ 0 length in order to retrieve the differential attenuation. Dual-wavelength radar algorithms have also been The dielectric factor depends on the thermodynamic proposed for the sizing of ice crystals in cirrus clouds phase and temperature of the scatterers. For liquid water, (Hogan and Illingworth 1999; Hogan et al. 2000), or the dielectric factor is weakly dependent on the tem- hailstones in convective storms (Atlas and Ludlam perature and it can be written that 20 log( | K()|/|Kw(, 1961; Eccles and Atlas 1973). In this context, the wave- 0) | ) ഡ 0 (e.g., Ray 1972). For ice, the dielectric factor length pairs are chosen in such a way that the particles is almost independent from the temperature and wave- to be sized at the higher frequency are in the Mie (or length, with | K()|2 ϭ 0.176 (for a density ϭ 0.92 non-Rayleigh) scattering region (Deirmendjian 1969). gcmϪ3), but it does depend on the density for air±ice The sizing depends on the re¯ectivity difference as a mixture. function of the wavelength, since, for the Mie scattering The differential-attenuation dual-wavelength radar region, the re¯ectivity is lower than for the Rayleigh methods consider the dual-wavelength ratio (DWR) de- scattering. Of course, these algorithms assume that dif- ®ned for a wavelength pair (s, l)as ferential attenuation is negligible, because if not, an Z ambiguity also appears between Mie scattering and dif- DWR ϭ 10 logm,l , (4) Z ferential attenuation. In the present paper, the use of the m,s concept of the triple-wavelength radar for particle sizing where the subscripts s and l stand for short and long is also considered. wavelength, respectively.
In the absence of non-Rayleigh scatterers, Ze,l ϭ
2. Theory Ze,s. Using (3) in (4) then gives
r The re¯ectivity factor Z of a cloud measured with m, DWR ϭ 2(A Ϫ A ) du ϩ R , (5) a radar of wavelength , at distance r, depends on the ͵ sl ls, 0 equivalent re¯ectivity factor of the scatterers Ze, and on the attenuation along the radar-target propagation with path:
r |K(lws)K ( , 0)| Ϫ0.2 # A(u) du R ϭ 20 log . (6) Zm, ϭ Ze, 100 , (1) ls, |K(swl)K ( , 0)| where A is the one-way attenuation factor for cloud For liquid water clouds, R1,s ഡ 0. For ice clouds, and gas, assuming that there is no precipitation on the R ϭϪ0.23 dB for the ( , ) and ( , ) wave- path other than drizzle and ice crystals, as discussed 1,s S Ka X Ka length pairs, and Ϫ1.27 dB for the (S, W) and (X, above; Z is in mm6 mϪ3 and A in decibels per kilometer. W) pairs. For Rayleigh scattering, DWR is thus equal, In this paper, four radar frequency bandsÐS ( f ϭ 3 within a constant, to the cumulative differential atten- GHz, ϭ 10 cm), X ( f ϭ 9.4 GHz, ϭ 3.2 cm), Ka uation along the radar-target path. (f ϭ 35 GHz, ϭ 0.86 cm), and W ( f ϭ 94 GHz, ϭ In the Rayleigh domain of approximation, the atten- 0.32 cm), where f is the frequencyÐare considered. uation by liquid water is proportional to the liquid water For the Rayleigh scattering, the radar re¯ectivity fac- content Mw. Neglecting attenuation by ice (e.g., Gosset tor is Z ϭ # D 6N(D) dD, where N(D) is the size dis- and Sauvageot 1992), tribution of the equivalent spherical diameter D of the scatterers, which means that Z is independent of . Aϭ CMW, (7) The equivalent re¯ectivity factor Ze, is related to the where C is the attenuation coef®cient. For a radial path ordinary re¯ectivity factor (e.g., Sauvageot 1992) by between r and r ϩ⌬r, over which Mw is assumed ho- |K()|2 mogeneous and uniform, the variation of DWR is, from Z ϭ Z, (2) (5) and (7) and after correction for atmospheric gas e, 2 |Kw(, 0)| attenuation,
2 where | Kw (, 0) | is the dielectric factor for liquid ⌬DWR 2 2(C C )M (r), (8) water at 0ЊC and | K()| is the actual dielectric factor ϭ slϪ w 2 ⌬r of the scatterers. For example, | Kw | ϭ 0.934 for the
S band, 0.930 for the X band, 0.881 for the Ka band, where Csland C are the attenuation coef®cients for and 0.686 for the W band at 0ЊC (e.g., Ray 1972; Me- water clouds at s and l, respectively. The cloud liquid neghini and Kozu 1990). water content is thus proportional to the DWR variation From (1) and (2), along the radial path, namely,
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC 1266 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20
1 ⌬DWR 3. Ambiguity between attenuation and scattering M (r) ϭ . (9) w 2(C Ϫ C ) ⌬r sl Figure 1 presents the variations of the non-Rayleigh
