Rain Observation by an X- and Ka-Band Dual-Wavelength Radar

October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 509

Rain Observation by an X- and Ka-band Dual-Wavelength Radar

By Kenji Nakamura, Hideyuki Inomata, Toshiaki Kozu, Jun Awaka and Ken'ichi Okamoto

Communications Research Laboratory, Koganei, Tokyo 184, Japan (Manuscript received 2 March 1990, in revised form 7 July 1990)

Abstract

A rain observation by an X- and Ka-band dual-wavelength radar has been performed. The objective of this experiment is to explore the possibility of multi-wavelength radar for measuring rainfall rate. Simultaneous rain observations by C- and Ku-band radars were also performed. Correlations among measured Z- factors show that rain attenuation is significant only in the Ka-band for a short range when the observing range is a few km. After a method of obtaining an optimum averaging hit number is proposed, a dual-wavelength analysis using rain attenuation is applied to Ka- and X-band radar data and the result confirms the capability of providing an estimation of rainfall rate other than that by the conventional method. The dual-wavelength analysis is compared with a single wavelength analysis using rain attenuation and an advantage of dual-wavelength analysis is verified. The capability of the dual-wavelength analysis for retrieving a vertical structure of rain is demonstrated. A radar calibration using the dual-wavelength analysis is tested and a more accurate calibration than that comparing the rain gauge data is obtained.

1. Introduction Lion switching mechanism, but the existing transmitter and receive can commonly continue to be Conventional rain radars which usually operate used. Another candidate for multi-parameter radars at S-, C-, and X-band wavelengths measure the re- is a multi-wavelength radar. Radiowave scattering turn signal from hydrometeors, which means that characteristics of rain and propagation characteris- the radars measure only one physical quantity, i. e. tics in rain differ frow one frequency to another. the so-called Z-factor. However, the most important physical quantity of rain is rainfall rate which Contrary to the dual-polarization radar, the cost of a dual-wavelength radar might be expensive, be- directly determines the amount of water produced cause nearly two complete radar systems are re- by rain. The total amount of water has a close relationship not only to human activities but also quired. Also, a multi-wavelength radar has a disadvantage in observable range which is limited by atmospheric dynamics because the total amount of rain attenuation at the higher frequency. However, rain gives the total amount of latent heat released to the atmosphere. Unfortunately, the radar-measured a multi-wavelength radar is a better candidate for a spaceborne radar than a dual-polarization radar. It Z-factor has a large variation even at the same rain- is difficult to direct the spaceborne radar beam at fall rate due to raindrop size distribution variations, large incident angles for measuring the polarization because the Z-factor is proportional to the sixth characteristics because of range smearing and the power of raindrop diameter, but the rainfall rate large range from the radar to targets. On the con- is proportional nearly to the 3.5th power of rain- trary, the disadvantage of short observable range of drop diameter (Battan, 1973). To overcome this, a multi-wavelength radar is not crucial, because the multi-parameter rain radars are investigated exten- radio path through the rain area is mainly limited sively. One of the strong candidates for a multi- by the height of the rain and is short, which results parameter radar is a dual-polarization radar. Dual- in a small rain attenuation. polarization radars have some variations but all measure the polarization characteristics of rain. One The study of dual-wavelength radar observation of the advantages of the dual-polarization radar is has a long history. The first study is Atlas and that the cost for installing the polarization capabil- Ludlam's (1961) work on hail detection as far as ity may not be so expensive, because what addi- we know. As the first trial was for hail detection, tionally are required is an antenna and a polariza- many measurements were performed for hail detection. Eccles and Atlas (1973) proposed an S- and X- c1990, Meteorological Society of Japan band radar. Tuttle and Rinehart (1983) presented a 510 Journal of the Meteorological Society of Japan Vol. 68, No. 5 simple technique to correct for attenuation in dual- provide an estimation of rainfall rate over a short wavelength analyses based on data taken by S- and range. The estimation is independent of the one us- X-band radars. They also showed some effects of ing a conventional rain retrieval method where the mismatched antenna beam patterns (Rinehart and received power of radar is simply converted to rain- Tuttle, 1984). The basic concept of hail detection fall rate by a semi-empirical formula. Fortunately, is to use a large difference of the so-called effective C- and Ku-band radars were also available. We will Z-factors of hail in S-, C- and X-band radio bands, present some characteristics of data other than X- since the size of a hail is large enough to make the and Ka-band radiowaves and show that a radiowave scattering deviate from the Rayleigh condition. of more than 14 GHz is needed for dual-parameter Contrary to hail detection, dual-parameter mea- rainfall measurement for a range of a few km. The surement of rainfall rate by a dual-wavelength radar capability of an X- and Ka-band dual-wavelength uses rain attenuation along a radio path. The size of radar to provide an independent estimation of rain- a raindrop is usually small enough to allow the as- fall rate will be verified. An advantage of a dual- sumption that the scattering is Rayleigh. In this wavelength radar over a single-wavelength radar us- case, the difference of the measured Z-factors is ing rain attenuation will be presented. Though caused by the rain attenuation. Eccles and Mueller other rain retrieval algorithms are proposed (see At- (1971) studied the possibility of the estimation of las and Meneghini's review, 1988), they are methods liquid water content using S- and X-band radars. peculiar to the rain observation with a downward- Then Eccles (1979) compared the estimated total looking radar and were not applied here. A range rainfall rates from X-band rain attenuation and S- profiling capability for dual-wavelength radar will be band radar-derived total rainfall and also the rain demonstrated. Finally, an application of the dual- gauge-derived total rainfall for more than 40 days, wavelength radar for calibration will be proposed and he concluded that the estimation from rain at- and tested. tenuation is more accurate than that from the radar 2. Instruments reflectivity factors. So far, ground-based dual-wavelength radar ex- In the Kashima Space Communication Center of periments have used an X-band radiowave as the the Communications Research Laboratory, many highest frequency. The main reason seems to be meteorological instruments including a C-band rain that the severe rain attenuation limits the observ- radar and a Ku-band FM-CW rain radar are in- able range. The biggest feature of a ground-based stalled for centimeter radiowave propagation exper- rain radar is the capability of observing rain over a iments using the Japanese geostationary satellites. large area. A typical S-band radar has an excellent Experiments using CS (Medium-capacity Commu- sensitivity and the observable range is limited by the nications Satellite for Experimental Purposes), BSE curvature of the earth's surface. C-band radars have (Medium-scale Broadcasting Satellite for Experi- an observable range of more than 100 km, and X- mental Purposes), or ETS-II (Experimental Test band radars have an around 50 km observable range. Satellite Type II) have been conducted. Using this A radar with an observable range of less than a few equipment and also a dual-wavelength radar which ten km is not attractive for observations of horizon- employs X- and Ka-band radiowaves, simultaneous tal extent of rain. However, as mentioned before rain observations have been performed since June, the limited observable range for airborne or space- 1982. borne radars is not so crucial as for ground-based Figure 1 shows the instruments of the observation. radars. A spaceborne dual-wavelength radar with 10 The instruments include four rain radars, and the GHz and 24 GHz is proposed for the future manned CS propagation experimental system. The radars station (Okamoto et al., 1989). Meneghini et al. are operated at C-, X-, Ku- and Ka-band wave- (1989) performed experiments using an X- and Ka- lengths. Besides the radars, four rain gauges are band airborne dual-wavelength radar and tested var- also used. Two rain gauges are shown in Fig. 2. Two ious rain retrieval algorithms using rain attenuation. other rain gauges are located 2 km and 6 km south Fujita (1983) proposed a rain retrieval algorithm in of the radar sites. Table 1 shows the characteris- which the received powers in both frequencies are tics of the radars. Figure 2 shows the locations of combined and rainfall rate is estimated in a kind of the instruments in the Kashima Space Communica- least square sense. Fujita et al. (1985) tested the al- tion Center and the directions of radar beams. All gorithm using X- and Ka-band airborne rain radar the beams are in the direction of the CS (Az: 190*, data. El: 48*). The beams of the X- and Ka-band of Keeping the application to a future spaceborne the dual-wavelength radar coincide with each other. radar in mind, we performed an experiment using The narrow C-band radar beam is within that of the a ground-based X- and Ka-band dual-wavelength dual-wavelength radar. radar. The main objective is to show the potential of X- and Ka-band dual-wavelength radar to October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 511

