Characteristics of the Mirror Image of Precipitation Observed by the TRMM Precipitation Radar

Transcription

1 VOLUME 19 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY FEBRUARY 2002 Characteristics of the Mirror Image of Precipitation Observed by the TRMM Precipitation Radar JI LI ANDKENJI NAKAMURA Institute for Hydrospheric Atmospheric Sciences, Nagoya University, Nagoya, Japan (Manuscript received 15 November 2000, in final form 22 May 2001) ABSTRACT A mirror image is a virtual image of precipitation from below the ocean surface when an airborne or a spaceborne radar is used to view rainfall over the ocean. It is due to a reflection of energy from the sea surface to the precipitation and back to the radar via a second reflection at the sea surface. The mirror image characteristics were investigated using Tropical Rainfall Measuring Mission (TRMM) precipitation radar data and the following was found. 1) The radar can detect the mirror image clearly over the ocean. 2) The mirror image echo corresponds well to the direct rain echo at nadir and near-nadir incidence angles. 3) In a weak rain region, the mirror echo intensity is nearly proportional to the direct echo power except near the radar noise level. 4) In the strong rain region, rain attenuation effects clearly appear. 5) The ratio of the mirror echo power to the direct echo power is affected by the rain attenuation, which varies with the brightband height and the range of the target rain from surface. Further, a simple simulation was performed in order to confirm the above characteristics. The signal fluctuation, noise contamination, rain attenuation, and surface cross section are taken into account in the simulation. The results of simulation confirmed the observation results. 1. Introduction The Tropical Rainfall Measuring Mission (TRMM) satellite was successfully launched in November 1997 at Tanegashima Space Center of Japan. The primary goal of TRMM is to measure tropical rainfall with sufficient accuracy. In order to meet this goal a spaceborne precipitation radar (PR) was installed on the satellite. Since PR uses a frequency of 13.8 GHz, which suffers from rain attention, it is essential to correct the attenuation before radar echo intensities are converted into rainfall rates. TRMM PR rain estimation algorithms use a hybrid of the surface reference method and the Hitschfeld Bordan method to correct the attenuation (Iguchi and Meneghini 1994; Meneghini and Iguchi 1998). In the standard surface reference method, the unknown backscattering cross section of the surface, 0,isobtained from measurements in the absence of rain (Meneghini et al. 1983). In order to reduce the errors caused by the variability in 0, one approach is to measure both 0 and rain attenuation simultaneously. An early study about the mirror image the virtual image of precipitation from below the ocean surface was done in 1983 by Atlas and Meneghini (Atlas and Meneghini 1983). Meneghini and Atlas (1986) proposed to utilize the mir- Corresponding author address: Dr. Ji Li, Institute for Hydrospheric Atmospheric Sciences, Nagoya University, Furo-Cho 1, Chikusaku, Nagoya , Japan. jli@ihas.nagoya-u.ac.jp ror image of rain echo to derive a four-way path attenuation. A further theoretical investigation was done by Meneghini and Nakamura (1988). They compared the estimated rain rates derived from mirror image return with those from the Z R method using an airborne radar experiment data. Despite an apparent bias in the mirror results, good relations between the mirror image and other methods are obtained. The direct and mirror image rain volumes should be better matched for a typical spaceborne radar than that for an airborne radar that has the same beamwidth as the spaceborne radar, since the pixel size of the spaceborne radar is relatively large compared to that of the airborne radar, and the bettermatched mirror image and direct image should improve the capability of estimating the path attenuation and, therefore, rainfall rate. To apply the direct and mirror image to rain attenuation correction or rain-rate estimation, one needs to understand well the basic characteristics of the mirror image using real observation data. This paper describes results by using the TRMM PR data in 1998 in order to reveal characteristics of the mirror image and its relationship with the surface cross section, storm height, et cetera. 2. Basic theory of mirror image Figure 1 is a schematic diagram of the mirror image. The mechanism is the double reflection of the rain echo at the sea surface. The radar radiowave is scattered from the surface to the precipitation cell at the height of the 2002 American Meteorological Society 145