Knowing Mw(r), it is possible to compute an estimate term Fls, , as a function of D0, for four pairs of wave- of the ice content Mi(r) from the re¯ectivity pro®le using lengths and for liquid and ice scatterers. The non-Rayleigh empirical Z±Mw, Z±Mi relationships. This algorithm ap- term increases with the radioelectric size, ϭ D/, of plies to mixed and to warm clouds. It is not applicable the scatterers, that is, when D0 increases and decreas- to ice clouds because the attenuation by ice crystals is es. For a same D0, the non-Rayleigh term is smaller for too small to produce an accurately measurable differ- ice than for liquid water. The results are not sensitive ential attenuation. What can be used in ice-only clouds to the choice of S and X (and so for the wavelength are the conventional Z±Mi algorithm or a sizing dual- between s and x) as the longer wavelength, but using wavelength algorithm. the Ka band as short wavelength rather than the W band In the presence of non-Rayleigh scatterers, that is, in results in a marked decrease of the non-Rayleigh term. the Mie scattering region, the radar re¯ectivity factor is The differential attenuation algorithm described in no longer the sixth moment of the scatterer size distri- section 2 can be considered as reliable when Fls, (D 0), bution and depends on the wavelength. For a distribu- the non-Rayleigh contribution to ⌬DWR, is negligible tion of non-Rayleigh scatterers, it can be written (e.g., or not too large with respect to the cumulative differ-
Sekelsky et al. 1999) ential attenuation Ad⌬r. To discuss this point, two as- ϱ pects have to be considered. First, M ¯uctuates along 1012 4 w Z ϭ |K ()|22 (D, , )DN(D) dD, (10) a radial and the cumulative differential attenuation de- e, 44 w ͵ b 0 pends on the length of the integration path. Second, F (D ) depends on the particular value of Z in the where b is the backscattering ef®ciency (or normalized ls, 0 e, 2 range bin in which it is computed. Generally, F (D ) radar backscattering cross section), that is, b ϭ 4b/(D ), ls, 0 6 Ϫ3 with D in millimeters, in meters, and Z in mm m decreases with Ze,. Moreover, as discussed by Vivek- anandan et al. (1999), ⌬DWR is not affected by a Mie (e.g., Ulaby et al. 1981, p. 296). Here, b is a function of D, , particle density , and shape. In the present scattering if two Rayleigh range bins with low Ze, are study, it is assumed that the scatterers can be approxi- available at each end of the segment ⌬r where ⌬DWR mated by a spherical shape. For liquid water, the density is derived. However, in ®eld cases, such an opportunity is constant, whereas for the ice particles, it is assumed may not arise and more general conditions compatible (Brown and Francis 1995) that with a sampling process of radials with a constant ⌬r have to be used. 0.916 g cmϪ3 for D Ͻ 0.1 mm In order to illustrate the contribution of D and A to (D) ϭ (11) 0 d Ά0.0706DϪ1.1 g cmϪ3 for D Ͼ 0.1 mm. the dual-wavelength ratio, an integration path of length equal to 5000 m with an attenuating cloud liquid water Here, b is computed using the algorithm of Deir- content of 0.2 g mϪ3, that is, an integrated liquid water mendjian (1969). The size distribution of the scatterers amount of 1000 g mϪ2, is considered. We have com- is assumed to be exponential, namely, N(D) ϭ N 0 puted the corresponding values of the cumulative in- exp[Ϫ(3.67)D/D 0], where N 0 is a parameter and D 0 is tegrated differential attenuation and maximum D 0, such the mean volume diameter. Using (10), the ratio of the as F (D ) be equal to 10% of A . Table 1, where the effective re¯ectivity factors is ls, 0 d results are given, suggests that the condition Fls, (D0) Z Ͻ 0.1Ad is not very frequently observed in nature, be- 10 log e,l ϭ F (D ) ϩ R , (12) Z ls, 0 ls, cause drizzle is very common in warm clouds and ice e,s crystals are large in mixed clouds. That is why it is with relevant to look for an algorithm able to overcome the ϱ non-Rayleigh scattering problem for liquid water re- 42(D, )DeϪ3.67D/D0 dD trieval. l ͵ bl 0 Fls, (D0) ϭ 10 logϱ . 4. Triple-wavelength algorithm 42Ϫ3.67D/D0 s bs(D, )De dD ͵ 0 To remove the ambiguity between Fls, (D 0) and Ad In the presence of non-Rayleigh scatterers, DWR is in the presence of a warm or mixed cloud, including thus a function of the attenuation and of D , namely, non-Rayleigh scatterers, a triple-wavelength approach 0 is proposed.