C-band rain radar The backscattered signal is sampled at a time inter- The C-band rain radar operates at a frequency val of 1.67*sec, which means that the range resolu- of 5.33 GHz (wavelength is 5.6 cm) and has a peak tion is 250 m. This radar is controlled by a computer transmitting power of 250 kW. The pulse repetition (Tanaka et al., 1980). frequency is 900 Hz, and the pulse width is 0.5 *sec. X- and Ka-band dual-wavelengthradar The X- and Ka-band dual-wavelength radar was designed as an airborne type, and the system is light in weight and small in size (Okamoto et al., 1982). Frequencies used are in the X-band (10.0 GHz, 3 cm) and Ka-band (34.5 GHz, 0.87 cm). The antennas are designed to have the same beam widths at each frequency. The polarization can be changed as V/V, i. e., transmits a vertically polarized radiowave and receives a vertically polarized radiowave, or H/H, i. e., transmits a horizontally polarized radiowave and receivesa horizontally polarized radiowave. The pulse repetition frequency and the pulse width can also be changed from 220 Hz and 1*sec to 440 Hz and 0.5*sec. The sampling interval is changed with the pulse repetition frequency. When the pulse repetition frequency is 440 Hz or 220 Hz, the sampling interval is 0.5*sec or 1.0,*sec, respectively. In the rain observation presented in this paper the pulse repetition frequency is fixed to 440 Hz and the range resolutions of both X- and Ka-band are fixed to 75 m in order to observe precise rain structures. Fig. 1. Experimental system. Four frequen- Ku-band rain radar cies are used for the radars. This radar has been developed to investigate prop-