2 146 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 FIG. 1. Schematic presentation of the mirror image echo. The H j is the height of the target rain, P d is the direct return power, and P m is the mirror return power. jth range gate H j (hereafter the target height), then returns to the surface and is scattered the second time from the surface to the radar. If the radar directly receives the backscattering power (P d ) from the rain cell at time t and get the secondary surface return from the same rain cell (P m ) at time t, the times t and t must be related as t t 4H j /c, where c is the speed of radiowave. It is quite evident that P m includes effects of the scattering properties of the surface as well as the rain reflectivity and the path attenuation. Meneghini and Atlas (1986) derived a closed expression for the mirror image return as 4 0 C j 0.2(A n A j) P m(t ) 10, (1) H 2.76 H 0 B j where C is the radar constant, j the backscattered rain reflectivity factor, 0 normalized backscattering cross section of the surface, H 0 the height of the radar, B the 3-dB beamwidth, 2 the Fresnel reflectivity of the surface, A n the path-integrated attenuation from storm top to surface, and A j the path-integrated attenuation from surface to H j. The expression for direct target rain return power P d is basically equivalent to what was derived as the conventional radar equation, FIG. 2. Reduction of the ratio of mirror echo strength to direct echo for the TRMM PR at several target heights. Here, the reduction due to rain attenuation is not considered. FIG. 3. The distribution of rain pixel samples over the ocean used in this study.

3 FEBRUARY 2002 LI AND NAKAMURA 147 FIG. 4. Vertical profile of reflectivity factor observed by the TRMM PR at a nadir incidence on 4 Jun The right side shows the profiles at scan number 2910 over the land surface (dashed line) and at scan number 2950 over the ocean surface (solid line). C j 0.2(An A j) d 2 2 (H0 H j) B P (t) 10. (2) The ratio of mirror echo power to direct rain echo power at H j can be written as P (t ) (H0 H j) m 0.4A 10 j. (3) P (t) H 11 H / d 0 j B If we use the decibels unit, Eq. (3) can be written as 10 log[p m(t )] 10 log[p d(t)] 4Aj (H0 H j) 10 log. (4) H 2.76 H / [ ] 0 j B This equation shows that the received mirror power depends on three factors. The first term is due to the target intensity. The second term is the four-way path integral attenuation term. One of the purposes of developing the mirror image method is to estimate the rain attenuation. This term depends on the vertical profile of rain below the target height. Because the mirror image return is proportional to the four-way, instead of the two-way, path attenuation, the accuracy at light rain rates should be improved relative to the one obtained by other methods using rain attenuation. On the other hand, as the rain intensity increases, the mirror image will be masked by the system noise because of excessive attenuation. The last term is the reduction caused by surface reflections and surface scattering. This term shows that the reduction of the mirror return is a function of 0, 2, target height, and some radar parameters (such as sensor height H 0 and 3-dB beamwidth B ). When the target height is near the surface (H j 0), the last term becomes 10 log ( 4 ) or about 4.4 db for the ocean surface. This indicates that P m is basically 4.4 db smaller than P d even when rain is over a very smooth ocean and no rain attenuation occurs. Incident energy on a rough surface is scattered in a broad direction. The diffusion loss of the energy increases with the height. The ratio of P m to P d over an ocean surface for 2 0.6, is presented in Fig. 2 using Eq. (3). The ratio is calculated considering a spaceborne radar at 350-km height and with a 0.71 beamwidth (same as PR), which corresponds a 4.3-km beam field of view (FOV). The figure shows the ratio of P m to P d to changes in 0 for five different target heights ranging from 1 to 5 km. Rain attenuation is not included. From this figure one can see that when the target height is much smaller than the size of FOV (e.g., 1 and 2 km), even for 0 decreases as large as from 20 to 6 db the effect on the ratio of P m /P d is very small, this means that the amount of reduction is almost constant for some layers near surface. In this case, the ratio of P m /P d is actually independent of the surface cross section 0 (Meneghini and Atlas 1986; Liao et al. 1999) and goes to 4 ( 4.4 db). In other words, the radiowave energy that goes out of the radar beam can be negligible. When the target is at 5 km, the ratio depends significantly on 0. It should be noted that Eq. (4) does not include path