DWR ϭ Fls, (D0) ϩ Ad ϩ R ls, , (13) where A is the differential attenuation, that is, d a. Principle r A ϭ 2(A Ϫ A ) du. (14) A triple-wavelength radar is considered. The three d ͵ sl 0 wavelengths are noted l, m, and s, where the sub-
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC SEPTEMBER 2003 GAUSSIAT ET AL. 1267
IG F . 1. Variation of the non-Rayleigh scattering term Fls, (D0) for water and for ice, written Fw and Fi, respectively, as a function of the mean volume diameter D0. Here s, x, Ka, w are wavelengths for S, X, Ka, and W bands, respectively; is the density in g cmϪ3, with D in mm. scripts l, m, and s stand for long, medium, and short, (16) can be computed. Then a ®rst estimate of the cu- respectively. In the present work, l corresponds to an mulative differential attenuation for the (l, s) pair is S, C, or X band; m to a Ka band; and s to a W band. obtained in each range bin from the difference, in (16),
Using the range distribution of re¯ectivities observed between the DWRls, observed and the F ls, (D0) com- with such a radar, a linear system of two independent puted. equations similar to (13) can be written: The cumulative differential attenuation ®rst neglected
r in (15) for the (l, m) pair can now be deduced from DWR ϭ F (D ) ϩ 2(A Ϫ A ) du the cumulative differential attenuation computed for the lm, lm, 0 ͵ m l ( , ) pair. In fact, for an attenuating medium made 0 l s ϩ R , (15) up of water droplets satisfying the Rayleigh approxi- lm, mation conditions, it is possible to write from (7) r
DWR ϭ F (D ) ϩ 2(A Ϫ A ) du (AmlϪ A ) ϭ k(A slϪ A ), (17) ls, ls, 0 ͵ s l 0 where the coef®cient k ( 0.19; see Table 1) is dimen- ϩ R . (16) ഡ ls, sionless and depends on the temperature.
Differential attenuation for the (l, m) pair is much Taking into account the attenuation term in (15) to smaller than that of the (l, s) pair. Assuming, in a ®rst compute a better estimate of the non-Rayleigh term step, that the cumulative differential attenuation is neg- Flm, (D 0), a new pro®le of the cumulative differential ligible, (15) is used to compute D 0 by solving attenuation can be obtained and so on. The iterative
DWRlm,ϭ F lm,(D 0) ϩ R lm, for each range bin. From process ends when the pro®le of cumulative differential this pro®le of D 0, the non-Rayleigh scattering term of attenuation is stable.
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC 1268 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20
TABLE 1. (upper) Difference between attenuation coef®cients by liquid water at 0ЊC for the four wavelength pairs and values of factor k Ϫ2 of (17); (lower) total differential attenuation and corresponding D0max for LWP ϭ 1000 g m and F(D0) Ͻ 0.1 Ad.