Fig. 2. Locations and beam directions of radars. The C-band radar and the dual-wavelength radar have overlapped antenna beams, but the Ku-band radar has a different antenna beam. 512 Journal of the Meteorological Society of Japan Vol. 68, No. 5

Table 1. Characteristics of radars

agation characteristics at 14 GHz (wavelengthis 2.1 cm), which was used in the Japanese BSE. The transmitter and the transmitting antenna are those used in the BSE experiment. The maximum transmitting power is 1 kW. The antenna beam is very narrow (0.1*) because the diameter of the transmitting antenna is large (13 m). This radar is of a FM- CW or pulse compression type (Kozu et al., 1987). Fig. 3. The rainfall rate on July 7, 1982. The 3. Correlations among radar reflectivity fac- rainfall rate was measured every minute. tors The maximum rainfall rate in this rain was First we showthe characteristics of the data taken more than 40 mm/h. by radars and rain gauges. Though each characteristics is not new, we think it is worth showing because (1) the observations were performed simul- size of the antenna. Though it is easy to manufac- taneously, and (2) the data give an idea of what type ture and install an antenna of 1 m, rain attenuation of analysis is feasible. We conducted rain observa- still limits the observable range to only around 5 km. tions about ten times in June and July in the rainy The correlations between radar-derived effective season of Japan. The rain on July 7, 1982, was the Z-factors and ground rainfall rate-derived Z-factors heaviest, and this paper describes the results of this are shown in Fig. 5. The slant range of the observed event exclusively. point is 1.5 km. The rainfall rate on the ground Figure 3 shows time sequence of rainfall rate on measured by a rain gauge was converted to Z-factor July 7. The rain continued for about 6 hours and by using the well known empirical relation between the maximum rainfall rate was more than 40 mm/h Z-factor, Z (mm6/m3), and rainfall rate, R (mm/h), (the rainfall rate was measured every minute). Fig- (Marshall and Palmer, 1948) as ure 4 shows an example of the height distributions of the effective Z-factor. In this paper the effective z = 200R1.6 (1) Z-factors include the effect of rain-induced attenua- Effective Z-factors at C-, X- and Ka-band are ob- tion. The distributions are similar except that of the tained by averaging successive 32, 128, and 128 hits Ka-band, the longer range part of which is below the every minute, respectively. noise level, because of the strong rain-induced at- The correlations between C- and Ka-band radar- tenuation. This short observable range of Ka-band derived Z-factors and Z-factors derived from the radar compared to other radars shows the defect of a radar in Ka-band. One of the reasons for the poor ground rainfall rate shown in Fig. 5a and 5b are poor. The horizontal separation between radar- sensitivity of the Ka-band radar we used is the small observed volume and the rain gauge is more than October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 513

of data in Fig. 5e is larger than 0.6 dB which is expected from the signal fluctuation of the X- and Ku- band radar. This is thought to be due to the sampling volume separation of 300 m. There exist no systematic differencesin the correlation between C-, X- and Ku-band radar-derived effective Z-factors. This fact means that dual-wavelength radars which adopt only C-, X-, or Ku-band radiowaves do not give new information on rain. The reason for the poor correlation between Ka-band radar-derived Z- factor and X-band radar-derived Z-factor (an example is shown in Fig. 5f) is the rain-induced attenuation. Sampling volume separation is not likely to be the cause because the radar beams are nearly identical at the two frequencies. Another conceiv- able cause is the Mie scattering effect which causes deviations from Rayleigh scattering. The Mie scattering effect is large for a large raindrop and causes a measured effective Z-factor deviation from the actual Z-factor. To confirm the effect of the rain attenuation, two theoretical curves are also depicted in Fig. 5f. These curves are obtained by assuming that: (1) the raindrop size distribution is the well known Marshall and Palmer's one (Marshall and Palmer, 1948), (2) rain is uniform, that is, the raindrop size distribution, phase, temperature, etc. are uniform. The calibration constants of the dual-wavelength radar are determined from the correlations between the effective Z-factors of X- and Ka-band, and that between the Z-factors of X-band and ground rainfall rate-derived Z-factors by eye fitting. The curve Fig. 4. The height profiles of the effective Z- (a) is assuming that rain-induced attenuation does factors (including the attenuation effect) not exist, but the scattering is Mie scattering. The derived from each radar data. The echo curve (b) includes the rain-induced attenuation and signal level in a longer range part of Ka- the Mie scattering effect. The curve (a) is almost band radar is below the noise level. linear and has an inclination of about 45 degrees, which means that the Mie scattering effect is small 1000 m and the vertical separation is more than 1100 compared to the rain attenuation effect. The curve m, and the poor correlation is mainly due to the (b) qualitatively agrees with the measured points, physical separations in the sampling volumes, which which means that the rain-induced attenuation is is confirmed by correlation degradation among rain the cause of the degradation of correlation. Figure gauge-derived Z-factors with distance (not shown). 6 is the same as Fig. 5f except the slant range is The correlations among C-, X-, and Ku-band radar- 0.75 km. The correlation is better than that shown derived Z-factors shown in Fig. 5c, 5d and 5e are in Fig. 5f. This is reasonable, because the rain at- good. The main cause of the data scattering is tenuation is small for a short range. the signal fluctuation due to incoherent scattering. The rain attenuation at the second highest fre- For the C-band radar the standard deviation of the quency of 14 GHz does not appear in Fig. 5c or 5e. signal fluctuation is estimated as 3 dB, because the The estimated rain attenuation at 14 GHz for a two- number of the independent samples of the C-band way path length of 3.0 km is around 0.3 dB and 1.2 radar is estimated as only around 6. For X- and dB for Z-factors of 30 dBZ and 40 dBZ, respectively, Ku-band radars, the standard deviations of the sig- and the rain attenuation is easily masked by the nal fluctuation are estimated to be around 0.5 dB, fluctuations. and 0.35 dB, respectively. The scattering of data From the characteristics mentioned above it is is larger in Fig. 5d than that in Fig. 5e, which is concluded that (1) sampling volume separation will as expected since the large signal fluctuation of the cause large errors, (2) the signal fluctuation needs C-band radar causes large errors. The scattering to be suppressed, and (3) only the rain attenuation 514 Journal of the Meteorological Society of Japan Vol. 68, No. 5