4 148 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 FIG. 5. Scatter diagrams of direct reflectivity factor vs mirror reflectivity factor over (a) ocean and (b) land at nadir. The target height is 1 km. integral attenuation from rain top to target height (A n A j ), since above this layer the rain attenuation for P m and P d is the same. 3. TRMM PR and dataset Table 1 shows the major system parameters of TRMM PR. This radar uses a frequency of 13.8 GHz. The TRMM satellite height is about 350 km, and the PR has a beamwidth, so that the horizontal resolution of this radar is near 4.3 km at nadir. The range resolution of PR is 250 m, which is equal to the vertical resolution at nadir. The observable range of PR was designed to be sufficiently long so as to allow the variation of the satellite height. The radar echo of PR consists of rain echo, surface echo, and mirror image echo. The surface echo is measured so that the PR algorithms can use it to correct rain attenuation. Independent measurement of system noise level is performed for each angle bin in order to correct the noise pedestal. For this measurement, four range bins are allocated where sidelobe-coupled surface clutter and rain echo could be negligible. This results in 256 independent samples for system noise (Kummerow 2000). In this paper, we mainly use the first-level products 1B21 and 1C21 to obtain the received power and the reflectivity factor for both rain echo (P d, Z d ) and mirror echo (P m, Z m ). The level-1b data also include housekeeping data of the instrument and noise level. The 1C21 data are calculated just by applying a radar equation for volume scatter with PR system parameters without any rain or atmospheric gases attenuation correction. 1 In order to reduce the volumes of radar data, all pixels that do not exceed the rainfall threshold of 14 dbz are omitted in level 1C21, so that the minimum detectable reflectivity factor of the PR is 14 dbz. According to the documents of the TRMM, the noise level is about 111 dbm in 1B21 and equivalently 20.8 dbz in 1C21. Actually the rain echo power is calculated by the subtraction of the system noise power from the total receiver. The accuracy of rain echo power can be characterized by the effective signal-to-noise ratio, the ratio of mean to standard deviation of rain echo power. The rain rate, rain type, storm height, and brightband height are obtained from the 2A25 product. FIG. 6. Histograms of the surface return power for (a) an ocean surface and (b) a land surface obtained for all pixels with rain. 1 See TRMM documents online at tsdis/.

5 FEBRUARY 2002 LI AND NAKAMURA 149 FIG. 7. Scatter diagrams between direct reflectivity vs mirror reflectivity over the ocean: (a) off-nadir two-angle bin (1.44 ); (b) off-nadir five-angle bin (3.6 ). The data used in this study were obtained in April and June The dataset of April includes 36 granules and the dataset of June includes 184 granules. A granule means data for one rotation of the satellite around the earth. We picked up all pixels with a rain certain flag for the central 11 rays over the ocean and land surface. In each pixel, the surface range bin is determined by return power P or reflectivity Z. We took the surface bin to be where the maximum received power or reflectivity is detected without any averaging. Though the level-1 dataset contains oversampled data, all of the data in the study are from the normal sampled data and each has a range space of 250 m. Figure 3 shows distribution of the over ocean samples used in this study. 4. Results a. Observed characteristics of the mirror image As an example, the vertical cross section of a rainfall system with plots of the vertical profile at two pixels, observed by the PR at a nadir incidence angle on 4 June 1999 (orbit number 8734), is presented in Fig. 4. This event occurred over the east coast of the Indochina pen- FIG. 8. Correlation coefficient between P m and P d, and the rms of P d P m at 1 km for angle bins from nadir to 5 (3.55 ).

6 150 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 FIG. 9. Scatter diagrams between direct reflectivity vs mirror reflectivity over the ocean. The incidence angle is at nadir. The target heights are (a) 3 and (b) 5 km. insula and the South China Sea. The approximate latitude and longitude corresponding to the midpoint of this figure is (14.5 N, E). From the image we can see that the segment from scan number 2900 to 2920 is over a land surface where the mirror image is very weak, and the surface echo is slightly undulant due to the topography. In contrast to the segment over the land surface, the segment from scan number 2930 to 2960 is over the ocean surface, where the mirror image is very clear and the surface is smooth. We can also see a bright band at near 5-km height both over land and over ocean, but the virtual bright band only occurs under the ocean surface. On the right side of this figure, vertical profiles at the scan number 2910 (over land) and 2950 (over ocean) were plotted. These show that the echo power of the mirror image is very small when the radar is over the land surface. This case illustrates that the PR can hardly detect the mirror image over land. As a further investigation, scatter diagrams between the direct image reflectivity and the mirror image reflectivity over both ocean (Fig. 5a) and land (Fig. 5b) at a target height of 1 km were made. The data are from the 1C21 product observed by the PR in April Only nadir data were used in this figure. Comparing Fig. 5a with Fig. 5b, we can find the following facts. 1) Most of the mirror return power over land seems TABLE 1. Major system parameters of TRMM precipitation radar. System parameters Radar type Frequency Swath width Range resolution Horizontal resolution Sensitivity Number of independent samples Data rate Antenna subsystem parameter Beamwidth Scan angle Gain Transmitter/receiver subsystem Transmitter type Peak power Pulse width Pulse repetition frequency Dynamic range Active phased-array radar and GHz 215 km 250 m 4.3 km (at nadir) 0.7 mm h 1 rain at rain top 64 (rain echo), 256 (noise) 93.5 kbps db Solid-state power amplifiers 500 W 1.6 s for 2 ch Hz 70 db FIG. 10. Same as Fig. 9b, but includes only data in which the brightband height is higher than 5 km.