Wavelength pair (S, W )(S, Ka)(X, W )(X, Ka) CCϪ at 0ЊC (dB g mϪ3 kmϪ1) 5.34 1.05 5.25 0.97 s l k at 0ЊC in (17) 0.20 0.18 ϱ 2 #0 (AAs Ϫ l ) dr (dB) 10.70 2.10 10.50 1.90 D0max in ice (mm) 0.44 0.53 0.42 0.51
D0max in water (mm) 0.41 0.41 0.40 0.40
The pro®le of Mw is obtained by taking the derivative this computation. At the melting level, the scattering of the cumulative differential attenuation with respect term is interpolated between the values observed at the to the distance, assuming that Mw is proportional to the lower and upper limits of this level. Of course, the mea- differential attenuation. To obtain the ice content pro®le, sured radar re¯ectivity factors have to be corrected for the relation between Mi and the ice particle size distri- the attenuation by gas, notably for W and Ka bands. bution N(D) is ®rst considered, that is, Mi ϭ (/6) # This is done with data obtained from a radio sounding 3 D (D)N(D)dD. This relation depends on N0 and D 0, or from a mesoscale model, and from the radar data for the parameters of N(D). The pro®le of D 0 is given by the propagation in the cloud. the algorithm, as explained above, and the N0 pro®le is The organization of the three-wavelength algorithm obtained from the re¯ectivity factor pro®le at l (un- is summed up in Fig. 2 where Mw and Mi are written attenuated) and from the D 0 pro®le by inverting the as the liquid water content (LWC) and ice water content analytical relation Zl ϭ f(D 0, N 0). The same derivation (IWC), respectively. is used by Sekelsky et al. (1999). The relation used in the present work is similar to (24) of Sekelsky et al. (1999) for ϭ 0. b. Simulation The non-Rayleigh scattering term F depends on the A simulation of the proposed algorithm was imple- thermodynamic phase of the non-Rayleigh scatterers. A mented for the case of a mixed cloud. The non-Rayleigh temperature pro®le (obtained, e.g., by radio sounding scatterers are ice particles. The mixed cloud is assumed or by a mesoscale model) is thus useful to implement to be made up of the superimposition of a non-Rayleigh ice particle distribution and a Rayleigh supercooled droplet distribution. Figure 3 shows the assumed radial variations of the size distribution for the liquid water
Mw(D) and ice Mi(D) components. The corresponding re¯ectivity factor pro®les used for the simulation are obtained by resolving the radar equation for Z, for each wavelength, from the radial variation of the size distri-
butions Mw(D) and Mi(D). The backscattering and at- tenuation cross sections are computed with the Mie scat- tering model (Deirmendjian 1969). The attenuation by gas is not considered in this simulation. Figure 4a displays the simulated radial variation of differential attenuation computed from the condition of
Fig. 3 for the (S, W) pair as well as Ad,SW retrieved from the triple-wavelength method. The agreement between
Ad,SW assumed and retrieved is satisfactory. Figure 4b displays the radial variation of the liquid water content simulated (i.e., proportional to the derivative with re- spect to the distance of the simulated differential atten-
uation Ad,SW) and retrieved from the dual-wavelength algorithm for the (S, Ka) and (S, W) pairs, and using the triple-wavelength algorithm. These curves show that the triple-wavelength algorithm enables a correct re- trieval of the liquid water content variations. As ex- pected, the dual-wavelength method, in the presence of a signi®cant non-Rayleigh component, provides biased results. The (S, W) pair seems slightly better than the FIG. 2. Schematic of the triple-wavelength radar algorithm for cloud liquid and ice water content and mean volume diameter pro®les re- (S, Ka) one. Of course, this last remark should be qual- trieval. Symbols are de®ned in section 4a. i®ed because the W band suffers much more than the
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC SEPTEMBER 2003 GAUSSIAT ET AL. 1269
FIG. 3. Assumed radial variation of (a) LWC, (b) size distribution of the droplets Mw(D), (c) size
distribution of the ice particles Mi(D), and (d) resulting radial variation of the ``observed'' radar re¯ectivity factors at S, Ka, and W bands.