Fig. 5. The correlations among the Z-factors derived from each radar data at a slant range of 1.5 km and ground rainfall rate. (a): The correlation between C-band radar-derived Z-factors and ground rainfall rate-derived Z-factors. (b): The correlation between Ka-band radar-derived Z-factors and ground rainfall rate-derived Z-factors. (c): The correlation between C-band radar-derived Z-factors and Ku-band radar-derived Z-factors. (d): The correlation between C-band radar-derived Z-factors and X-band radar-derived Z-factors. (e): The correlation between X-band radar-derived Z-factors and Ku-band radar-derived Z-factors. (f): The correlation between X-band radar-derived Z-factors and Ka-band radar-derived Z-factors. Two solid curves are theoretical curves assuming (a) only the Mie scattering effect exists and (b) the Mie scattering effect and rain-induced attenuation effect exist. (From top to bottom right) October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 515

Fig. 6. The same as Fig. 5(F) except the slant Fig. 7. The variance V as a function of the range is 0.75 km. averaged hit number N.

in the Ka-band can give another physical quantity than the Z-factor when the observing range is only a few km. The data from the X- and Ka-band radar where Zi is a logarithmic average of the effective are worth further analysis, because the sampling vol- Z-factor over N hits as umes are the same and the frequencies are suitable. 4. Averaging hit number It is well known that the received power of each hit fluctuates to have an exponential distribution, where Zi is the measured effective Z-factor at the because the scattering is incoherent (Marshall and i-th hit. The logarithmic averaging instead of sim- Hitschfeld, 1953). It is necessary to average received ple averaging is included to express the actual av- power over several hits. An averaging procedure eraging process of the radar receiver. This variance is more essential for dual-wavelength analysis than gives the scale of the difference between successive for conventional rain retrieval, because the differ- averaged Z-factors. If the rain is stationary, V will ence in the received powers are taken twice as de- decrease as N increases. If the rain is not station- scribed later and the result is sensitive to the fluc- ary V will first decrease, but then stop decreasing tuation. If the rain is stationary, the fluctuations and increase as N increases. The N which gives the of the averaged received power may reduce as the minimum V can be considered to be the optimum average number increases. However, under actual averaging number. Figure 7 shows the variance V as conditions, the rain cannot be considered to be sta- a function of the averaging hit number N from ac- tionary, and too many averaging hit numbers may tual data. The measured points are in a "V" shape cause other errors, because the time of the overall as expected. In the left part the variance is almost averaging becomes long and the rain condition may proportional to N-1, which is the nature of the av- change in that time. erage of independent variables. In the right part of Even though there exists an optimum averaging the variance is almost proportional to N1.5. In the hit number, there seems not to be any conventional former part, the variance is due to the incoherence way to determine the optimum number. One rea- and in the latter part the variance is due to the tem- son may be that the time scale of the rain variation poral variations of the rain condition. To verify the is usually long enough to suppress the signal fluc- characteristics of the variance in the left part, we tuations and no serious degradation of data quality simulated the characteristics by generating a ran- results from the time required for a large number of dom variable which has an exponential distribution. averaging hits. However, for rapidly varying rain, The average of the logarithm of the N variables is the time scale of rain variation might be only a few calculated, and we obtain the variance V. The sim- seconds, and the averaging time to suppress signal ulated results are also depicted in Fig. 7. The vari- fluctuations may mask the detailed time variation of ance for N =1 can be theoretically obtained to be rain. approximately 31 dB2, which confirms the validity Here we propose a simple method to get the op- of the simulations. The simulated points are well timum averaging hit number. We define a variance fitted to the measured points at Ka-band, but they V (N) which is expressed as are in some disagreement with the measured points 516 Journal of the Meteorological Society of Japan Vol. 68, No. 5

at X-band. The reason for this is due to the lack Z: Z-factor, of independence of the received power of each hit at Ze: effective Z-factor including the rain attenua- X-band. Even though the scattering is almost inco- tion effect (= AZ), herent, the scattered radiowaves by raindrops have r: range, coherence over a short time interval. The time T for 1, 2: frequency. which the scattering radiowaves can be considered as The rain attenuation can be expressed as incoherent is given as