7 FEBRUARY 2002 LI AND NAKAMURA 151 FIG. 11. Vertical profiles of direct reflectivity (solid) and mirror reflectivity (dash) for cases with TRMM satellite orbit numbers shown at the top of each panel. much lower than that over ocean. The Fresnel reflectivity of an ocean surface is approximately 0.6 ( 2.2 db) at nadir incidence angles, while it is only 0.2 ( 7 db) for many land surface (Meneghini and Kozu 1990), which means that the mirror image return over land will be at least 9.6 db [ 2x(7 2.2)] smaller than that over ocean surface. 2) For the same direct image echo intensity, the variation of the mirror image echo over land is much larger than that over ocean. This might be because the condition of the land surface is complex, and then the variation of the roughness of the land surface is much larger than that of the ocean surface. Figure 6 shows histograms of the surface reflectivity over ocean (Fig. 6a) and over land (Fig. 6b). From this figure we can see that the ocean surface return (Fig. 6a) has a mean value of about 79 dbz equivalently with a standard deviation of about 3 db, while the land surface return power has a low mean value and a large variation. Sometimes the land 0 can be abnormally so large that it is more than 90 dbz. One suggestion is that there may be a very flat region such as a lake in the inner land (T. Kozu 1999, personal communication). 3) Some mirror echoes over land are larger than the corresponding direct echoes. We have checked the locations where the mirror echoes are much stronger than direct echoes and found that those points are in mountain regions, such as the Himalaya and the Andes mountain ranges. This suggests that over undulated surface, the surface contamination on the mirror echo may extend much more range bin than over a flat surface. This contaminated echo may be misinterpreted as a rain mirror echo. FIG. 12. Scatter diagrams between direct reflectivity vs mirror reflectivity over the ocean. The target height is at 3 km. The rainfall was divided into (a) stratiform and (b) convective type.

8 152 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 FIG. 13. Scatterplots of surface 0 (Z g ) in db, (right axis), and direct image reflectivity factor (Z d ) and mirror image reflectivity factor (Z m ) (left axis) vs rain rate (mm h 1 ) or (a) stratiform rain and (b) convective rain. In summary, the correlation between the direct echoes and the mirror echoes is good over ocean as in Fig. 5a, but poor over land as in Fig. 5b. Comparison of the characteristics of mirror image over the land surface with that over the ocean surface indicates that it is difficult to use the mirror method over the land surface. Therefore, the following discussion will only concentrate on the ocean areas. Meneghini and Atlas (1986) and Meneghini and Nakamura (1988) discussed only the mirror echoes at nadir incidence angle. In order to get more information on the mirror image, we checked the off-nadir data from the PR and found that even at some off-nadir incidence angles, the correlation between the direct image and the mirror image is also very good. Figure 7 is a scatterplot of the direct reflectivity versus mirror reflectivity at off-nadir angles of 1.44 (Fig. 7a) and 3.6 (Fig. 7b) with a target height of 1 km from the surface. For this figure we use the 1C21 dataset of April. It is evident that the correlation between the mirror and the direct echoes is better in Fig. 7a than in Fig. 7b. Comparing these with the nadir case (Fig. 5a), we can see that the fluctuation becomes large as off-nadir angle increases. At the same time, there is a bunch of points where mirror image returns are greater than direct returns over the range of reflectivity from 13 to 20 dbz in both Figs. 7a,b. We believe that this is due to the noise effect and the mismatching between the direct and mirror image. The correlation coefficient between P d and P m at 1 km and the standard deviation of P d P m were also calculated by using the same dataset. Figure 8 shows the results as a function of the incidence angles. Even at the two angle bins off nadir (1.42 ), the correlation coefficient is about 0.85, and the standard deviation is smaller than 4 db. As the incidence angle increases, the correlation coefficient decreases and the standard deviation increases. For example, when the off-nadir angle bin is 5 (3.55 ), the correlation coefficient between P d and P m decreases to 0.4 and the standard deviation increases to about 6 db. Theory says that the ratio of P m to P d is reduced, as