Ka band from gaseous attenuation and the limit of ex- up on the edge of the dish of the CAMRa radar, so that tinction. Replacing an S band by an X band (or other the axes of the beams of the three radars were parallel. wavelength between S and X) as long wavelength does The characteristics of the three radars are given in Table not modify the results (curves for the X band are not 2. The radars were carefully calibrated, the CAMRa given to avoid redundancy). from a polarimetric procedure proposed by Goddard et al. (1994), Rabelais and Galileo by comparison with CAMRa. The data from the three radars are interpolated c. Use on the ®eld data case of 13 April 1999 inside a common grid of mesh 100 m ϫ 100 m. The triple-wavelength algorithm was applied to the Figure 6 displays the re¯ectivity factor distribution case of 13 April 1999 observed with three radars in- in range±height indicator (RHI) mode observed with the stalled at the Chilbolton Radar Observatory, an exper- three radars on 13 April 1999 along the south±southeast imental site of the Rutherford and Appleton Laboratory direction (163Њ), on a cluster of cumulus congestus managed by the Radio-Communication Research Unit clouds. Three different RHIs corresponding to the three (RCRU), located in the southern part of the United columns of Fig. 6 are presented. The data are corrected Kingdom, about 100 km west of London (50.1ЊN, for the attenuation by gas with coef®cients calculated 1.3ЊW, altitude 80 m). The upper-air data for this case using radiosonde ascent at 1200 UTC. The three RHIs are given in Fig. 5. are separated by about 100 s. The cloud cluster was The three radars are the CAMRa 3-GHz radar with drifting toward the east, with the general circulation, at a 25-m dish (Goddard et al. 1994), the Rabelais 35-GHz a velocity of about 20 m sϪ1, in such a way that the radar of the Laboratoire dAeÂrologie (Universite Paul RHIs approximately represented three parallel planes Sabatier, France), and the Galileo 94-GHz radar of the about 2000 m from each other. The top of the cloud, European Space Agency. Rabelais and Galileo were set near 4500 m AGL, was at a temperature of Ϫ27ЊC. The
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC 1270 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20
FIG. 5. Radio sounding of Herstmonceux (50.90ЊN, 0.31ЊW) on 13 Apr 1999 at 1200 UTC. Abscissa is temperature in ЊC, ordinate is pressure in hPa. The wind, on the right part, is given in kt with values FIG. 4. (a) Simulated radial variation of DWR and differential of 5, 10, 50 for half barb, full barb, and triangle, respectively. attenuation, (Ad), for the (S, W) pair and simulated radial variation of DWR for the (S, Ka) pair; Mie scattering term FS,W and differential attenuation Ad,SW for the (S, W) pair retrieved with the triple-wave- 15 km, in the middle and right columns. Clearly, what length algorithm. (b) LWC simulated and retrieved from the dual- is presented in the three RHIs is a three-dimensional wavelength algorithm for the (S, Ka) and (S, W) pairs, and from the structure in which precipitation shafts can cut the RHI triple-wavelength algorithm; the simulated water content to be com- planes (the RHIs are not in the plane of the precipitation pared with the retrieved one is obtained by derivating AS,W with re- spect to the distance. shafts since the azimuth is not in the wind direction). In the data used, the width of the radar beams is smaller than 174 m (the beamwidth of the Rabelais radar at 20 0ЊC isotherm was near 750 m AGL, but no melting band km of distance). Figure 7 shows the DWR distributions appears on the re¯ectivity distribution. The dynamical observed for the (3, 35), (35, 94), and (3, 94) GHz pairs, and microphysical processes involved in such clouds for the three RHIs of Fig. 6. Figure 8 shows the dis- are rather correctly understood (e.g., Young 1993). The tributions of the non-Rayleigh scattering term F3,94 for absence of melting band suggests that precipitations are the ®rst and last (fourth) steps of the iteration, and the made up of granular ice (graupels or snow pellets) as differential attenuation A3,94, for the three RHIs of Fig. frequently observed in convective clouds. Besides, ex- 6. Figure 9 gives the distribution of the mean volume tinction is only reached in the upper-right part of the diameter (D0), LWC, and IWC retrieved with the triple- 94-GHz panel, showing that the propagation medium is wavelength algorithm for the three RHIs of Fig. 6. not strongly attenuating. The main difference between The differences between the re¯ectivities observed at the three RHIs is that the convective structure observed the three frequencies (Fig. 6) reveal the dramatic dis- at a distance ranging between 5 and 11 km in the left torsions brought by the attenuation and non-Rayleigh column diminishes and disappears in the middle and scattering for increasing frequencies. The 3-GHz panel right columns, respectively, while the ``wall'' of strong represents the re¯ectivity ®eld in the absence of atten- re¯ectivity observed at 11 km of distance in the left uation and non-Rayleigh effects. The 35-GHz panel dis- column stands farther away, at a distance near 12 and plays a re¯ectivity distribution in which the larger-size
TABLE 2. Main characteristics of the radars. CAMRa Rabelais Galileo Frequency (GHz) 3.075 34.94 94.8 Peak power (kW) 600 50 2 Antenna diameter (m) 25 1.4 0.5 Beamwidth, 3 dB (Њ) 0.26 0.43 0.5 Pulse width (s) 0.5 0.3 0.5 Scan rate (Њ sϪ1) 1 1 1 Pulse repetition frequency (Hz) 610 3125 6250 Noise equivalent re¯ectivity (at 1 km) (dBZ) Ϫ34 Ϫ27 Ϫ34