where aR is specific rain attenuation coefficient where * is the wavelength of the radiowave and the (dB/km). Taking the ratio of Eq. (5) produces units of T and * are msec and cm, respectively (Battan, 1973). Since the pulse repetition frequency is 440Hz which means the hit interval of 2.3 msec, the receivedpower at each hit may be incoherent for Here, it is assumed that the Z-factor is a Rayleigh Ka-band but not for X-band. Then, for X-band the one, which means that the Z-factors are the same number of independent data is reduced and the vari- at the two frequencies 1 and 2. The Mie scatter- ance become large compared to that for Ka-band. ing effects may not be small for the Ka-band, and This fact indicates that a higher frequency is more this assumption sometimes does not hold. But since adequate for observing rapidly varying rain. the rain attenuation effect is much larger than the In Fig. 7, N of about 500-1000gives the minimum Mie scattering effect in the calculation of the specific variance, which corresponds to about 1-2 seconds. attenuation, this assumption may hold in practice. In this rain event an average number of about 500- Again, taking ratio of Eq. (7) at two range gates 1000 is the optimum one, which gives small errors (r and r + *r), the difference, DAtt, between the induced from the incoherenceand does not mask the specific attenuations at the two frequencies can be temporal variation of the rain condition. N which obtained as gives the minimum variance at Ka-band is slightly smaller than that at X-band, which verifies that the higher frequency needs less time for suppressing signal fluctuations. In the subsequent analyses an averaging hit number of more than 500 is used. 5. Rainfall rate retrieval using rain attenua- The rainfall rate is derived from DAtt using an ap- tion propriate raindrop size distribution (e.g., Marshall and Palmer, 1948). One feature of this method is It is known that the rainfall rate has a good cor- that the system constants (C-value) and the calibra- relation with rain attenuation especially the rain at- tion constants (F-value) do not affectDAtt. Another tenuation at 35 GHz (Atlas and Ulbrich, 1977). A feature is that the rainfall rate, which is one of the method of measuring rain attenuation using a dual- most important rain parameters, can be derived al- wavelength radar is proposed by Atlas (1954), and most directly, because the specific rain attenuation investigated for C- and X-band radars (Eccles and is approximately proportional to the rain fall rate. Mueller, 1971). Here, we applied the same method Figure 8 shows the correlation between DAtt and to an X- and Ka-band dual-wavelength radar. The the X-band radar derived rainfall rate RX which essence of this method is to get the difference of is converted from the effective Z-factors using the the difference of the received powers at two frequen- empirical formula Eq. (1). The reason why we did cies at two range gates. The difference between the not use the rainfall rate measured by a rain gauge specific rain attenuations of the two wavelengths is is twofold: (1) the sampling volume separation is deduced. too large as shown in Fig. 5a and 5b, and (2) the The receivedpower Pr and the Z-factor are related main purpose here is to demonstrate the capabil- as ity of an X- and Ka-band dual-wavelength radar to provide an estimation of the rainfall rate other than the convectional rain estimation from the Z-factors. Though the variation of raindrop size distribution causes errors in the comparison, the error is a few where decibels according to raindrop size measurements C: system constant, except for a special rain type such as orographic F: calibration constant, rain (Battan, 1973, Atlas et al., 1984), and the two A: rain induced attenuation, estimations must agree with each other to within October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 517