9 FEBRUARY 2002 LI AND NAKAMURA 153 FIG. 14. Scatter diagram between direct received power and mirror-received power at 1 km. Data are from the dataset 1B21. shown in Fig. 2, with increasing target height even when rain attenuation is negligible. The reduction is due to the divergence of the beam energy at the surface. This factor depends on the radar parameters and the surface characteristics. Observation data also show this characteristic clearly. A scatter diagram of the direct echo versus mirror echo with a nadir incidence angle at target height 1 km was shown in Fig. 5a. Figure 9 is the same as Fig. 5a, but with target heights of 3 (Fig. 9a) and 5 km (Fig. 9b). Comparing Fig. 5a with Fig. 9a, we can see that the basic reduction of the mirror echo power increases with the target height. Inspecting of the scatter diagram of P m versus P d in Fig. 9b, we find that this reduction becomes obscure at the target height of 5 km, and the correlation between P m and P d becomes poor. One possible reason is the difference of the direct and mirror brightband profiles, since the direct bright band is sharper than the mirror one, the correlation between direct and mirror echo decreases. Figure 10 is the same as Fig. 9b, but for rainfall systems in which the brightband heights are higher than 5 km. It shows that the relatively strong mirror echoes disappear. As a further investigation, vertical profiles of direct reflectivity (solid lines) and mirror reflectivity (dash lines) are presented in Fig. 11. The data are averaged from four stratiform rainfall events. (At the top of each panel in the figure are the TRMM satellite orbit number for each event.) The figures show that under the bright band the difference between direct dbz and mirror dbz increases with increasing height due to the contribution of rain attenuation and surface roughness for all cases. Above the bright band, however, this characteristic is obscure. These figures also indicate that the direct bright band is sharper than mirror one, and that the bright region needs more precise range matching. The main purpose of this study is to understand whether the ratio of mirror image return to direct return can be used to estimate rain attenuation or not. We have presented scatter diagrams between direct return and mirror return in Figs. 5a, 9a, and 10. These figures show that the ratio of mirror return to direct return decreases with height and also decreases with rainfall intensity, especially with a high reflection layer and with heavy rainfall. From these figures, we can also see that the correlation between the direct and mirror echoes is good for light rainfall (the effects of attenuation can be negligible, i.e., direct reflectivity smaller than 30 dbz). On the other hand, the relationship is complex when the rain attenuation becomes significant, since rainfall char- FIG. 15. (a) Simulated direct vs mirror received power and (b) radar reflectivity factor at 1 km. The solid line within the shaded area is the average.

10 154 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 FIG. 16. (a) Simulated direct vs mirror received power and (b) radar reflectivity factor at 3 km. The solid line within the shaded is the average. acteristics such as rain types, vertical profiles, et cetera, are complex. Therefore, one must consider these factors. It is well known that specific attenuation devaries linearly with rain rate, and is relatively independent of the raindrop size distribution (Doviak and Zrnic 1992). However, radar reflectivity has a nonlinear relationship with rain rate and the relationship strongly depends on the raindrop size distribution. As we know, convective rainfall has a much different raindrop size distribution from stratiform rainfall (Waldvogel 1974). Because of the differences of the raindrop size distribution for convective and stratiform rainfall with the same reflectivity, the rain rate from convective rainfall is higher than from stratiform rainfall; thus, the rain attenuation of convective rainfall should be larger than that of stratiform rainfall. From the 2A25 dataset we can determine rain type for each pixel. By using this information, we make the scatter diagrams of direct return versus mirror return for stratiform rain (Fig. 12a) and convective rain (Fig. 12b), respectively. In these figures only nadir data is used and the target height is 3 km. Comparing Fig. 12a with Fig. 12b, one can see that when the rain rate is high; for example, when direct return is larger than 30 dbz, the ratio of mirror return to the direct return reduces more in convective rainfall than in stratiform rainfall at the same reflectivity value. Comparison of Fig. 5a to Fig. 12b shows greater attenuation with greater target height. Comparison of Fig. 12a to Fig. 12b shows minimal ef- FIG. 17. Simulation of averaged the direct vs the mirror radar reflectivity factor at (a) 1 and (b) 3 km for several storm heights.