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC SEPTEMBER 2003 GAUSSIAT ET AL. 1271
FIG. 6. Re¯ectivity factor distribution observed in RHI mode with the three radars on 13 Apr 1999, at (left) 1328:14, (middle) 1329:57, and (right) 1331:28 UTC. scatterers do not correspond to the areas of maximum high values appearing at the lower boundary of bottom- re¯ectivities. A striking example is that of the areas of left panel of Fig. 7 (DWR3,94 for 13 April 1999) are an maximum D 0 appearing in the upper-left panel of Fig. artifact due to an edge effect. 9, notably at a distance between 5 and 10 km and a Figure 8, the distribution of the backscattering term height of 1.5 and 2.5 km in the left column. This max- without attenuation for the pair (3, 94) GHz, shows the imum does not appear at 35 GHz in the left column of ef®ciency of the iterative process. For the last step of
Fig. 6. On the 94-GHz panel, the re¯ectivity distribution iteration F3,94(D0) retrieves a distribution qualitatively is even further damaged with, in addition, a very strong mirroring the D0 repartition of Fig. 9, upper row. In gradient of attenuation. order to visualize the ef®ciency of the iterative process, iϩ1 Figure 7 emphasizes these distorsions. Because 35 Fig. 10 shows the evolution of the difference | Als Ϫ i GHz is not strongly attenuated (compared to 94 GHz; Als | at the end of the radials for the successive steps cf. Table 1) over short distance, high values of DWR3,35 (or iteration). The largest differences are observed in display mainly non-Rayleigh effects associated with the the presence of non-Rayleigh scatterers. The condition iϩ1 i distribution of large scatterers (non-Rayleigh effects be- | AAlsϪ ls | Ͻ , with ϭ 0.5 dB, is satis®ed after come signi®cant for scatterers larger than about 2 and four steps. In Fig. 8, the lower row displays the distri-
1 mm at 35 and 94 GHz, respectively). In the DWR35,94 bution of the (3, 94) GHz pair cumulative attenuation. row of Fig. 7, the attenuation effects at 94 GHz are The cumulative attenuation diminishes with the disap- dominant and the ratio increases regularly with the dis- pearance of the left-part-convective structure. tance, with the stronger gradients in the upper-right part. In Fig. 9, the upper row presents the retrieved mean
The DWR3,94 panels display the addition of the two volume diameter of the scatterers (D 0). The distribution previous distributions. The non-Rayleigh effects are is patchy because the precipitation shafts cross the plane dominant at short distances in the left part of the panels of the RHI scans. The LWC (i.e., Mw) distribution in and the attenuation is dominant in the right part. The the middle row of Fig. 9 retrieves the area of maximum
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC 1272 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20
FIG. 7. DWR for the (3, 35), (35, 94), and (3, 94) GHz pairs for the three RHIs of Fig. 6. values where the updrafts generating the precipitation the measurement of the three radars are thus expected in cumulus clouds can be expected, in the upper part of to corrupt the accuracy of the three-wavelength radar the clouds, at the head of the precipitation structure. In algorithm. Of paramount importance is the matching of such convective cells, the updrafts are usually strong the three radar beams; that is why it is preferable to set enough to create supercooled water clouds inside the up the three radar antennas on the same pedestal. The ice clouds because the deposition on the ice crystals pulse volumes, range bin distances, and dwell times does not totally consume the water vapor released by have to be the same. the air ascent (e.g., Young 1993). The IWC (i.e., Mi) A careful calibration of the three radars is necessary. distribution is presented in the lower row of Fig. 9. Ice As an example of sensitivity to calibration, Fig. 11 is present in all parts of the cloud with highest IWC shows the change of D0, LWC, and IWC, with respect values associated with the precipitation. The two areas to the value of Fig. 9, resulting from an error on the of high D 0 are not associated with high IWC, suggesting re¯ectivity measurements at 35 and 94 GHz, that is, Z35 that they are made up of large particles with low nu- and Z 94, respectively. The in¯uence of using, for the ice merical concentration and low IWC. particle density, a function different from (11) is also To validate the distribution of Fig. 9, simultaneous shown. The curves in Fig. 11 represent the variation in situ microphysical measurements would be necessary. with distance of the three parameters for the constant Such data are not available. However, qualitative con- height of 2500 m AGL in the RHI of 1329:57 UTC. siderations suggest that the retrieved distributions are For the three parameters, the shift induced in the results reasonable and realistic. by an error in Z can be positive or negative due to the non-Rayleigh response of the large scatterers. Of course, the errors considered independently in Fig. 11 can arise d. Practical aspects of implementation simultaneously giving cumulative effects that can be The three radars have to sample the same volume in additive or subtractive. These errors can signi®cantly the same conditions. All the terms that might decorrelate corrupt the results, suggesting that a calibration error
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC SEPTEMBER 2003 GAUSSIAT ET AL. 1273
FIG. 8. Distributions of F3,94 for the ®rst and last steps of the iteration and differential attenuation A3,34, for the three RHIs of Fig. 6.