signal fluctuation causes a fluctuation of DAtt with a standard deviation of around 0.6 dB according to Fig. 7. This fluctuation corresponds to a fluctuation in estimated rainfall rate of 1.3 mm/h. The fluctuations on a time scale of a few minutes which appeared especially from 1530 to 1600 are caused by the Mie scattering effect. The Mie scattering effect makes the scattering at Ka-band deviate from Rayleigh and breaks the basic assumption of the dual-wavelengthanalysis we applied here. This Mie scattering effect is a topic of another paper (Naka- mura and Inomata, 1990). There are other long- term differences. Before heavy rain the estimated rainfall rate from DAtt has a tendency to be smaller Fig. 8. The correlation between the difference than that from the X-band Z-factor. Though con- of the specific attenuations and the rainfall ceivablecauses are the variation of raindrop size dis- rate derived from the effective Z-factor of tribution and the energy loss of radiowaves due to X-band Rx . Data are taken from 1400 to a water sheet over the antenna, the reason has not 1600. Range cells to calculate the DAtt are at the ranges of 560 m and 1460 m, which yet been made clear. gives a *r of 900 m. The rainfall rate is 6. Comparison of a single wavelength analysis the averaged one from the range cell of 560 to the dual wavelength one m to that of 1460 m. The rain-induced attenuation is much larger at Ka-band than at X-band. Actually the attenuation a few decibels. In other words, the agreement to at Ka-band is more than 10 times as large as that within a few decibels is a necessary condition for at X-band. If the rain is almost uniform along the the validity of the rainfall rate estimation of the propagation path, the rainfall rate can be deduced dual-wavelength analysis. The rainfall rate is the from the effective Z-factor of Ka-bind (Goldhirsh averaged one along the slant path between the two and Katz, 1974). We estimated the rain-induced at- observed points. Since the rain-induced attenuation tenuation of Ka-band by using the effective Z-factor at X-band is small, the X-band radar-derived rain- of Ka-band. fall rate may well represent the real rainfall rate at We estimated the rain-induced specific attenua- the observed point provided the system is well cali- tion of Ka-band by defining KAtt as brated. The data points in Fig. 8 scatter along a linear line, which confirms that DAtt is proportional to the rainfall rate. This result gives validity to the estimation of rainfall rate from DAtt. A similar result was obtained by an airborne rain radar experiment where PrK is the received power at Ka-band. From Eqs. (5) and (9), KAtt is expressed as (Meneghini et al., 1989). They also showed the ap- plicability of the dual-wavelength analysis, but their data are from an airborne experiment and they averaged the measured Z-factors in range because the time variation is large, resulting in the loss of range This quantity should coincide with real attenuation resolution. along the propagation path between two observed The data in Fig. 8 still scatter with a standard points if the rainfall rate is the same at the two ob- deviation of more than 1 dB which corresponds to a served points (Z(r) = Z(r + *r)). It also almost rainfall rate of 4 mm/h. To see the characteristics of coincides with DAtt, because the contribution of the the scatter, we compare the estimated rainfall rate specific attenuation of X-band is much smaller than from DAtt with that from the X-band Z-factors in that of Ka-band in DAtt. Figure 10 shows the cor- Fig. 9. The rainfall rate from the X-band Z-factor is relation between the KAtt and the rainfall rate RX . smooth compared with that from DAtt. This is be- The data points are scattered much more than those cause the Z-factor is averaged over 12 range cells (*r in Fig. 8. = 900 m). The variations of the two rainfall rates We consider the errors in deducing the rainfall are alike in a time scale of more than five minutes, rate in those two analyses. The error variance E1 but they have a difference in a time scale of less in (dB2) in the dual wavelength analysis may be than a few minutes. The difference in a time scale of written as less than a minute is caused by fluctuations of the received power due to incoherent scattering. The 1 ::v": t

518 Journal of the Meteorological Society of Japan Vol. 68, No. 5

Fig. 9. Comparison of estimated rainfall rates (mm/h) from the DAtt (thin line) and the X-band Z-factor (thick smooth line). Range cells to calculate the DAtt are at the ranges of 560 m and 1460 m, which gives a *r of 900 m. The rainfall rate is the averaged one from the range cell of 560 m to that of 1460 m.

where c is the proportional constant. This assumption should hold for a short range. Substituting Eq. (13) in to Eq. (12) we have

Comparing Eq. (14) and (11) shows that the method using two-wavelength data has larger errors for a short range, but smaller errors for a long range. In Fig. 11 the curve (a) shows the variance of the difference between measured DAtt and X-band radar-estimated DAtt' as a function of the range difference of two observed points. The X-band radar- Fig. 10. The correlation between KAtt and estimated DAtt' is obtained from RX as rainfall rate derived from effective Z-factor of X-band Rx . Range cells to calculate KAtt are at the ranges of 560 m and 1460 where DAtt' is in dB/km. The proportional con- m. Rainfall rate is averaged one from a stant of 0.255 is determined from the relations of range cell of 560 m to that of 1460 m. specific attenuation of X- and Ka-band to rainfall rate presented by Olsen et al. (1978). The vari- where *K and *X are signal fluctuations in dB in ance of the difference between measured KAtt and the received signals at Ka- and X-band, respectively. X-band radar-estimated KAtt' is also shown by a The error E2 in the single wavelength analysis may curve (b) in Fig. 11. This figure shows that the vari- be expressed as ance for DAtt is much smaller than that for KAtt for a large range difference. This result qualitatively agrees with the above error consideration. However, there exist some discrepancies: (1) the dependence of the variance of the curve (a) in Fig. 11 on the where *Z is the difference between the true Z- range difference is proportional to *r-1 instead of factors at the two observed points. In the dual wave- r-2, (2) the dependence of the curve (b) is almost* length analysis, errors are due to signal fluctuations linear, and (3) the variance is too large if we assume in the two radiowaves. In the single wavelength anal- that the *2 is caused only by the signal fluctuations. ysis, errors are due to the signal fluctuations at one The reason for (1) and (2) is not clear so far. The frequency and the difference of the Z-factors which reason for (3) is found to be due to the Mie scatter- is caused by the non-uniformity of the rain. To make ing effect at Ka-band. The details will be described the problem simple, we assume that the difference of in another paper (Nakamura and Inomata, 1990). the Z-factors is proportional to the distance between Though KAtt is the better estimator for rainfall rate the two observed points, that is, over a short range, the variance is more than 2 dB and is too great for most applications. Hence, we can conclude that KAtt is not a practical rainfall rate estimator. October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 519