11 FEBRUARY 2002 LI AND NAKAMURA b). Comparison of Fig. 13a to Fig. 13b shows that there seems to exist some differences between the two types of rainfall system. The surface 0 of convective rainfall is smaller than that of stratiform rainfall. While the reason for this is not clear, it may be because of the roughness change due to rain or wind speed. At the weak rain regime, however, for example, where rain rate is smaller than 4 mm h 1, the ratio of Z m to Z d decreases with the rain rate increasing, while the surface return does not seem to decrease significantly at this regime for both types of rainfall. This means that the decrease of the mirror image return is not due to the surface scattering cross section. Another possible reason is the effect of noise level. In order to confirm this, a scatter diagram between direct received power and mirror power using 1B21 at a target height of 1 km was constructed. The result is presented in Fig. 14. The granules used are the same as in Fig. 5a. As stated above, the 1B21 data received power includes both signal and noise, while the 1C21 data are noise corrected and have been cut off at reflectivities less than 14 dbz. Comparing Fig. 14 with Fig. 5a, we can see that in the regime where the signal is free from the effect of noise, the ratio of P m to P d, and the ratio of Z m to Z d are nearly the same. When the signal becomes weak, both the direct and mirror-received power will approach the noise level (see Fig. 14), while the correlation between mirror and direct reflectivity will become poor due to the noise effect. Because the noise level is equivalently 20.8 dbz and the threshold of truncation is 14 dbz, the scatter diagram of direct and mirror reflectivity (see Fig. 5a) will cause a change of slope at the weak rain regime. FIG. 18. Scatter diagrams between observed direct reflectivity vs mirror reflectivity at (left) 1 and (right) 3 km in which the storm height is (a) 3, 4, and 5 km, and (right) 5, 6, and 7 km, respectively. The lines dashed are averaged simulation results. fect of drop size distribution on attenuation for high mirror image reflectivities. These results indicate that mirror reflectivity is different for convective and stratiform types of rainfall, which also confirms the raindrop size distribution differences in these two types of rainfall. If we take a close look of preceding scatter diagrams between direct return and mirror return, for example, in Figs. 5a, 9a, and 12a,b, one finds that there is another interesting characteristic in the ratio between mirror and direct return. That is, even when the rain is light, where the effect of attenuation can be negligible, the ratio of mirror return to direct return is not a constant, and there is a slope different from the 45 slope shown in the figures. One possible reason is that the surface backscattering cross section decreases rain rate increases. A scatter diagram of surface return echo, direct echo at 3 km, and the corresponding mirror echo versus 3-km rain rate is plotted in Fig. 13. In this figure, we divided the rain into stratiform (Fig. 13a) and convective rain (Fig. b. Simulated characteristics of the mirror image To see a little bit deeper, we tried to apply a simple model to simulate the mirror echoes and compare the simulated results with those observed by PR. The model is based on Eq. (4). It includes affects on the received power of the mirror echo, such as the normalized surface cross section, noise level, storm height, and storm type. The parameters of TRMM PR were used in this model. In an initial test, it was assumed that the vertical structure of the storm is uniform up to a specified height and the effect of the brightband is not considered. It was also assumed that the normalized surface cross section 0 is 12 db (Kozu et al. 1999). The 12 db is at nadir with a standard deviation of about 2 db. The Fresnel reflectivity ( 2 ) is assumed to be 0.6 for the ocean surface. The procedure of the simulation was as follows. First, the rain type and storm height is assumed. Once the rain type and storm height are specified, rain rate is varied from 0 to 100 mm h 1 (100 mm h 1 is the realistic limit for stratiform rainfall). According to the algorithm for PR 2A25, rain rate and reflectivity have the following Z R relationships for rain types:

12 156 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 FIG. 19. Statistical results of the mirror image reflectivity factor derived from (a) the observation dataset of Jun and (b) the simulation data. Only stratiform rainfall data are used. The target height is 3 km. This figure shows the averaged value (dark central line) and the std dev (vertical bars). 1.6 Z 232R (stratiform) (5) 1.6 Z 160R (convective), (6) where Z is in mm 6 m 3 andrinmmh 1. Considering the radar frequency is 13.8 GHz, we use the relationship between the attenuation coefficient k (db km 1 ) and the rainfall rate R intrapolated from the results given by Olsen et al. (1978): k 0.032R ; (7) then the profile of measured direct and mirror echoes can be obtained by using the above assumptions and equations. The radar signal fluctuates as a result of the incoherent scattering of raindrops. Therefore, in order to estimate the mean value of the rain echo power, it is essential to average the radar signals. As stated before, the PR does not directly measure the rain echo power P r ; instead it measures the total received power P t, which is the sum of P r and the received noise power P n. That is, Pt Pr P n. (8) The mean value of P r is estimated by taking the difference between P t and P n as in Pr Pt Pn. (9) It is well known that P r for a single pulse obeys an exponential distribution (Marshall and Hitschfield 1953), and the received noise power also obeys an exponential distribution (Skolnik 1980). Logarithmic averaging is employed by the PR as 64 1 log(p ) log(p ) (10) 256 t meas t,i 64 i 1 1 log(p ) log(p ). (11) n meas n,i 256 i 1 We should pay attention to the number of samples for averaging to obtain signal and noise. The numbers for the TRMM PR are 64 and 256 for signal and noise, respectively (Kozu et al. 1999). Then the terms P t and P n can be calculated from log(p t ) meas and log(p n ) meas, respectively, as log(p t) meas 0.25 (P t) meas 10, and (12) log(p n) meas 0.25 (P n) meas 10. (13) Logarithmic averaging causes a well known bias error of 2.5 db (Atlas 1964). The reflectivity factor (dbz) is converted from this received power as ( Pt /10) ( Pn /10) dbz 10 log(10 10 ) C 20 log(r). (14) After considering the radar signal fluctuation, samples were generated 600 for every rain rate, and for every sample, 64 radar signals and 256 noises that obey the exponential distribution were randomly generated. This yields a series of direct and mirror-received power and reflectivity. The first simulated result is presented in Fig. 15. This figure shows scatterplots of direct received powers versus mirror received powers (Fig. 15a) and direct reflectivity versus mirror reflectivity (Fig. 15b) at a target height of 1 km. In this figure, a storm height of 5 km and stratiform rain is assumed. The noise level is the same as for the PR, that is 111 dbm for received power and 20.8 dbz for reflectivity. In Fig. 15a, both the direct and mirror-received power will approach to noise level when the signal is weak. This result is similar to that observed. On the other hand, in Fig. 15b, because of the effect of noise, the correlation between direct and mirror reflectivity becomes poor when the reflectivity