not worse than Ϯ1 dB is required. However, D0 and the proposed method to all these terms, although useful LWC only depend on the relative calibration of the ra- for its evaluation, is out of the scope of the present paper. dars, while IWC depends on the absolute calibration. The error due to the change in the coef®cient of the ice 5. Conclusions density function appears rather strong in Fig. 11 for the three computed parameters; however, the test is for a In the presence of non-Rayleigh scatterers, dual- linear coef®cient of the density function reduced by 5 wavelength methods for liquid water content retrieval (from 0.916 to 0.175), which is very large. For moderate in warm and mixed clouds are biased. The reliability of variations of the coef®cients, the changes will be mod- the results depends in fact on the importance of the non- erate for D 0 and IWC, and almost negligible for LWC. Rayleigh scattering term Fls, (D0) with respect to the The optimization of the choice of the three wave- cumulative differential attenuation Ad⌬r. The present lengths, because it in¯uences the signal-to-noise ratio paper suggests that favorable conditions for the use of and the resolution of the retrieved distributions (e.g., a dual-wavelength method are not very frequent in na- Gosset and Sauvageot 1992), is also to be considered, ture, notably in mixed clouds where ice crystals are as well as the maximum observable distance, which usually large. That is why a triple-wavelength radar depends on s. method is proposed to overcome these dif®culties. However, the accuracy also depends on the particular In this method, a long wavelength (l), a medium one conditions of the observation, namely, spaceborne, air- (m), and a short one (s) are considered in order to borne (and in this case from above or below the melting observe two dual-wavelength ratios, one (DWRl,m) with band), or ground-based radars. Last, the accuracy of the low differential attenuation and the other (DWRl,s) with results is contingent on the genus and structure of the high differential attenuation. Using DWRl,mobservations clouds observed (stratiform, convective, or mixed, with and ignoring the differential attenuation, a ®rst estimate low or high re¯ectivity). of the D0 pro®le is computed. With this pro®le and A complete study of the accuracy and sensitivity of DWRl,sobservations, an estimate of the cumulative ra-
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC 1274 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 20
FIG. 9. Mean volume diameter of scatterers (D0), LWC, and IWC retrieved with the triple-wavelength algorithm for the three RHIs of Fig. 6.
dial variation of Ad is computed. From this, an estimate
of the differential attenuation Ad affecting the DWRl,m
pro®le is obtained. Then, from the DWRl,m and the Ad
pro®les, a new more exact D0 pro®le is computed, and
so on until obtaining stable LWC, IWC, and D 0 pro®les. Simulation and ®eld observations processing using
the s±Ka and s±w wavelength pairs are presented. The three wavelengths suggested for the implementation
of this method are x or higher for the long wavelength
and Ka and w for the medium and short wavelengths, respectively. The results show that the proposed method has an interesting potential to retrieve the pro®le of the liquid water content and the mean volume diameter of the non-Rayleigh component in mixed phase or in warm clouds.
Acknowledgments. We thank the Radio-Communi- cation Research Unit at the Rutherford Appleton Lab- oratory for providing the 3-, 35-, and 94-GHz radar data. We are grateful to Dr. Robin Hogan of the University
iϩ1 i of Reading for his helpful remarks regarding data anal- FIG. 10. Variation of residual attenuation AAlsϪ ls in dB, as a function of the elevation angle of the radar beams for the successive ysis and radar calibration. The 1994 Galileo radar was iterative steps of the triple-wavelength algorithm. developed for the European Space Agency by Of®cine
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC SEPTEMBER 2003 GAUSSIAT ET AL. 1275
FIG. 11. Variation with distance of the three retrieved parameters D0, LWC, and IWC resulting
from a calibration error of Ϯ1dBonZ35 and Z94, and from a change in the coef®cients of the ice density (D) formula. The curves are for a constant height of 2500 m AGL and the RHI scan of 1329:57 UTC.