Fig. 11. The variances of difference (a) between DAtt and estimated DAtt' from rainfall rate Rx which is derived from effective Z-factor of X-band and (b) between KAtt and estimated KAtt' from rainfall rate Rx. Fig. 12. The time-height cross section of (a) effective Z-factors of X-band and (b) dif- 7. Vertical profile of rain retrieved from rain ference of specific attenuations at X- and attenuation Ka-band. Contours of (a) are of 37, 42, 45, and 47 dBZ, and contours of (a) are One of the interesting features of the rain retrieval selected to correspond to the values of the mentioned above is that a rain profile can be ob- contours of (b), if the raindrop size distri- tained. As mentioned above, the specific rain at- bution is the Marshall and Palmer's one. tenuation between two range gates (r and r + *r) The averaging hit number is 6400, and the can be measured by dual-wavelength radar. r can difference (*r) is 300 m. be arbitrary as long as the range gate resides in rain area. However, *r cannot be too short, because the amount of rain attenuation must be large enough ferent and this may result in large errors. On the to be measured and the rain attenuation is propor- other hand, a calibration by comparing DAtt and tional to *r, but it may be possible to map the non-calibrated Z-factors may be more accurate than vertical profile of rain. that using the ground rainfall rate, because the ob- Figure 12 shows the height-time cross section of served volumes are almost the same. The KAtt is not affected by the calibration constant either, but the effective Z-factor of X-band (a) and the differ- we did not use KAtt, because KAtt has large errors ence between specific attenuations at X- and Ka- band (b). The Z-factor at the higher altitude in Fig. due to the spatial variation of rain as shown in the 12b is not shown, because the back-scattered signal previous section. Figure 13 shows the results of the calibrations. level of the Ka-band is below the noise level. The two figures are similar, which confirms the capabil- The curve in Fig. 13 shows the variance Vcal of the ity of rain profiling of the dual wavelength analysis. difference between DAtt and the estimated DAtt' But some discrepancies are apparent. One is that from the Z-factor of the X-band using various F- many streaks are seen in Fig. 12b, but they do not values for trial. Vcai is expressed as appear in Fig. 12a. The main reason for this is the Mie scattering effect. This fact suggests that there is a potential for the dual-wavelength radar to be an The suitable calibration factor F will give the min- useful tool for estimating the raindrop size distribu- imum value of Vcal. The variance of the difference tion aloft. between the Z-factor of the X-band and that de- 8. Radar calibration by dual wavelength anal- rived from the ground rainfall rate is also shown ysis by the curve (b) in Fig. 13. From Fig. 13, an F- value may be determined to be 9.6 dB and 9 dB, re- The fact that the DAtt is not affected by the spectively. Though these two methods are different calibration constant suggests that a radar can be and cannot be compared directly, we compared them calibrated by comparing the DAtt and the non- as follows: (1) take the minimum variance Vm, (2) calibrated Z-factors. A conventional calibration take the variance V1 at the F-value 1 dB more than method is to compare non-calibrated Z-factors and that which gives the minimum variance, (3) obtain the ground rainfall rate. A defect of this compar- the differencebetween Vmand V1,and (4) calculate ison method is that the observed volumes are dif- the ratio of the difference to the minimum variance 520 Journal of the Meteorological Society of Japan Vol. 68, No. 5

Communications Research Laboratory who kindly helped to conduct the experiment.