13 FEBRUARY 2002 LI AND NAKAMURA 157 is smaller than noise level (20.8 dbz). In this case, the data are also cut off for values less than 14 dbz, which is done in the PR process. Such truncation leads to the averaged ratio of the direct to the mirror reflectivity to approach 1. In other words, noise contamination still remains after the noise reduction technique is applied. Figure 16 is the same as Fig. 15, but the target height is 3 km. What was seen in Fig. 15 also appears in Fig. 16. The comparison of Fig. 15 with Fig. 16 shows that the reduction of mirror echo increases with the target height, and the effect of noise level plus the effect of surface scattering causes the slope to seem to increase with the target height. This result confirms the observation result. At the strong rainfall regime, the patterns of Figs. 15 and 16 are much different. This is because the rain attenuation becomes the main effect above and below the target height. Since the storm height is assumed to be 5 km in these cases, both the direct echo and mirror echo decrease greatly due to the attenuation above the target height for the target height of 1 km case. On the other hand, when the target height is 3 km, the reduction of attenuation for direct echo is small, while the mirror echo is reduced greatly because of the four-way attenuation. This leads to the ratio of mirror return to direct return being significant. In order to find out how the storm height affects the pattern of the scatter diagram between direct echoes and mirror echoes, we simulated the reflectivities (using the 1C21 data sets) for several storm heights and averaged the output. The result is presented in Fig. 17. The data with the same rain rate have been averaged. In Fig. 17a, the target height is 1 km and the storm height varies from 1 to 5 km, and in Fig. 17b, the target height is 3 km and the storm height varies from 3 to 7 km. Generally speaking, a storm height of 7 km is too high to be realistic, but it can be used to clearly demonstrate the storm height effect. Apart from the noise effect, at least two other significant characteristics can be found in those figures. First, before the attenuation influence takes place, the correlation between direct and mirror image can be expressed by a simple linear equation in dbz. Second, the rain attenuation associated with storm height causes a complex correlation, but the ratio of mirror echo to direct echo does not change as the storm height changes. According to the above results, if we want to compare simulation results with observation results by using a scatter diagram, we have to consider the effect of storm height. In Fig. 18 the observed result is presented in the scatter diagram (dots) between direct and mirror reflectivity. In this figure, the rainfall is divided by several storm heights in each panel. The target height is 1 (lefthand side) and 3 km (right-hand side) with storm heights of 4, 5, and 6 km, respectively for the 1-km storm target height storms, and 5, 6, and 7 km for the 3-km target height storms. The dash curve in each panel is the average of the simulated results. The observation data are from the dataset of June. From these figures we can see that the matching of observation and simulation is improved significantly, especially for strong rain-rate regimes. Figure 19 is a simple statistical result for both observed (Fig. 19a) and simulated (Fig. 19b) mirror image reflectivity (1C21). The target height is 3 km with a stratiform rainfall. It shows us the averaged mirror echo intensity (curve) and its standard deviation (vertical bar) for different direct echo intensity. Because the statistic is based on the direct reflectivity, the mean and the standard deviation become fuzzy at the strong rain regime. However, we can still find the following results from this figure. 1) The effect of noise appearing in both observed and simulated results as well as the effect of surface scattering cause a nonlinear correlation between the direct and mirror reflectivity at the weak rain regime. 2) If compared with simulation, the observed mirror reflectivity fluctuation is mainly caused by the signal and noise fluctuation in weak rain regime. 3) For a frequency of 13.8 GHz, when the reflectivity is bigger than 30 dbz, which corresponds to the rain rate of 2.7 mm h 1, the rain attenuation becomes significant. 5. Conclusions In this study the mirror image characteristics using TRMM PR data were investigated and the following were found. 1) The precipitation radar can detect the mirror image clearly over the ocean. Because of the limitation of the transfer power, the PR does not detect the mirror image over the land surface. 2) The mirror image echo corresponds well to the direct rain echo at nadir and near-nadir incidence angles. Over 200 granules of data were checked from PR and it was found that if the rainfall is over the ocean and the target height is near the surface or the rainfall weak, the correlation coefficient of the mirror image echo and the direct echo is over In the weak rain region, the mirror echo intensity approaches the direct echo power because of the effect of the noise level, while in the strong rain region, the rain attenuation effect is quite clear. 3) The storm height, as well as the rain-rate intensity, affect the altitude range of detectable mirror image returns. Further, a simple simulation was performed in order to confirm the above characteristics. The signal fluctuation, noise contamination, rain attenuation, and surface cross section were taken into account in the simulation. The simulation results clearly show that the ratio of mirror echo to direct echo varies with the rain rate, rain type, target height, and the storm height. If the observed data are divided into several types, the com-