Galileo, the Rutherford Appleton Laboratory, and the dual-wavelength radar to make global measurements of cirrus University of Reading, under NERC Grant GR3/13195 clouds. J. Atmos. Oceanic Technol., 16, 518±531. ÐÐ, ÐÐ, J. W. Goddard, S. C. Jongen, and H. Sauvageot, 1999: and EU Grant CVK2/CT/2000/00065. Stratocumulus liquid water content from dual wavelength radar. Int. Workshop Proc. CLARE '98 Cloud Lidar and Radar Ex- periment, Noordwijk, Netherlands, ESA, ESTEC, 197±109. REFERENCES ÐÐ, ÐÐ, and H. Sauvageot, 2000: Measuring crystal size in cirrus using 35- and 94-GHz radars. J. Atmos. Oceanic Technol., 17, Atlas, D., 1954: The estimation of cloud parameters by radar. J. 27±37. Meteor., 11, 309±317. Martner, B. E., R. A. Krop¯i, L. E. Ash, and J. B. Snider, 1993: Dual- ÐÐ, and F. H. Ludlam, 1961: Multi-wavelength radar re¯ectivity of wavelength differential attenuation radar measurements of cloud hailstorms. Quart. J. Roy. Meteor. Soc., 87, 523±534. liquid water content. Preprints, 26th Int. Conf. on Radar Me- Brown, P., and P. Francis, 1995: Improved measurements of ice water teorology, Norman, OK, Amer. Meteor. Soc., 596±598. content in cirrus using a total water probe. J. Atmos. Oceanic Meneghini, R., and T. Kozu, 1990: Spaceborne Weather Radar. Ar- Technol., 12, 410±414. tech House, 197 pp. Cess, R. D., and Coauthors, 1996: Cloud feedback in atmospheric Ray, P. S., 1972: Broadband complex refractive indices of ice and general circulation models: An update. J. Geophys. Res., 101, water. Appl. Opt., 11, 1836±1844. 12 761±12 795. Sauvageot, H., 1992: Radar Meteorology. Artech House, 366 pp. Deirmendjian, D., 1969: Electromagnetic Scattering on Spherical Po- ÐÐ, and J. Omar, 1987: Radar re¯ectivity of cumulus clouds. J. Atmos. Oceanic Technol., 4, 264±272. lydispersion. Elsevier, 290 pp. Sekelsky, S. M., W. L. Ecklund, J. M. Firda, K. S. Gage, and R. E. Eccles, P. J., and E. A. Muller, 1971: X-band attenuation and liquid McIntosh, 1999: Particle size estimation in ice-phase clouds us- water content estimation by dual-wavelength radar. J. Appl. Me- ing multifrequency radar re¯ectivity measurements at 95, 33, teor., 10, 1252±1259. and 2.8 GHz. J. Appl. Meteor., 38, 5±28. ÐÐ, and D. Atlas, 1973: A dual wavelength radar hail detector. J. Stephens, G. L., S. C. Tsay, P. W. Stakhouse, and P. J. Flatan, 1990: Appl. Meteor., 12, 847±854. The relevance of microphysical and radiative properties of cirrus Fox, N. I., and A. J. Illingworth, 1997: The retrieval of stratocumulus clouds to climate and climatic feedback. J. Atmos. Sci., 47, 1742± cloud properties by ground-based cloud radar. J. Appl. Meteor., 1752. 36, 485±492. Ulaby, F. T., R. K. Moore, and A. K. Fung, 1981: Microwave Remote Goddard, J. W. F., J. Tan, and M. Thurai, 1994: Technique for cali- Sensing. Vol. 1. Addison-Wesley, 456 pp. bration of meteorological radars using differential phase. Elec- Vivekanandan, J., B. Martner, M. K. Politovich, and G. Zhang, 1999: tron. Lett., 30, 166±167. Retrieval of atmospheric liquid and ice characteristics using Gosset, M., and H. Sauvageot, 1992: A dual-wavelength radar method dual-wavelength radar observations. IEEE Trans. Geosci. Re- for ice±water characterization in mixed-phase clouds. J. Atmos. mote Sens., 37, 2325±2334. Oceanic Technol., 9, 538±547. Young, K. C., 1993: Microphysical Processes in Clouds. Oxford Uni- Hogan, R. J., and A. J. Illingworth, 1999: The potential of spaceborne versity Press, 427 pp.
Unauthenticated | Downloaded 10/01/21 04:22 PM UTC