References

Atlas, D., 1954: The estimation of cloud parameters by radar. J. Meteor., 11, 309-317. Atlas, D. and F.H. Ludlam, 1961: Multi-wavelength radar reflectivity of hailstorms. Quart. J. Roy. Me- teor. Soc., 87, 523-534. Atlas, D. and C.W. Ulbrich, 1977: Path- and area- integrated rainfall measurement by microwaveatten- uation in the 1-3 cm band. J. Appl. Meteor., 16, 1322-1331. Atlas, D., C.W. Ulbrich and R. Meneghini, 1984: The multiparameter remote measurement of rainfall. Ra- Fig. 13. Variance of difference between (a) dio Sci., 19, 3-22. DAtt and estimated DAtt' from the non- Atlas, D. and R. Meneghini, 1988: Rain retrieval al- calibrated X-band Z-factors, and (b) mea- gorithms for spaceborne radar, in Tropical Rainfall sured X-band Z-factors and estimated Z- Measurements, ed. J.S. Theon and N. Fugono, A. factors from the ground rainfall rate. Deepak Pub., 255-263. Battan, L.J., 1973: Radar observation of the atmosphere, Univ. Chicago Press, 324pp. (V1 - Vm)/Vm . If we regard the minimum variance Eccles, P.J. and E.A. Mueller, 1971: X-band attenua- as a noise, this ratio may be considered as a kind of tion and liquid water content estimation by a dual- signal-to-noise ratio for the signal of 1 dB. For the wavelength radar. J. Appl. Meteor., 10, 1252-1259. calibration using the DAtt and ground rainfall rate Eccles, P.J. and D. Atlas, 1973: A dual-wavelength radar these ratios are about 0.5 and 0.1, respectively. This hail detector. J. Appl. Meteor., 12, 847-856. fact means that the calibration using the difference Eccles, P.J., 1979: Comparison of remote measurements by single- and dual-wavelength meteorologi- between the specific attenuations is much more pre- cal radars. IEEE Trans. Geosci. Electron., GE-17, cise than that using the ground rainfall rate. 205-218. 9. Summary Fujita, M., 1983: An algorithm for estimating rain rate by a dual-frequency radar. Radio Sci., 18, 697-708. A rain observation by an X- and Ka-band dual- Fujita, M., K. Okamoto, S. Yoshikado and K. Nakamura, wavelength radar has been performed. The objec- 1985: Inference of rain rate profile and path- tive of this experiment is to explore the possibility of integrated rain rate by an airborne microwave rain using multi-wavelength radar for measuring rainfall scatterometer. Radio Sci., 20, 631-642. rate. Simultaneous rain observations by C- and Ku- Goldhirsh, J. and I. Katz, 1974: Estimation of raindrop band radars radiowaves were also performed. Corre- size distribution using multiple wavelength radar systems. Radio Sci., 9, 439-446. lations among measured Z-factors showed that rain Kozu, T., K. Nakamura, A. Awaka and M. Takeuchi, attenuation is significant only at Ka-band when the 1987: Development of Ku-band FM-CW/pulse com- observing range is a few km. After a method of pression radar for rain observation on a slant path. obtaining an optimum averaging hit number was J. Radio Res. Lab., 34, 95-113. proposed, a dual-wavelength analysis was applied to Marshall, J.S. and W.M.K. Palmer, 1948: The distribu- Ka- and X-band radar data and the result confirmed tion of raindrops with size. J. Meteor., 5, 165-166. the capability of providing an estimation of rainfall Marshall, J.S. and W. Hitschfeld, 1953: Interpretation rate other than that by a conventional method. The of the fluctuations echo from randomly distributed dual-wavelength analysis was compared with a sin- scatters. Part I. Canadian J. Physics, 31, 962-994. gle wavelength analysis using rain attenuation and Meneghini, R., K. Nakamura, C.W. Ulbrich and an advantage of the dual-wavelength analysis was D. Atlas, 1989: Experimental tests of methods for verified. The capability of the dual-wavelength anal- the measurement of rainfall rate using an airborne dual-wavelength radar. J. Atmos. Oceanic Tech., 6, ysis for retrieving a vertical structure of rain was 637-651. demonstrated. A radar calibration using the dual- Nakamura, K. and K. Inomata, 1990: Non-Rayleigh wavelength analysis was tested and a more accurate scattering effects in rain observations by an X- and calibration than that comparing the rain gauge data Ka-band dual-wavelength radar. submitted to J. At- was obtained. mos. Oceanic Tech., Okamoto, K., S. Yoshikado, H. Masuko, T. Ojima, Acknowledgement N. Fugono, K. Nakamura and H. Inomata, 1982: Airborne microwave rain-scatterometer/radiometer. The authors are grateful to many people in the Int. J. Remote Sensing, 3, 277-294. October 1990 K. Nakamura, H. Inomata, T. Kozu, J. Awaka and K. Okamoto 521

Okamoto, K., J. Awaka, T. Ihara, K. Nakamura, Rinehart, RE. and J.D. Tuttle, 1984: Dual-wavelength T. Kozu and T. Manabe,1989: Conceptual designs of processing: Some effects of mismatched antenna rain radars in the tropical rainfall measuring mission beam patterns. Radio Sci., 19, 123-131. and on the Japanese Experimental Module at the Tanaka, H., T. Shinozuka, K. Nakamura, K. Koike and manned space station program. Preprint 4th Conf. H. Kuroiwa, 1980: ETS-II experiments Part III: Sat. Meteor. Ocean., 18-21. Weather radar system. IEEE Trans. Aero. Elec. Olsen, R.L., D.V. Rogers and D.B. Hodge, 1978: The Sys., AES-16, 567-580. aRb relationship in the calculation of rain attenua- Tuttle, J.D. and R.E. Rinehart, 1983: Attenuation cor- tion. IEEE Trans. Antenna Propagat., AP-26, 318- rection in dual-wavelength analysis. J. Climate Appl. 329. Meteor., 22, 1914-1921.

X一,・Ka一バンド2周波レーダによる降雨の観測中村健治・猪股英行・古津年章・阿波加純・岡本謙一 (郵政省通信総合研究所)

X一およびKa一バンドの二周波レーダによる降雨の同時観測を行った。目的は、多周波レーダによる降雨強度測定可能性の検討である。同時にC一およびKu一バンドのレーダによる観測も行った。その結果、近距離ではKa一バンドにのみ降雨減衰の影響が現れることが分かった。降雨減衰を用いた降雨強度の推定が可能であること、さらに、降雨のプロファイルも得られることが実証された。Ka一バンドのみを使った降雨強度手法も検討したが、2周波数を用いる方が誤差が少ないことが判明した。降雨減衰の測定には絶対校正が必要の) 無いことを利用して、レーダの絶対校正を試みたところ、地上雨量計による校正よりも正確な校正ができた。