14 158 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 19 parison results between the simulation and the observation are improved significantly. The characteristics of mirror image of rain measured by the PR are well understood. This is a good base for starting a study on PR rain estimation validation using the direct and mirror images. We do not think that the direct-mirror image technique can be applied on pixelby-pixel basis. We believe, however, that the statistical results can be applied. Acknowledgments. The authors would like to express their gratitude to Dr. T. Iguchi of Communications Research Laboratory, Prof. J. Awaka of Hokaido University, and Prof. T. Kozu of Shimane University for discussions. The TRMM data were provided by the National Space Development Agency of Japan. The authors would like to express their thanks to anonymous reviewers for many valuable comments. REFERENCES Atlas, D., 1964: Advances in Radar Meteorology, H. E. Landsberg, Ed., Vol. 10, Academic Press, , and R. Meneghini, 1983: Simultaneous ocean cross section and rainfall measurements from space with a nadir pointing radar. Preprints, 21st Conf. on Radar Meteorology, Edmonton, AB, Canada, Amer. Meteor. Soc., Doviak, R. J., and D. S. Zrnic, 1992: Precipitation measurements. Doppler Radar and Weather Observations, R. J. Doviak, Ed., Academic Press, Iguchi, T., and R. Meneghini, 1994: Intercomparison of single-frequency methods for retriving a vertical rain profile from airborne or spaceborne radar data. J. Atmos. Oceanic Technol., 11, Kozu, T., and Coauthors, 1999: Development of precipitation radar onboard the tropical rainfall measuring mission (trmm) satellite. IEEE Trans. Geosci. Remote Sens., 37, Kummerow, C., 2000: The status of the Tropical Rainfall Measuring Mission (TRMM) after two years in orbit. Appl. Meteor., 12, Liao, L., R. Meneghini, and T. Iguchi, 1999: Simulation of mirror image returns of air/space-borne radars in rain and their application in estimating path attenuation. IEEE Trans. Geosci. Remote Sens., 37, Marshall, J. S., and W. Hitschfeld, 1953: The interpretation of the fluctuation echo for randomly distributed scatters. Part I. Can. J. Phys., 31, Meneghini, R., and D. Atlas, 1986: Simultaneous ocean cross section and rainfall measurements from space with a nadir-looking radar. J. Atmos. Oceanic Technol., 3, , and K. Nakamura, 1988: Some characteristics of the mirrorimage return in rain. Proc. Int. Symp. on Tropical Rainfall Measurements, Tokyo, Japan, NOAA/NASA, 235., and T. Kozu, 1990: Radar equations. Spaceborne Weather Radar, R. Meneghini, Ed., Artech House, , and T. Iguchi, 1998: Use of the surface reference technique for path attenuation estimates from the trmm radar. Proc. Int. Symp. on the Precipitation Observation from Non-Sun Synchronous Orbit, Nagoya, Japan, Nagoya University, , J. Eckerman, and D. Atlas, 1983: Determination of rain rate from a spaceborne radar using measurements of total attenuation. IEEE Trans. Geosci. Remote Sens., 21, Olsen, R. L., D. V. Rogers, and D. B. Hodge, 1978: The ar b relation in the calculation of rain attenuation. IEEE Trans. Antennas Propag., 26, Skolnik, M. L., 1980: The radar equation. Introduction to Radar Systems, 2d ed., M. L. Skolnik, Ed., McGraw-Hill, Waldvogel, A., 1974: The n 0 jump of raindrop spetrca. J. Atmos. Sci., 31,